## Wizard Endorsed Internet Casinos

This appendix shall explain and analyze some blackjack side bets I have seen. In the U.S. a W2G tax form is generated on any table game win that exceeds $600 and pays 300 to 1 or more.

## Super Sevens

The following is the payoff table for Super Sevens:

### Super Sevens Payoff Table

Hand | Pays |
---|---|

First Card a seven | 3-1 |

First two cards unsuited sevens | 50-1 |

First two cards suited sevens | 100-1 |

First three cards unsuited sevens | 500-1 |

First three cards suited sevens | 5000-1 |

These awards are not cumulative. In other words, if you get three sevens you don't get paid for one and two sevens as well. If the dealer gets a blackjack the player can still get paid for at least two sevens. At some casinos if the player has two sevens and the dealer gets a blackjack a third card will be dealt to the player for the chance to get three sevens.

The following table shows the probability, permutations, payoff, and expected return of each hand. This table assumes(1) a third card is **NOT** dealt if the player has two sevens and the dealer gets a blackjack and (2) six decks.

### Super Sevens — No Third Card on Dealer BJ

Hand | Pays | Permutations | Probability | Return |
---|---|---|---|---|

1 seven | 3 | 203,926,947,840 | 0.071234 | 0.213703 |

2 unsuited 7's | 50 | 11,884,713,984 | 0.004151 | 0.207574 |

2 Suited 7's | 100 | 3,301,309,440 | 0.001153 | 0.115319 |

3 unsuited 7's | 500 | 1,056,338,496 | 0.000369 | 0.184496 |

3 suited 7's | 5000 | 43,470,720 | 0.000015 | 0.075924 |

Non-paying hand | -1 | 2,642,553,365,760 | 0.923077 | -0.923077 |

Total | 2,862,766,146,240 | 1.000000 | -0.126061 |

The following table shows the permutations, probability, payoff, and expected return of each hand. This table assumes (1) a third card is dealt if the player has two sevens and the dealer gets a blackjack and (2) six decks.

### Super Sevens — Third Card on Dealer BJ

Hand | Pays | Permutations | Probability | Return |
---|---|---|---|---|

1 seven | 3 | 2,142,720 | 0.071234 | 0.213703 |

2 unsuited 7's | 50 | 124,416 | 0.004136 | 0.206809 |

2 suited 7's | 100 | 34,560 | 0.001149 | 0.114894 |

3 unsuited 7's | 500 | 11,664 | 0.000388 | 0.193883 |

3 suited 7's | 5000 | 480 | 0.000016 | 0.079787 |

Non-paying hand | -1 | 27,766,080 | 0.923077 | -0.923077 |

Total | 30,079,920 | 1.000000 | -0.114000 |

The tables above show a house edge of 12.61% if the player does not get a third card if the dealer gets a blackjack and a house edge of 11.40% if the player is guaranteed to get three cards.

## Royal Match

The royal match is a simple bet that pays a bonus if the first two cards are suited (an easy match) and a top bonus for a suited king and queen (a royal match). Below are probability tables for two versions I have seen.

### Royal Match — Version 1 — Six Decks

Event | Pays | Combinations | Probability | Return |
---|---|---|---|---|

Royal match | 25 | 144 | 0.002968 | 0.074202 |

Easy match | 2.5 | 11,868 | 0.244620 | 0.611551 |

No match | -1 | 36,504 | 0.752412 | -0.752412 |

Total | 48,516 | 1.000000 | -0.066658 |

### Royal Match — Version 2 — One Deck

Event | Pays | Combinations | Probability | Return |
---|---|---|---|---|

Royal match | 10 | 4 | 0.003017 | 0.030166 |

Easy match | 3 | 308 | 0.232278 | 0.696833 |

No match | -1 | 1,014 | 0.764706 | -0.764706 |

Total | 1,326 | 1.000000 | -0.037707 |

The following table displays the house edge for each version given the number of decks used.

### Royal Match House Edge

Number of Decks | Version 1 | Version 2 |
---|---|---|

1 | 0.108597 | 0.037707 |

2 | 0.083271 | 0.008215 |

4 | 0.070792 | -0.006317 |

6 | 0.066658 | -0.011130 |

8 | 0.064597 | -0.013531 |

The probabilities for the royal match are easy to derive.Lets use n for the number of decks of cards. The number of two card combinations is combin(52×n,2). The number of ways to make a royal match is 4*n^{2}. This is because there are 4 suits and n ways to choose the queen and n ways to choose the king. The number of ways to make an easy match is 4×(combin(13×n,2)-n^{2}). The 4 is the number of suits and combin(13×n,2) is the number of ways to arrange 2cards from a given suit. You must also subtract the number of ways to make a royal match.

The probability of an easy match is 4×(combin(13×n,2)-n^{2})/combin(52×n,2).

The probability of a royal match is 4×n^{2}/combin(52×n,2).

## Royal Match - Version 3

In a third version there is a separate pay for a suited blackjack as follows.

- Royal Match pays 25 to 1
- Suited Blackjack pays 5 to 1
- Easy Match pays 5 to 2

The following table shows the expected value for a 6-deck game is -3.70%.

### Royal Match Version 3- Six Decks

Hand | Combinations | Probability | Pays | Return |
---|---|---|---|---|

Royal match | 144 | 0.002968 | 25 | 0.074202 |

Suited blackjack | 576 | 0.011872 | 5 | 0.059362 |

All other matches | 11292 | 0.232748 | 2.5 | 0.58187 |

Loss | 36504 | 0.752412 | -1 | -0.752412 |

Total | 48516 | 1 | -0.036977 |

The next table shows the house edge for various number of decks for version 3.

### Royal Match Version 3- 1 to 8 Decks

Decks | House Edge |
---|---|

1 | 7.84% |

2 | 5.34% |

3 | 4.52% |

4 | 4.11% |

5 | 3.86% |

6 | 3.70% |

7 | 3.58% |

8 | 3.49% |

## Royal Match - Version 4

The Shufflemaster TMS 300 is an electronic blackjack game, played facing a giant video screen of a dealer. It features a Royal Match side bet, adding a pay for the player and dealer both having a royal match. Following is the return table for six decks.

### Royal Match — Version 4 — Six Decks

Event | Pays | Combinations | Probability | Return |
---|---|---|---|---|

Player and Dealer Royal Match | 1000 | 19152 | 0.000008 | 0.008242 |

Player royal match | 25 | 6877728 | 0.00296 | 0.073996 |

Suited | 2.5 | 568417860 | 0.24462 | 0.611551 |

Loser | -1 | 1748359080 | 0.752412 | -0.752412 |

Total | 2323673820 | 1 | -0.058622 |

The next table shows the house edge by number of decks.

### Royal Match — Version 4 — 1-8 Decks

Number of Decks |
House Edge |
---|---|

1 | 10.14% |

2 | 7.59% |

3 | 6.73% |

4 | 6.3% |

5 | 6.04% |

6 | 5.86% |

7 | 5.74% |

8 | 5.64% |

## Royal Match - Version 5

Version 5 of the Royal Match is a progressive jackpot on ShuffleMaster TableMax units. These are the electronic blackjack games with a big screen, usually showing a pretty and very buxom dealer.

In this version, the side bet is always $1. It pays a progressive jackpot for a "Crown Treasure," which is both the dealer and player having a Royal Match. Smaller pays are $60 for a player only royal match, and $10 for a player straight flush, which I assume means the player's first two cards are suited and consecutive, including A-2.

There is also a $500 envy bonus, which pays if you make the side bet, and another player gets a Crown Treasure. The other player does not have to make the side bet for other players to qualify for the Envy Bonus.

The following table shows a hypothetical return table, for six decks, a $10,000 jackpot, and no other players.

### Six-Deck Progressive Royal Match — $10,000 Jackpot and No Other Players

Event | Pays | Combinations | Probability | Return |
---|---|---|---|---|

Crown Treasure | $10,000 | 19,152.00 | 0.000008 | 0.082421 |

Royal Match | $60 | 6,877,728.00 | 0.002960 | 0.177591 |

Straight Flush | $10 | 82,762,560.00 | 0.035617 | 0.356171 |

Loser | $0 | 2,234,014,380.00 | 0.961415 | 0.000000 |

Total | 2,323,673,820.00 | 1.000000 | 0.616183 |

The general formula for the return in a six-deck game is 0.533762 + 0.082421×j + 0.004121× p, where j is the jackpot divided by $10,000, and p is the number of **other** players (not counting yourself).

The next table shows the breakeven points, in which the expected return is exactly 100%, given the number of other players, in a six-deck game.

### Progressive Royal Match Breakeven Points

Other Players | Breakeven Point |
---|---|

6 | $53,567.70 |

5 | $54,067.70 |

4 | $54,567.70 |

3 | $55,067.70 |

2 | $55,567.70 |

1 | $56,067.70 |

0 | $56,567.70 |

## Streak

Streak is an optional blackjack side bet I noticed at Caesars in Atlantic City in April of 2000. Since that time I have seen it displayed at the Global Gaming Expo, where I have been given rule updates. Streak is a simple bet on winning a specified number of consecutive bets. If the player splits then it is the net win that counts toward whether the hand as a whole won or lost. For example if the player split and won one hand and pushed the other the hand would count as a net win. In the event of a push or breaking even after a split the hand would not count for purposes of the side bet, neither advancing the number of consecutive wins nor breaking the winning streak. The player may bet on a winning streak from 2 to 5, or as many of these as desired.

My blackjack appendix 4 addresses the probability of a net win or loss. However that table includes surrender, which is usually not offered, and a player may decline to take anyway, if a Streak bet were on the line. So I reran my simulation with the following rules: six decks, dealer stands on soft 17, no surrender, player may split up to four hands, double on any two cards, double after split allowed, resplit aces not allowed, cut card used. Here are the results of the simulation.

### Net Win in Blackjack

Net win | Simulation Total |
Probability | Return |
---|---|---|---|

8 | 1400 | 0.000001 | 0.000006 |

7 | 12763 | 0.000007 | 0.000048 |

6 | 76258 | 0.000041 | 0.000245 |

5 | 284607 | 0.000152 | 0.000762 |

4 | 1435913 | 0.000769 | 0.003077 |

3 | 4584941 | 0.002456 | 0.007368 |

2 | 114511009 | 0.061343 | 0.122686 |

1.5 | 84495618 | 0.045264 | 0.067896 |

1 | 603601989 | 0.323348 | 0.323348 |

0 | 163884660 | 0.087793 | 0 |

-1 | 805017526 | 0.431246 | -0.431246 |

-2 | 83647458 | 0.04481 | -0.089619 |

-3 | 3984819 | 0.002135 | -0.006404 |

-4 | 963035 | 0.000516 | -0.002064 |

-5 | 180925 | 0.000097 | -0.000485 |

-6 | 37217 | 0.00002 | -0.00012 |

-7 | 5072 | 0.000003 | -0.000019 |

-8 | 417 | 0 | -0.000002 |

Total | 1866725627 | 1 | -0.004521 |

The lower right cell shows a house edge of 0.4521%. This may look a bit high for the rules, especially against my blackjack calculator. Most house edge figures, including those of my calculator are based on a continuously shuffled game. The use of a cut card, as was the case in this simulation, adds 0.02% to the house edge with six decks. For more information on the cut card effect please see my blackjack appendix 10.

Adding up the wins and losses we get the following.

### Net Win in Blackjack

Event | Probability |
---|---|

Win | 43.34% |

Loss | 47.88% |

Tie | 8.78% |

Win given no tie | 47.51% |

Loss given no tie | 52.49% |

The probability of winning n hands in a row is simply 0.4751^{n}. The following return tables show the pay table, probability of winning, and return for all four streak bets, under both the new and old rules.

### Streak Bet Return Table- New Rules

Streak Bet |
Pays | Probability Win |
Return |
---|---|---|---|

2 | 3 | 0.225712 | -0.097154 |

3 | 8 | 0.107234 | -0.034898 |

4 | 18 | 0.050946 | -0.032032 |

5 | 38 | 0.024204 | -0.05605 |

The table above shows that under the new, more liberal, rules the best bet is on a streak of 4, with a house edge of 3.20%.

### Streak Bet Return Table- Old Rules

Streak Bet |
Pays | Probability Win |
Return |
---|---|---|---|

2 | 3 | 0.225712 | -0.097154 |

3 | 7 | 0.107234 | -0.142132 |

4 | 17 | 0.050946 | -0.082978 |

5 | 37 | 0.024204 | -0.080254 |

**Fire Bet**

After going 13 years without seeing the Streak bet I suddenly saw it, under another name, at the Palms casino in Managua, Nicaragua, on April 29, 2013. There it is called the *Fuego* bet, which means fire. They use a different pay table, as shown in the following pay table. For splitting, they use the first hand played out for purposes of the Streak bet. Otherwise, the rules are a little different, but still use six decks and the dealer stands on a soft 17. To simplify the analysis, I'm going to assume the same 47.51% of a net win as I do under the Atlantic City rules.

### Streak Bet Return Table — Nicaragua Rules

Streak Bet |
Pays | Probability Win |
Return |
---|---|---|---|

3 | 8 | 0.107240 | -0.034844 |

4 | 16 | 0.050950 | -0.133858 |

5 | 35 | 0.024206 | -0.128580 |

## Over/Under 13

This pair of side bets pay even money if the player can correctly bet if the sum of the player's first two cards will be over or under 13. Aces count as 1. At the Majestic Casino in Panama City, Panama, the player may also bet on exactly 13, which pays 10 to 1. The following is the house edge according to the number of decks. The house edge for exactly 13 is calculated at 10 to 1.

### Over/Under 13

Decks | Over 13 | Under 13 | Exactly 13 |
---|---|---|---|

1 | 6.79% | 10.11% | 7.09% |

2 | 6.65% | 10.08% | 7.99% |

4 | 6.58% | 10.07% | 8.44% |

6 | 6.55% | 10.07% | 8.58% |

8 | 6.54% | 10.06% | 8.66% |

## Bet the Set/Pair Square

"Pair Square," which also goes by the name "Bet the Set," is one of the most successful blackjack side bets, which I've seen lots of places.. It wins if the player's first two cards are a pair, usually more for a suited pair. I have seen or heard of a number of pay tables through the years. Following are return tables for some of them.

### Pair Square — 12-10 Pay Table — Six Decks

Event | Pays | Combinations | Probability | Return |
---|---|---|---|---|

Suited pair | 12 | 780 | 0.016077 | 0.192926 |

Non-suited pair | 10 | 2808 | 0.057878 | 0.578778 |

No pair | -1 | 44928 | 0.926045 | -0.926045 |

Total | 48516 | 1.000000 | -0.154341 |

### Pair Square — 12-12 Pay Table — Six Decks

Event | Pays | Combinations | Probability | Return |
---|---|---|---|---|

Suited pair | 12 | 780 | 0.016077 | 0.192926 |

Non-suited pair | 12 | 2808 | 0.057878 | 0.694534 |

No pair | -1 | 44928 | 0.926045 | -0.926045 |

Total | 48516 | 1.000000 | -0.038585 |

### Pair Square — 15-10 Pay Table — Six Decks

Event | Pays | Combinations | Probability | Return |
---|---|---|---|---|

Suited pair | 15 | 780 | 0.016077 | 0.241158 |

Non-suited pair | 10 | 2808 | 0.057878 | 0.578778 |

No pair | -1 | 44928 | 0.926045 | -0.926045 |

Total | 48516 | 1.000000 | -0.106109 |

### Pair Square — 20-10 Pay Table — Six Decks

Event | Pays | Combinations | Probability | Return |
---|---|---|---|---|

Suited pair | 20 | 780 | 0.016077 | 0.321543 |

Non-suited pair | 10 | 2808 | 0.057878 | 0.578778 |

No pair | -1 | 44928 | 0.926045 | -0.926045 |

Total | 48516 | 1.000000 | -0.025723 |

### Pair Square — 25-10 Pay Table — Two Decks

Event | Pays | Combinations | Probability | Return |
---|---|---|---|---|

Suited pair | 25 | 52 | 0.009709 | 0.242718 |

Non-suited pair | 10 | 312 | 0.058252 | 0.582524 |

No pair | -1 | 4992 | 0.932039 | -0.932039 |

Total | 5356 | 1.000000 | -0.106796 |

### Pair Square — 15 Pay Table — One Deck

Event | Pays | Combinations | Probability | Return |
---|---|---|---|---|

Non-suited pair | 15 | 78 | 0.058824 | 0.882353 |

No pair | -1 | 1248 | 0.941176 | -0.941176 |

Total | 1326 | 1.000000 | -0.058824 |

The next table summarizes the house edge for all known pay tables by number of decks. A negative house edge denotes a player advantage, for a combination of pay table and number of decks you're unlikely to ever see, but let me know if you do.

### Pair Square — House Edge Summary

Decks | 0-15 Pay table |
12-10 Pay table |
12-12 Pay table |
15-10 Pay table |
20-10 Pay table |
25-10 Pay table |
---|---|---|---|---|---|---|

1 | 5.88% | 35.29% | 23.53% | 35.29% | 35.29% | 35.29% |

2 | 5.83% | 23.30% | 11.65% | 20.39% | 15.53% | 10.68% |

3 | 5.81% | 19.35% | 7.74% | 15.48% | 9.03% | 2.58% |

4 | 5.80% | 17.39% | 5.80% | 13.04% | 5.80% | -1.45% |

5 | 5.79% | 16.22% | 4.63% | 11.58% | 3.86% | -3.86% |

6 | 5.79% | 15.43% | 3.86% | 10.61% | 2.57% | -5.47% |

7 | 5.79% | 14.88% | 3.31% | 9.92% | 1.65% | -6.61% |

8 | 5.78% | 14.46% | 2.89% | 9.40% | 0.96% | -7.47% |

## Bet the Set - Progressive

I noticed this variation of Bet the Set on April 19, 2013 at the Red Rock casino in Las Vegas. It was dealt from a six-deck game. The bet wins if the player has a pair for his initial two cards, more if they are suited. Unlike the normal Bet the Set, if the player has a pair he has a chance for big wins if the dealer also has a pair of the same rank.

If the player gets a colored four of a kind not only is he paid 250 to 1, but also wins a progressive jackpot. In addition, there are envy bonuses if another player gets a colored four of a kind. The minimum bet to qualify for the jackpot and envy bonuses is $1.

Rack card. Click on either image for a larger version.

The following table shows the odds for a six-deck game, before considering the jackpot and envy bonuses. The lower right cell shows a house edge of 27.74%.

### Bet the Set — Progressive — Six Decks

Event | Pays | Combinations | Probability | Return |
---|---|---|---|---|

Colored four of a kind | 250 | 77,220 | 0.000033 | 0.008308 |

Four of a kind | 100 | 751,608 | 0.000323 | 0.032346 |

Suited pair | 20 | 37,177,920 | 0.016000 | 0.319993 |

Pair | 5 | 133,840,512 | 0.057599 | 0.287993 |

Loser | -1 | 2,151,826,560 | 0.926045 | -0.926045 |

Total | 2,323,673,820 | 1.000000 | -0.277405 |

**Jackpot**

For a $1 bet, every $1,000 in the jackpot meter increases the expected return by 0.033232. If the player bets more than $1, then divide that increase by the amount bet.

**Envy Bonus**

For a $1 bet, every other player at the table (not counting yourself) increases the expected return by 0.001662. If the player bets more than $1, then divide that increase by the amount bet.

For a $1 bettor, the jackpot break-even point is $8,347.58, less $50 for every additional player at the table. When I saw this bet on April 20, 2013 the meter was at $7,817.44.

## Tie - Version 1

Caesars Palace in Las Vegas at one time offered a side bet on a tie at two of their blackjack tables. If the player and dealer do tie the side bet pays 10 to 1. The player may bet no more than 50% of their original blackjack wager on the side bet. If the player splits he must also split the side bet. If the player doubles, he does not double the side bet. For the analysis I assumed for the following blackjack rules:

- Winning blackjack pays 3 to 2.
- Six decks.
- Dealer hits soft 17.
- Double after split allowed.
- No surrender.
- No re-splitting aces.

Assuming the rules and strategy above, I show an overall house edge of 0.24%, which is the expected player win divided by the initial 1.5 units bet. If a winning blackjack paid 6-5, then the house edge would be 1.15%.

## Tie - Version 2

In August 2010 I noticed another version of side betting on a tie in blackjack at Harrah's Las Vegas. Unlike version 1, where all ties pay 10 to 1, at Harrah's you could bet on all six possible ties individually, or on a low or a high tie. As I recall, the rules were:

- Six decks
- Blackjack pays 6 to 5.
- Dealer hits soft 17
- Double after split allowed.
- No surrender.
- No re-splitting aces.
- If player doubles, he does not double the tie wagers.
- If player splits, he does not double the tie wagers. Any tie wagers will be resolved based on the first hand played out.
- An ace and 10 after splitting aces is considered 21 points for purposes of both the blackjack and tie wagers.
- If the player re-splits, then all tie wagers are lost.

The layout has betting circles for 17, 18, 19, and LS (left side) tie wagers on the left of the betting circle for the blackjack wagers. The other four tie wagers are on the right side. The player may bet up to half his blackjack wager on the sum of the four left side tie wagers, and likewise up to half on on the right side.

If the player does bet a tie, it significantly changes the strategy. The player will do more hitting, and less of everything else. There is a separate strategy for each tie wager. I won't bother to publish them unless the game gets a significant number of placements.

I spent all day trying to analyze this one, but the doubling and splitting rules made it too difficult. So I'm quoting below pay table #4 from the game owner's web site, blackjacktie.com, with permission.

### Tie (version 2) House Edge

Tie Wager | Pays | House Edge |
---|---|---|

17 | 50 | 2.41% |

18 | 45 | 5.79% |

19 | 50 | 3.67% |

20 | 25 | 8.47% |

21 | 125 | 10.85% |

BJ | 400 | 7.18% |

LS (17, 18, 19) | 15 | 8.07% |

RS (20, 21, BJ) | 20 | 9.39% |

## 21+3

**Version 1**

Version 1 of 21+3 I noticed at the Las Vegas Hilton in April, 2001. The side bet pays based on the player's first two cards and the dealer's up card. If the three cards equal a flush, straight, straight flush, or three of a kind the side bet pays 9 to 1. The following table shows the probability of each hand in a six-deck game,as played at the Hilton.

### 21+3 - 6 decks

Hand | Combinations | Probability | Pays | Return |
---|---|---|---|---|

Straight flush | 10368 | 0.002068 | 9 to 1 | 0.018613 |

Three of a kind | 26312 | 0.005248 | 9 to 1 | 0.047236 |

Straight | 155520 | 0.031021 | 9 to 1 | 0.279192 |

Flush | 236736 | 0.047221 | 9 to 1 | 0.424993 |

Pair+flush | 56160 | 0.011202 | 9 to 1 | 0.100819 |

Pair (no flush) | 977184 | 0.194918 | Loss | -0.194918 |

Nothing | 3551040 | 0.708321 | Loss | -0.708321 |

Total | 5013320 | 1 | -0.032386 |

The house edge under these rules is 3.24%.

**Version 2**

At the Regent (now known as the Rampart) in Las Vegas all hands listed above, plus a pair, pay 5 to 2. I'll call this version 2. Two decks are used in this version. The following table shows a house edge under these rules of 2.78%.

### 21+3 — 2 decks

Hand | Combinations | Probability | Pays | Return |
---|---|---|---|---|

Straight flush | 384 | 0.002109 | 2.5 to 1 | 0.005272 |

Three of a kind | 728 | 0.003998 | 2.5 to 1 | 0.009994 |

Straight | 5760 | 0.03163 | 2.5 to 1 | 0.079076 |

Flush | 8768 | 0.048148 | 2.5 to 1 | 0.120371 |

Pair | 34944 | 0.19189 | 2.5 to 1 | 0.479726 |

Nothing | 131520 | 0.722225 | Loss | -0.722225 |

Total | 182104 | 1 | -0.027786 |

Version 3

I have an unconfirmed report that Internet casinos using Wagerworks software use the following pay table, which I will call "Version 3."

### 21+3 — Version 3 — Six Decks

Hand | Pays | Combinations | Probability | Return |
---|---|---|---|---|

Suited three of a kind | 100 | 1040 | 0.000207 | 0.020745 |

Three of a kind | 33 | 25272 | 0.005041 | 0.166352 |

Straight flush | 35 | 10368 | 0.002068 | 0.072383 |

Straight | 10 | 155520 | 0.031021 | 0.310214 |

Flush | 5 | 292896 | 0.058424 | 0.292118 |

Loss | -1 | 4528224 | 0.903239 | -0.903239 |

Total | 5013320 | 1 | -0.041427 |

Although Wager Works only uses six decks in their blackjack game, as far as I know, here is the house edge for 3 to 8 decks.

### 21+3 — Version 3 — 3-8 Decks

Decks | House Edge |
---|---|

3 | 7.76% |

4 | 5.99% |

5 | 4.89% |

6 | 4.14% |

7 | 3.60% |

8 | 3.18% |

**Version 4**

This version, with a 30-20-10-5 pay table, is known as "21+3 Xtreme." The following return table shows the house edge for six decks is 13.39% (ouch!).

### 21+3 — Version 4 — Six Decks

Hand | Pays | Combinations | Probability | Return |
---|---|---|---|---|

Straight flush | 30 | 10,368 | 0.002068 | 0.062043 |

Three of a kind | 20 | 26,312 | 0.005248 | 0.104968 |

Straight | 10 | 155,520 | 0.031021 | 0.310214 |

Flush | 5 | 292,896 | 0.058424 | 0.292118 |

Loser | -1 | 4,528,224 | 0.903239 | -0.903239 |

Total | 5,013,320 | 1.000000 | -0.133896 |

If you happen to see it with other than six decks, here is the expected value for various number of decks.

### 21+3 — Version 4 -- 1 to 8 Deck Summary

Decks | Expected Value |
---|---|

1 | -0.227330 |

2 | -0.172736 |

4 | -0.143780 |

5 | -0.137863 |

6 | -0.133896 |

8 | -0.128912 |

The Caesars Entertainment Blog mentions that the xtreme version of 21+3 can be found in the Party Pit at the Paris casino in Las Vegas. I had to chuckle at their sense of humor with this remark,

*"We would calculate the odds of hitting these side bets, but being in Vegas isn't about math, it's about having fun. And just never-you-mind that this is the blog of a casino company. Check out the new Ooh La La Party Pit at Paris Las Vegas the next time you’re in the neighborhood.*

Hey, it is about the math everywhere, even in the Party Pit!

## Sweet Sixteen

Sweet Sixteen is a blackjack side bet I noticed at the Las Vegas Club in April 2001. It is played with a six-deck shoe and pays based on the player's first two cards. The following table shows each paying hand, the probability, payoff, and contribution to the total return.

### Sweet Sixteen

Hand | Probability | Pays | Return |
---|---|---|---|

16-21 points | 0.31907 | 1 to 1 | 0.63814 |

One ace | 0.142468 | 1 to 1 | 0.284937 |

Two aces | 0.005689 | 2 to 1 | 0.017067 |

Pair 2's-7's | 0.034133 | Push | 0.034133 |

Total | 0.50136 | 0.974277 |

The lower right cell shows a return of 97.43%, for ahouse edge of 2.57%. Here is the house edge for other numbers of decks.

- 1 deck: 3.62%
- 2 decks: 2.99%
- 4 decks: 2.68%
- 8 decks: 2.52%

## Dare any Pair

Dare any Pair is a side bet I noticed at the Lady Luck in April 2001. It simply pays 11 to 1 if the player's first two cards are a pair. Six decks are used. The probability of a pair is 0.073954984 for a house edge of 11.25%. Here is the house edge for other numbers of decks.

- 1 deck: 29.41%
- 2 decks: 18.45%
- 4 decks: 13.04%
- 8 decks: 10.36%

## Lucky Ladies

This is a common side bet found in many casinos such as the Wizard's Casino (nice name) in Seattle. Any player 20-point hand wins something. There are three possible pay tables, A-C, as follows:

### Lucky Ladies — Pay Table A and B

Hand | Table A | Table B |
---|---|---|

Q of hearts pair & dealer has BJ | 1000 to 1 | 1000 to 1 |

Q of hearts pair | 125 to 1 | 200 to 1 |

Matched 20 (same rank and suit) | 19 to 1 | 25 to 1 |

Suited 20 | 9 to 1 | 10 to 1 |

Unsuited 20 | 4 to 1 | 4 to 1 |

Non-20 | -1 to 1 | -1 to 1 |

### Lucky Ladies — Pay Table C

Hand | Table C |
---|---|

Pair of queens with dealer BJ | 250 to 1 |

Pair of queens | 25 to 1 |

Ranked 20 | 9 to 1 |

Suited 20 | 6 to 1 |

Any 20 | 3 to 1 |

Non-20 | -1 to 1 |

The next table is an analysis of pay table A with six decks.

### Lucky Ladies Pay Table A — 6 decks

Hand | Permutations | Probability | Pays | Return |
---|---|---|---|---|

Q of hearts pair & dealer has BJ | 135360 | 0.000015 | 1000 to 1 | 0.014563 |

Q of hearts pair | 2738340 | 0.000295 | 125 to 1 | 0.036827 |

Matched 20 (same rank and suit) | 43105500 | 0.004638 | 19 to 1 | 0.088115 |

Suited 20 | 193112640 | 0.020777 | 9 to 1 | 0.186990 |

Unsuited 20 | 744863040 | 0.080139 | 4 to 1 | 0.320554 |

Non-20 | 8310740400 | 0.894138 | -1 to 1 | -0.894138 |

Total | 9294695280 | 0 | -0.247089 |

The lower right cell shows a return of 75.29%, or a house edge of 24.71%.

The next table is an analysis of pay table C with one deck.### Lucky Ladies Pay Table C — 1 deck

Hand | Permutations | Probability | Pays | Return |
---|---|---|---|---|

Pair of queens with dealer BJ | 1344 | 0.000207 | 250 to 1 | 0.051713 |

Pair of queens | 28056 | 0.004318 | 25 to 1 | 0.107951 |

Ranked 20 | 88200 | 0.013575 | 9 to 1 | 0.122172 |

Suited 20 | 137200 | 0.021116 | 6 to 1 | 0.126697 |

Any 20 | 411600 | 0.063348 | 3 to 1 | 0.190045 |

Non-20 | 5831000 | 0.897436 | -1 to 1 | -0.897436 |

Total | 6497400 | 1 | To 1 | -0.298858 |

The lower right cell shows a house edge of 29.89%.

The final Lucky Ladies table shows the house edge according to the pay table and number of decks. Note that the top hands with pay table A and B are impossible with 1 deck.

### Lucky Ladies — Summary

Decks | Table A | Table B | Table C |
---|---|---|---|

1 | 38.16% | 36.05% | 29.89% |

2 | 30.05% | 24.94% | 25.51% |

3 | 27.37% | 21.28% | 24.07% |

4 | 26.04% | 19.46% | 23.35% |

5 | 25.24% | 18.37% | 22.92% |

6 | 24.71% | 17.64% | 22.64% |

7 | 24.33% | 17.12% | 22.43% |

8 | 24.05% | 16.73% | 22.28% |

## Bonus Blackjack - Version 1

This is a simple pair of side bets that the player and/or dealer will get a blackjack. Wins pay 15 to 1. The player may bet on a player blackjack and/or dealer blackjack. If the player bets both and the player gets a blackjack composed of an ace and jack of spades, then the player will win a progressive bonus.

As the number of decks increases, the probability of a blackjack decreases, making the player's odds worse. The following table shows pertinent information about this bet as explained below.

First column: Number of decks

Second column: House edge if just one bet is made

Third column: Overall reduction in house edge for each $100 in meter if both bets are made

Fourth column: Point meter must reach for bet to have zero house edge.

### Bonus Blackjack — Version 1

Decks | House Edge | Reduction in House for each $100 in Meter |
Break-even Meter |
---|---|---|---|

1 | 22.78% | 3.77% | $604.00 |

2 | 23.53% | 3.73% | $630.00 |

4 | 23.89% | 3.72% | $643.00 |

6 | 24.02% | 3.71% | $647.33 |

8 | 24.08% | 3.71% | $649.50 |

## Bonus Blackjack - Version 2

This is another side bet called "Bonus Blackjack." I noticed it at the Sycuan casino near San Diego on October 25, 2009. The only bet amounts permitted were 50¢ and $1. The following table shows the pay table, probabilities, and return for a six-deck game. The lower right cell shows a house edge of 40.78% (ouch!). This assumes the player always tries for a 678 or 777 if possible, even if it violates basic strategy. The cost of such strategy deviations are not indicated.

### Bonus Blackjack (Sycuan) — Six Decks

Hand | Pays | Combinations | Probability | Return |
---|---|---|---|---|

777 | 500 | 12144 | 0.000404 | 0.201862 |

678 | 50 | 82944 | 0.002757 | 0.137873 |

Suited BJ | 20 | 357120 | 0.011872 | 0.237447 |

Loser | -1 | 29627712 | 0.984966 | -0.984966 |

Total | 30079920 | 1 | -0.407784 |

The next table shows the house edge for various number of decks.

### Bonus Blackjack (version 2) — House Edge

Decks | House Edge |
---|---|

2 | 45.16% |

4 | 41.92% |

5 | 41.24% |

6 | 40.78% |

8 | 40.20% |

## Bonus Blackjack - Version 3

I noticed this third version of Bonus Blackjack at the Riviera casino on November 17, 2012. It was played on a single-deck game. Wins are based on the player's first two cards, and for the highest win, on the dealer's cards as well. The following table shows everything you need to know.

### Bonus Blackjack — Version 3

Event | Pays | Combinations | Probabity | Return |
---|---|---|---|---|

Player and dealer blackjack | 25 | 2,880 | 0.001773 | 0.044325 |

Player suited blackjack | 10 | 18,880 | 0.011623 | 0.116231 |

Player unsuited blackjack | 3 | 56,640 | 0.034869 | 0.104608 |

Pair | 2 | 95,550 | 0.058824 | 0.117647 |

Suited | 1 | 362,600 | 0.223228 | 0.223228 |

All other | -1 | 1,087,800 | 0.669683 | -0.669683 |

Total | 1,624,350 | 1.000000 | -0.063644 |

The lower right cell shows a house edge of 6.36%.

## Progressive Blackjack

As the name implies, this is a blackjack side bet with a progressive jackpot. For an optional $1, the blackjack player may win $3 to the progressive jackpot, which starts at $25,000. I saw this side bet at the New York New York casino, where they had three tables tied into the same progressive. On July 30, 2001, the jackpot meter was at $35,537.36. At this time, I was told they recently put it in place and nobody had hit the jackpot yet. On August 11 the meter had risen to $37,746.28.

Just like in Caribbean Stud, the player puts the $1 for the Progressive side bet in a slot. Before dealing a new hand, the dealer presses a button, the dollars vanish, and a light designates who made the bet. The following table shows what each winning hand pays, the probability (based on the dealer peeking for blackjack), and the contribution to the return.

The following table shows the return based on a meter of $35,537.36, the amount the last time I observed it.

### Progressive Blackjack

Hand | Permutations | Probability | Pays | Return |
---|---|---|---|---|

4 red/black aces | 23760 | 0.000003 | 35537.36 | 0.090844 |

4 aces | 231264 | 0.000025 | 2000 | 0.049763 |

3 suited aces | 138240 | 0.000015 | 1000 | 0.014873 |

3 non-suited aces | 3359232 | 0.000361 | 200 | 0.072283 |

2 Suited aces | 10679040 | 0.001149 | 50 | 0.057447 |

2 non-suited aces | 38444544 | 0.004136 | 15 | 0.062043 |

1 ace | 662100480 | 0.071234 | 3 | 0.213703 |

No aces | 8579718720 | 0.923077 | 0 | 0 |

Total | 9294695280 | 1 | 0 | 0.560955 |

The above table shows an expected return of 56.10% per dollar bet, or a house edge of 43.90%. The general formula for the return is 47.01%, plus 2.56% for each $10,000 in the meter. To have no house edge, the meter would need to reach $207,287.85. Also note there are no basic strategy deviations for this side bet. If the player gets two aces, then he should split anyway, which guarantees two more cards.

It is unclear to me what events cause the meter to go up and down. Sometimes the meter goes up by 28 cents for each $1 bet made. According to the Mikohn's web site, the house edge is 22%. If this is the case, then the meter contribution rate is 24.60%. Mikohn also mentions that part of each dollar goes to a higher reseed of the next jackpot. So 24.60% would be divided between the current meter and the next one. Based on this contribution rate, the average jackpot when won would be $121,225.86.

## Twin Blackjack

Twin blackjack is not a side bet, but a variation of the game of blackjack. I saw the game at the Stardust in August, 2001. Each position has two betting spots. If the player makes a bet in both of them he will play out two hands against the dealer's up card. In the event the player gets two blackjacks (called twin blackjacks) they both shall pay 2-1. If the player gets two identical blackjacks (called identical twin blackjacks) both shall pay 4-1.

The following table shows what this is worth to the player.

### Twin Blackjack

Event | Probability | Pays Extra | Return |
---|---|---|---|

Twin BJ | 0.002142 | 0.5 | 0.001071 |

Identical twin BJ | 0.000025 | 2.5 | 0.000062 |

Total | 0.002167 | 0 | 0.001133 |

The lower right cell in the table shows the twin blackjack rules add about 0.1133% to the players return. However, as usual with novelty games, you give more than you get back. In this case, the player may NOT double after a split and the number of splits per hand is lowered from 3 to 2. Under the normal Stardust 6-deck rules the house edge is 0.4066%. Under these rules, not including the twin blackjack bonuses, the house edge is 0.5527%. Overall the house edge is 0.4394%, 0.0328% higher than the conventional rules.

## Perfect Pairs

Perfect Pairs is a blackjack side bet found in casinos in Australia, Macau, and London. It pays if the player's first two cards are a pair. The following table shows the specifics. A "perfect pair" is two identical cards (like two ace of spades). A "colored pair" is two cards of the same rank and color (like the ace of spades and ace of clubs). There are four pay tables that I am aware of, which are referred to as A to D below. The following four tables show how the odds of each pay table.

### Pay Table A — 8 decks

Hand | Pays | Combinations | Probability | Return |
---|---|---|---|---|

Perfect pair | 25 | 1456 | 0.016867 | 0.421687 |

Colored pair | 12 | 1664 | 0.019277 | 0.231325 |

Red/black pair | 6 | 3328 | 0.038554 | 0.231325 |

Non-pair | -1 | 79872 | 0.925301 | -0.925301 |

Total | 86320 | 1 | -0.040964 |

### Pay Table B — 8 decks

Hand | Pays | Combintions | Probability | Return |
---|---|---|---|---|

Perfect pair | 30 | 1456 | 0.016867 | 0.506024 |

Colored pair | 10 | 1664 | 0.019277 | 0.192771 |

Red/black pair | 5 | 3328 | 0.038554 | 0.192771 |

Non-pair | -1 | 79872 | 0.925301 | -0.925301 |

Total | 86320 | 1 | -0.033735 |

### Pay Table C — 8 decks

Hand | Pays | Combintions | Probability | Return |
---|---|---|---|---|

Perfect pair | 25 | 1456 | 0.016867 | 0.421687 |

Colored pair | 12 | 1664 | 0.019277 | 0.231325 |

Red/black pair | 5 | 3328 | 0.038554 | 0.192771 |

Non-pair | -1 | 79872 | 0.925301 | -0.925301 |

Total | 86320 | 1 | -0.079518 |

### Pay Table D — 8 decks

Hand | Pays | Combintions | Probability | Return |
---|---|---|---|---|

Perfect pair | 25 | 1456 | 0.016867 | 0.421687 |

Colored pair | 15 | 1664 | 0.019277 | 0.289157 |

Red/black pair | 5 | 3328 | 0.038554 | 0.192771 |

Non-pair | -1 | 79872 | 0.925301 | -0.925301 |

Total | 86320 | 1 | -0.021687 |

The next table shows the expected return under all four pay tables, according to the number of decks.

### Perfect Pairs Expected Returns

Decks | Pay Table A | Pay Table B | Pay Table C | Pay Table D |
---|---|---|---|---|

2 | -0.223301 | -0.252427 | -0.262136 | -0.203883 |

4 | -0.101449 | -0.106280 | -0.140097 | -0.082126 |

5 | -0.077220 | -0.077220 | -0.115830 | -0.057915 |

6 | -0.061093 | -0.057878 | -0.099678 | -0.041801 |

8 | -0.040964 | -0.033735 | -0.079518 | -0.021687 |

## Bonanza Blackjack

Bonanza Blackjack is a side bet found on a fully-electronic 6-deck game at the Boulder Station in Las Vegas. If the player has any 20 (including a soft 20) and the dealer has a 10-point card, then the player will win something. This is a $1 side bet, no more and no less.

### Bonanza Blackjack

Player's hand | Dealer's hand | Permutations | Probability | Pays | Return |
---|---|---|---|---|---|

Same rank and suit | First two cards match | 5760 | 0.00000062 | 25000 | 0.015493 |

Same rank and suit | Up card matches | 587520 | 0.00006321 | 2500 | 0.158026 |

Same rank and suit | Up card any 10 | 13348800 | 0.00143617 | 100 | 0.143617 |

Same rank | Up card any 10 | 50191488 | 0.00540001 | 30 | 0.162 |

Same suit | Up card any 10 | 50191488 | 0.00540001 | 20 | 0.108 |

Different rank and suit (including soft 20) | Up card any 10 | 184747392 | 0.01987665 | 10 | 0.198766 |

Loser | 8995622832 | 0.96782332 | -1 | -0.967823 | |

Total | 9294695280 | 1 | -0.18192 |

The lower right cell shows a house edge of 18.19%.

## Hi/Low

This is a simple pair of side bets I noticed at the Casablanca in Mesquite, Nevada. The player simply bets if his first card will be higher or lower than the dealer's up card. In the event the two cards are the same rank, except aces, the tie shall go to the dealer. Two aces push. The game I saw it on was 6-decks but here is the house edge for all numbers of decks.

### Hi/Low

Decks | House Edge |
---|---|

1 | 5.43% |

2 | 6.27% |

3 | 6.55% |

4 | 6.69% |

5 | 6.77% |

6 | 6.83% |

7 | 6.87% |

8 | 6.9% |

## 2 Through 6

"2 Through 6" is a side bet I noticed at the Four Queens on April 24, 2004. Except as noted all winnings hands involve a dealer up card of 2 through 6. The following table shows all the winning events, permutations, probability, payoff, and contribution to the return. The lower right cell shows a house edge of 7.48%.

### 2 Through 6

Event | Permutations | Probability | Pays | Return |
---|---|---|---|---|

Ace/king of hearts | 34560 | 0.001149 | 40 | 0.045958 |

Blackjack | 518400 | 0.017234 | 8 | 0.137873 |

Total of 9 to 11* | 1707888 | 0.056778 | 5 | 0.283892 |

Total of 17 to 20 | 2957760 | 0.09833 | 2 | 0.19666 |

Blackjack (dealer has 7 to A) | 875520 | 0.029106 | 2 | 0.058213 |

All other | 23985792 | 0.797402 | -1 | -0.797402 |

Total | 30079920 | 1 | 0 | -0.074807 |

*: includes soft 19 and soft 20

The maximum bet allowed is the lesser of $50 and the blackjack bet.

## Jack Magic

Jack Magic is a Shufflemaster side bet that has been seen at the Spirit Mountain casino in Grande Ronde, Oregon. It is played on a 5-deck blackjack game with a continuous shuffler. Wins are based on the player's initial two cards and the dealer's up card, thus no basic strategy changes are necessary. The following table shows the probability and return for each win. The lower right cell shows a house edge of 20.06%.

### Jack Magic

Event | Combinations | Probability | Pays | Return |
---|---|---|---|---|

Three one eyed jacks | 120 | 0.000041 | 500 | 0.020721 |

Three jacks | 1020 | 0.000352 | 100 | 0.035226 |

Two one eyed jacks | 10800 | 0.00373 | 30 | 0.111893 |

Two jacks | 34800 | 0.012018 | 10 | 0.120182 |

One one eyed jack | 286800 | 0.099046 | 2 | 0.198092 |

One jack | 286800 | 0.099046 | 1 | 0.099046 |

No jacks | 2275280 | 0.785766 | -1 | -0.785766 |

Total | 2895620 | 1 | 0 | -0.200606 |

## Match the Dealer

Match the Dealer is a side bet found in both blackjack and Spanish 21. The player wins for each of his initial two cards that match the dealer's up card. Matches in rank only pay less than a match in rank and suit. The following tables show the various versions I am aware of.

### Match the Dealer - Blackjack - Six Decks

Event | Pays | Combinations | Probability | Return |
---|---|---|---|---|

Two suited matches | 22 | 10 | 0.000207 | 0.004564 |

One suited and one non-suited match | 15 | 90 | 0.001867 | 0.028005 |

One suited match | 11 | 1440 | 0.029872 | 0.328597 |

Two non-suited matches | 8 | 153 | 0.003174 | 0.025392 |

One non-suited matches | 4 | 5184 | 0.107541 | 0.430163 |

No matches | -1 | 41328 | 0.857338 | -0.857338 |

Total | 48205 | 1 | -0.040618 |

### Match the Dealer- Blackjack- Eight Decks

Event | Combinations | Probability | Pays | Return |
---|---|---|---|---|

Two suited matches | 21 | 0.000244 | 28 | 0.006845 |

One hard and one each match | 168 | 0.001956 | 17 | 0.033246 |

Two non-suited matches | 276 | 0.003213 | 6 | 0.019277 |

One suited match | 2688 | 0.03129 | 14 | 0.438065 |

One non-suited match | 9216 | 0.107281 | 3 | 0.321844 |

No matches | 73536 | 0.856015 | -1 | -0.856015 |

Total | 85905 | 1 | 0 | -0.036738 |

### Match the Dealer- Spanish 21- Six Decks

Event | Combinations | Probability | Pays | Return |
---|---|---|---|---|

Two suited matches | 10 | 0.000244 | 18 | 0.004386 |

One hard and one each match | 90 | 0.002193 | 13 | 0.028508 |

Two non-suited matches | 153 | 0.003728 | 8 | 0.029824 |

One suited match | 1320 | 0.032163 | 9 | 0.289467 |

One non-suited match | 4752 | 0.115787 | 4 | 0.463147 |

No matches | 34716 | 0.845886 | -1 | -0.845886 |

Total | 41041 | 1 | 0 | -0.030555 |

### Match the Dealer- Spanish 21- Eight Decks

Event | Combinations | Probability | Pays | Return |
---|---|---|---|---|

Two suited matches | 21 | 0.000287 | 24 | 0.00689 |

One hard and one each match | 168 | 0.002297 | 15 | 0.034448 |

Two non-suited matches | 276 | 0.003773 | 6 | 0.022637 |

One suited match | 2464 | 0.033683 | 12 | 0.404194 |

One non-suited match | 8448 | 0.115484 | 3 | 0.346452 |

No matches | 61776 | 0.844477 | -1 | -0.844477 |

Total | 73153 | 1 | 0 | -0.029855 |

## Blackjack Only

Some casinos offer a simple side bet that pays from 15 to 19 to 1 for a player blackjack. It is also possible for the bet to be based on a dealer blackjack, or both bets may be available. The Cal Neva in Reno, where the picture above was taken, pays 17 to 1. There is no particular name for this and I think it is a "common domain" bet, meaning nobody owns the idea so no royalties are required.

The following table shows the house edge for 1 to 8 decks and a payoff of 15 to 19 to 1.

### Blackjack Only

Number of Decks | 15 to 1 | 16 to 1 | 17 to 1 | 18 to 1 | 19 to 1 |
---|---|---|---|---|---|

1 deck | 22.78% | 17.95% | 13.12% | 8.30% | 3.47% |

2 decks | 23.53% | 18.75% | 13.97% | 9.19% | 4.41% |

3 decks | 23.77% | 19.01% | 14.24% | 9.48% | 4.71% |

4 decks | 23.89% | 19.14% | 14.38% | 9.62% | 4.87% |

5 decks | 23.97% | 19.22% | 14.46% | 9.71% | 4.96% |

6 decks | 24.02% | 19.27% | 14.52% | 9.77% | 5.02% |

7 decks | 24.05% | 19.3% | 14.56% | 9.81% | 5.06% |

8 decks | 24.08% | 19.33% | 14.59% | 9.84% | 5.10% |

## Lucky Lucky

Lucky Lucky is a side bet based on the player's first two cards and the dealer's up card. It can be found at various casinos in Las Vegas and Alberta, Canada. The following tables shows the various winning hands, probability, payoff, and contribution to the total return, based on a six deck game. The lower right cell shows a house edge of 2.66%, one of the lowest for any side bet.

### Lucky Lucky- Six Decks

Event | Combinations | Probability | Pays | Return |
---|---|---|---|---|

Suited 777 | 80 | 0.000016 | 200 | 0.003191 |

Suited 678 | 864 | 0.000172 | 100 | 0.017234 |

Unsuited 777 | 1944 | 0.000388 | 50 | 0.019388 |

Unsuited 678 | 12960 | 0.002585 | 30 | 0.077553 |

Suited 21 | 26568 | 0.005299 | 15 | 0.079492 |

Unsuited 21 | 406296 | 0.081043 | 3 | 0.24313 |

Any 20 | 377568 | 0.075313 | 2 | 0.150626 |

Any 19 | 364320 | 0.07267 | 2 | 0.145341 |

All other | 3822720 | 0.762513 | -1 | -0.762513 |

Total | 5013320 | 1 | -0.026556 |

## Bonus Spin

Bonus Spin is a side bet in which the player gets to spin a wheel if he gets a blackjack. Also, a hand with at least one ace, but not a blackjack, pays 1 to 1. The prizes on the wheel are 5x, 15x, 25x, 20x, 10x, and 100x, where the x represents the bet amount. All wins are on a to one basis. Assuming all wins were equally likely the average win would be 29.17x, resulting in a player edge of 63.4%. Obviously the stops on the prize wheel were not equally weighted. I asked the table games manager what the average win was and he said it was right around 14. As the table below shows this results in a house edge of 8.63%, based on six decks.

### Bonus Spin — Six Decks

Event | Combinations | Probability | Pays | Return |
---|---|---|---|---|

Blackjack | 2304 | 0.047489 | 14^{*} |
0.664853 |

Ace | 4884 | 0.100668 | 1 | 0.100668 |

Loss | 41328 | 0.851843 | -1 | -0.851843 |

Total | 48516 | 1 | -0.086322 |

* Based on an estimated average win.

The next table shows the house edge for 1 to 8 decks, again assuming an average win of 14.

### Bonus Spin — 1 to 8 Decks

Decks | House Edge |
---|---|

1 | 7.39% |

2 | 8.14% |

3 | 8.39% |

4 | 8.51% |

5 | 8.58% |

6 | 8.63% |

7 | 8.67% |

8 | 8.69% |

## Wheel of Madness

Similar to Bonus Spin, this is $1 side bet on a blackjack. If the player wins, then he gets to spin a prize wheel. According to Scott Brynen, the average win is about 15 to 1, based on personal observation. Casinos will often allow bets of larger than $1, with a win equal to the product of the prize wheel and the bet made. The following table shows the probability of winning and house edge according to the number of decks, assuming an average win of 15 to 1.

### House Edge in Wheel of Madness

Decks | Prob. Win | House Edge |
---|---|---|

1 | 4.83% | 22.78% |

2 | 4.78% | 23.53% |

3 | 4.76% | 23.77% |

4 | 4.76% | 23.89% |

5 | 4.75% | 23.97% |

6 | 4.75% | 24.02% |

7 | 4.75% | 24.05% |

8 | 4.75% | 24.08% |

This bet is vulnerable to card counting. Using indices of +1 for 2 to 9, 0 for 10-K, and -9 for aces, the odds swing in the player's favor at a true count (running count divided by decks remaining, rounding down) of 12. The next table shows how often this happens and the average advantage when it does in a 6-deck game according to the penetration, again assuming an average win of 15 to 1.

### Card Counting in Wheel of Madness

Penetration | Bets Made | Avg. Adv. |
---|---|---|

75% | 3.58% | 10.72% |

80% | 4.46% | 12.36% |

85% | 5.49% | 14.69% |

90% | 6.43% | 16.79% |

## High Tie Bonus Blackjack

Version 1 of this is a side bet I noticed at the MGM Grand on November 26, 2005. It was played on a six-deck game.

### High Tie Bonus Blackjack- Version 1- Six Decks

Event | Pays | Permutations | Probability | Return |
---|---|---|---|---|

Blackjack tie | 50 | 20136960 | 0.002167 | 0.108325 |

Suited blackjack | 15 | 105315840 | 0.011331 | 0.169961 |

Suited pair | 10 | 149432400 | 0.016077 | 0.160772 |

Blackjack | 6 | 315947520 | 0.033992 | 0.203953 |

Pair | 3 | 537956640 | 0.057878 | 0.173633 |

Other | -1 | 8165905920 | 0.878556 | -0.878556 |

Total | 9294695280 | 1 | -0.061911 |

Version 2 of this is a side bet I noticed at the Eldorado casino in Henderson on March 16, 2007. It was played on a six-deck game.

### High Tie Bonus Blackjack- Version 2- Six Decks

Event | Pays | Permutations | Probability | Return |
---|---|---|---|---|

Blackjack tie | 25 | 20136960 | 0.002167 | 0.054163 |

Suited pair | 6 | 149432400 | 0.016077 | 0.096463 |

Suited blackjack | 4 | 105315840 | 0.011331 | 0.045323 |

Blackjack | 3 | 315947520 | 0.033992 | 0.101977 |

Pair | 2 | 537956640 | 0.057878 | 0.115756 |

Suited | 1 | 2041476480 | 0.219639 | 0.219639 |

Other | -1 | 6124429440 | 0.658917 | -0.658917 |

Total | 9294695280 | 1 | -0.025597 |

## Field of Gold

Field of Gold is a side bet I'm told can be found at the Spirit Mountain Casino in Grand Ronde, Oregon. All wins are based on the player's first two cards. For side bet purposes, aces always count as one. The following return table is based on six decks. The lower right cell shows a house edge of 5.66%.

### Field of Gold Six Decks

Event | Pays | Permutations | Probability | Return |
---|---|---|---|---|

Ace/jack suited | 25 | 144 | 0.002968 | 0.074202 |

Two aces | 10 | 276 | 0.005689 | 0.056888 |

3 or 4 total | 3 | 1428 | 0.029434 | 0.088301 |

9 or 10 total | 2 | 4884 | 0.100668 | 0.201336 |

Any other blackjack | 1.5 | 2160 | 0.044521 | 0.066782 |

11 to 12 total | 1 | 6612 | 0.136285 | 0.136285 |

All other | -1 | 33012 | 0.680435 | -0.680435 |

Total | 48516 | 1 | -0.056641 |

The following table shows the house edge for various numbers of decks.

### Field of Gold - House Edge

Decks | House Edge |
---|---|

1 deck | 6.64% |

2 decks | 6.05% |

4 decks | 5.76% |

5 decks | 5.7% |

6 decks | 5.66% |

8 decks | 5.62% |

## Automatic Win/Casino Surrender

Automatic Win/Casino Surrender is an optional rule in blackjack in which the player may force the dealer to surrender when the player has a 2-card 20 against a dealer 10. This option is known by both names. In other words the player may play out his hand or settle for a win of 50% of his bet. The option may only be invoked after the dealer checks for blacjack. The Stardust in Las Vegas has been seen offering this rule in May 2005.

The following table shows the player's expected return with a 20 agaisnt a dealer 10, after the dealer checks for blackjack, according to the number of decks and composition of the 20.

### Expected value of 20 vs 10

Decks | 10,10 | A,9 |
---|---|---|

1 | 58.5315% | 55.4551% |

2 | 56.8553% | 55.4572% |

4 | 56.1473% | 55.4561% |

5 | 56.0074% | 55.4558% |

6 | 55.9145% | 55.4555% |

8 | 55.7987% | 55.4551% |

The table shows the player always stands to win 55.46% to 58.53% of his bet by playing out the hand. In a typical 6-deck game the player will give up 5.91% of his bet with a 10,10 and 5.46% with an A,9 by invoking the surrender option. The bottom line is taking dealer surrender is a mistake and the player should go for the full win.

## Bust It

"Bust It" is a side bet seen at the Taj Majal in Atlanic City in April, 2007. In July 2010 I saw it at the Wynn in Las Vegas. The side bet can not exceed the lesser of the blackjack bet and $25. It wins if the dealer busts on the third card. The side bet is available on ordinary blackjack and Double Attack Blackjack, which uses a Spanish deck. It does not matter whether dealer hits or stands on soft 17, because either way busting with three cards is impossible on a two-card soft 17. Card counters may be interested to know that the dealer is more likely to bust when the count is high. So at some positive count the odds would swing to the player's favor.

The following return table is for ordinary blackjack with eight decks. The lower right cell shows a house edge of 6.814%.

### Bust It — Eight Ordinary Decks

Event | Pays | Combinations | Probability | Return |
---|---|---|---|---|

Suited 888 | 200 | 672 | 0.000019 | 0.003761 |

Colored 888 | 50 | 2688 | 0.000075 | 0.003761 |

Bust on 6 | 15 | 175616 | 0.004914 | 0.073713 |

Bust on 7 | 9 | 374272 | 0.010473 | 0.094258 |

Bust on 8 | 7 | 582400 | 0.016297 | 0.11408 |

Bust on 9 | 5 | 814080 | 0.02278 | 0.113900 |

Bust on 10 | 3 | 4233216 | 0.118456 | 0.355369 |

Loss | -1 | 29553536 | 0.826985 | -0.826985 |

Total | 35736480 | 1.000000 | -0.068143 |

The next table shows the house edge for the pay table above and rules above for one to eight decks.

### Bust It — Ordinary Decks

Decks | House Edge |
---|---|

1 | 8.127% |

2 | 7.568% |

3 | 7.267% |

4 | 7.096% |

5 | 6.987% |

6 | 6.912% |

7 | 6.856% |

8 | 6.814% |

The following return table is for eight Spanish decks. The lower right cell shows a house edge of 8.006%.

### Bust It — Eight Spanish Decks

Event | Pays | Combinations | Probability | Return |
---|---|---|---|---|

Suited 888 | 200 | 672 | 0.000024 | 0.004784 |

Colored 888 | 50 | 2688 | 0.000096 | 0.004784 |

Bust on 6 | 15 | 143872 | 0.005122 | 0.076825 |

Bust on 7 | 10 | 308736 | 0.010991 | 0.109907 |

Bust on 8 | 8 | 484096 | 0.017233 | 0.137866 |

Bust on 9 | 6 | 683008 | 0.024314 | 0.145886 |

Bust on 10 | 3 | 2683392 | 0.095526 | 0.286577 |

Loss | -1 | 23784288 | 0.846695 | -0.846695 |

Total | 28090752 | 1.000000 | -0.080064 |

The next table shows the house edge for the pay table above and rules above for one to eight Spanish decks.

### Bust It — Spanish Decks

Decks | House Edge |
---|---|

1 | 9.844% |

2 | 9.035% |

3 | 8.621% |

4 | 8.388% |

5 | 8.24% |

6 | 8.138% |

7 | 8.063% |

8 | 8.006% |

## Straight 8's

"Straight 8's" is a blackjack side bet seen in Calgary in March 2007. Like the Lucky Lucky, it pays based on the player's first two cards and the dealer's up card.

The following return table is based on six decks. The lower right cell shows a house edge of 2.696%.

### Straight 8's - Six Decks

Event | Pays | Combinations | Probability | Return |
---|---|---|---|---|

Three suited 8's | 200 | 80 | 0.000016 | 0.003191 |

Three 8's | 50 | 1944 | 0.000388 | 0.019388 |

5,6,7 | 25 | 13824 | 0.002757 | 0.068936 |

Three of a kind | 5 | 24288 | 0.004845 | 0.024223 |

Pair of 8's | 3 | 79488 | 0.015855 | 0.047566 |

8, 18, or 28 | 2 | 472032 | 0.094156 | 0.188311 |

Pair | 2 | 841248 | 0.167803 | 0.335605 |

Loser | -1 | 3580416 | 0.714181 | -0.714181 |

Total | 5013320 | 1.000000 | -0.026959 |

The next table shows the house edge for the pay table above and rules above for one to eight decks.

### Straight 8's - House Edge

Decks | House Edge |
---|---|

1 | 15.529% |

2 | 7.934% |

3 | 5.331% |

4 | 4.018% |

5 | 3.226% |

6 | 2.696% |

7 | 2.317% |

8 | 2.032% |

## 2 Run 21

2 Run 21 is a blackjack side bet I noticed at the Silver Dollar casino in Seattle on June 5, 2007. It pays based on the player's first two cards, and the dealer's first two cards.

The following return table is based on six decks. The lower right cell shows a house edge of 10.236%.

### 2 Run 21 — Six Decks

Event | Pays | Combinations | Probability | Return |
---|---|---|---|---|

Two straight flushes | 40 | 3242668 | 0.001395 | 0.055820 |

Straight flush and straight | 10 | 19445136 | 0.008368 | 0.083683 |

Two straights | 8 | 29173140 | 0.012555 | 0.100438 |

One straight flush | 3 | 147641008 | 0.063538 | 0.190613 |

One straight | 1 | 442923024 | 0.190613 | 0.190613 |

Loser | -1 | 1681248844 | 0.723530 | -0.723530 |

Total | 2323673820 | 1.000000 | -0.102364 |

The next table shows the house edge for the pay table above and rules above for one to eight decks.

### 2 Run 21 — House Edge

Decks | House Edge |
---|---|

1 deck | 4.82% |

2 decks | 8.13% |

3 decks | 9.19% |

4 decks | 9.72% |

5 decks | 10.03% |

6 decks | 10.24% |

7 decks | 10.38% |

8 decks | 10.50% |

In May 2008 I had an unconfirmed report that the above table is no longer the one in use. The writer claims the side bet is now based on only the player's first two cards, and the dealer's up card.

## Winners Option

Winners Option is a side bet seen at the Las Vegas Hard Rock in August, 2007. In addition to playing blackjack normally, the player may bet on the dealer's hand. Unfortunately, you can't deliberately lose your own hand, in this case. If you bet on the dealer, as indicated on the table by a "D" arrow, then you must play according to the same rules as the dealer, never doubling or splitting, and hitting to hard 17 or soft 18. In the event both player and dealer bust, the bet will lose half.

I was not told how many decks were used, so I analyzed it by random simulation for all number of decks from one to eight. Here are the results. The right column shows the expected player loss. In a six-deck game, for example, the house edge would be 4.09%.

### Winners Option

Decks | Win | Push | Lose Half | Lose All | Return |
---|---|---|---|---|---|

1 | 0.411247 | 0.093653 | 0.082833 | 0.412267 | -0.042436 |

2 | 0.411339 | 0.095404 | 0.081857 | 0.411400 | -0.040989 |

3 | 0.411138 | 0.096031 | 0.081745 | 0.411086 | -0.040821 |

4 | 0.411057 | 0.096290 | 0.081677 | 0.410976 | -0.040757 |

5 | 0.4109 | 0.096461 | 0.081608 | 0.411031 | -0.040935 |

6 | 0.410856 | 0.096566 | 0.081632 | 0.410946 | -0.040905 |

7 | 0.410842 | 0.096684 | 0.081592 | 0.410882 | -0.040836 |

8 | 0.410875 | 0.096734 | 0.081575 | 0.410816 | -0.040729 |

## 21 to the River

21 to the River is a blackjack side bet I noticed at the Hard Rock in Las Vegas on March 27, 2008. The rules are as follows.

- Player makes a blackjack and poker bet.
- The blackjack bet shall be adjudicated according to conventional blackjack rules. In the case of the Hard Rock, these rules were six decks, dealer hits soft 17, double after split allowed, no surrender, and no re-splitting aces.
- In the event the blackjack hand busts, a five-card poker hand will be created using the card that busted the player, and the next four cards in the shoe.
- The poker hand shall pay according to the return table below.
- If the player does not bust, then the poker bet will push.
- If the player splits, the first hand, if any, that busts will start the poker hand. If none bust, the poker bet will push.

The first step to analyze this game is to determine the probability that the blackjack hand will bust, and if so, with what card. To answer this, I ran the following simulation. My simulation treats all 10-point cards the same way, so I divided that total between the four 10-point cards.

### Blackjack Events

Event | Probability |
---|---|

Player busts with 6 | 0.003197 |

Player busts with 7 | 0.006978 |

Player busts with 8 | 0.012119 |

Player busts with 9 | 0.017238 |

Player busts with 10 | 0.023341 |

Player busts with J | 0.023341 |

Player busts with Q | 0.023341 |

Player busts with K | 0.023341 |

No bust | 0.867104 |

Total | 1.000000 |

The total probability of busting comes to 13.29%. This is higher than other places on my site, which say it is 13.00%. This is because of the splitting rule.

The next table shows the probability of each poker hand, with six decks, according to the first card dealt in the hand.

The next table combines the probability of each bust card, by the poker probabilities starting with that card.

### 21 to the River — Return Table

Event | Pays | Probability | Return |
---|---|---|---|

Royal flush | 500 | 0 | 0.000158 |

Straight flush | 250 | 0.000001 | 0.000365 |

Five of a kind | 100 | 0.000003 | 0.000308 |

Four of a kind | 50 | 0.000222 | 0.011081 |

Full house | 25 | 0.000485 | 0.012136 |

Flush | 15 | 0.000467 | 0.007010 |

Straight | 10 | 0.000453 | 0.004533 |

Three of a kind | 5 | 0.005558 | 0.027792 |

Two pair | 2 | 0.008712 | 0.017425 |

Jacks or better | 0 | 0.023288 | 0.000000 |

No bust | 0 | 0.867104 | 0.000000 |

All other | -1 | 0.093704 | -0.093704 |

Total | 1.000000 | -0.012895 |

The lower right cell shows a house edge of 1.29%, per bet made. The probability of the bet resolving with a win or loss is 10.96%. The house edge, per bet resolved, is thus 1.29%/10.96% = 11.76%.

## Buster Blackjack

Buster Blackjack is a side bet I noticed at the Sycuan casino, near San Diego, on November 30, 2008. The bet wins if the dealer busts, the more cards it takes, the more the player wins. The following table shows the probabilities and return for a six-deck game, where the dealer hits a soft 17. The lower right cell shows a house edge of 6.21%.

### Buster Blackjack — Six Decks, Dealer Hits Soft 17

Event | Pays | Probability | Return |
---|---|---|---|

Bust with 8+ cards | 250 | 0.000012 | 0.002986 |

Bust with 7 cards | 50 | 0.000214 | 0.010722 |

Bust with 6 cards | 12 | 0.002638 | 0.031651 |

Bust with 5 cards | 4 | 0.020473 | 0.08189 |

Bust with 4 cards | 2 | 0.089392 | 0.178784 |

Bust with 3 cards | 2 | 0.173032 | 0.346064 |

Dealer doesn't bust | -1 | 0.714241 | -0.714241 |

Total | 1.000000 | -0.062143 |

The next table shows the return, according to the number of decks, and whether the dealer hits or stands on a soft 17.

### Buster Blackjack — Expected Return

Decks | Stand Soft 17 | Hit Soft 17 |
---|---|---|

1 | -0.087690 | -0.068890 |

2 | -0.084766 | -0.065097 |

4 | -0.083066 | -0.062915 |

5 | -0.082707 | -0.062455 |

6 | -0.082462 | -0.062143 |

8 | -0.082153 | -0.061749 |

As long as I went to the trouble to analyze this bet, the next table shows a finer breakdown of the possible dealer outcomes in a six-deck game, and the dealer hits a soft 17.

### Possible Dealer Outcomes — Six Decks, Dealer Hits Soft 17

Event | Probability |
---|---|

Total of 17 | 0.133459 |

Total of 18 | 0.141205 |

Total of 19 | 0.135682 |

Total of 20 | 0.181531 |

Total of 21 | 0.0748744 |

Blackjack | 0.0474895 |

Bust with 3 cards | 0.173032 |

Bust with 4 cards | 0.0893918 |

Bust with 5 cards | 0.0204726 |

Bust with 6 cards | 0.0026376 |

Bust with 7 cards | 0.000214444 |

Bust with 8 cards | 0.000011528 |

Bust with 9 cards | 0.00000040805 |

Bust with 10 cards | 0.00000000909509 |

Bust with 11 cards | 0.00000000011986 |

Bust with 12 cards | 0.000000000000824386 |

Bust with 13 cards | 0.00000000000000222834 |

## Super Split

Super Split is a blackjack side bet I noticed at the Viejas casino in California on December 1, 2008. It was closed at the time, so I don't know the number of decks used. The following return table is based on a six-deck game. The lower right cell shows a house edge of 23.40%.

### Super Split — Six Decks

Event | Pays | Combinations | Probability | Return |
---|---|---|---|---|

Two aces on original hand, with two face cards after splitting, all suited | 2500 | 9180 | 0.000004 | 0.009877 |

Two aces on original hand, with two face cards after splitting | 200 | 696276 | 0.0003 | 0.059929 |

Two aces on original hand, with one face card after splitting | 50 | 4769280 | 0.002052 | 0.102624 |

Two aces | 25 | 7744284 | 0.003333 | 0.083319 |

Two identical face cards | 15 | 8621100 | 0.00371 | 0.055652 |

Ace plus face card | 6 | 82762560 | 0.035617 | 0.213703 |

Two face cards | 3 | 113798520 | 0.048974 | 0.146921 |

All other | -1 | 2105272620 | 0.90601 | -0.90601 |

Total | 2323673820 | 0 | -0.233987 |

The next table shows the return, according to the number of decks.

### Super Split — Exected Return

Decks | Return |
---|---|

2 | -0.277397 |

4 | -0.244818 |

5 | -0.238317 |

6 | -0.233987 |

8 | -0.228577 |

## Lucky Pairs

Lucky Pairs is a side bet that wins if the player’s first two cards are a pair. Many baccarat tables also offer this bet. I understand it can be found in blackjack at some casinos in South Africa, where they pay 11 to 1. I do not know the number of decks used there.

The following table shows the house edge for 1 to 8 decks and various wins.

### Lucky Pairs

Decks | Pays | Probability | Return |
---|---|---|---|

1 | 15 | 0.058824 | -0.058824 |

1 | 14 | 0.058824 | -0.117647 |

1 | 13 | 0.058824 | -0.176471 |

1 | 12 | 0.058824 | -0.235294 |

1 | 11 | 0.058824 | -0.294118 |

2 | 13 | 0.067961 | -0.048544 |

2 | 12 | 0.067961 | -0.116505 |

2 | 11 | 0.067961 | -0.184466 |

3 | 12 | 0.070968 | -0.077419 |

3 | 11 | 0.070968 | -0.148387 |

4 | 12 | 0.072464 | -0.057971 |

4 | 11 | 0.072464 | -0.130435 |

5 | 12 | 0.073359 | -0.046332 |

5 | 11 | 0.073359 | -0.119691 |

6 | 12 | 0.073955 | -0.038585 |

6 | 11 | 0.073955 | -0.11254 |

7 | 12 | 0.07438 | -0.033058 |

7 | 11 | 0.07438 | -0.107438 |

8 | 12 | 0.074699 | -0.028916 |

8 | 11 | 0.074699 | -0.103614 |

If d is the number of decks, the probability of a pair is (4*d-1)/(52*d-1).

## Kings Bounty

I have an unconfirmed report that The Red Dragon Casino in Lynnwood, Washington offers the Kings Bounty side bet. I do not know the number of decks used. The following return table is based on six decks. The lower right cell shows a house edge of 23.16%.

### Kings Bounty — Six Decks

Event | Pays | Combinations | Probability | Return |
---|---|---|---|---|

2 King of Spades + Dealer BJ | 1000 | 33840 | 0.000015 | 0.014563 |

2 King of Spades | 100 | 684585 | 0.000295 | 0.029461 |

2 Suited Kings | 30 | 2155275 | 0.000928 | 0.027826 |

2 Suited 10, Jack, or Queens | 20 | 8621100 | 0.00371 | 0.074202 |

Suited 20 | 9 | 48278160 | 0.020777 | 0.18699 |

2 Kings | 6 | 10345320 | 0.004452 | 0.026713 |

Unsuited 20 | 4 | 175870440 | 0.075686 | 0.302745 |

Loser | -1 | 2077685100 | 0.894138 | -0.894138 |

Total | 2323673820 | 1 | -0.231637 |

The next table shows the house edge for various numbers of decks, assuming no change in the pay table.

### Kings Bounty — House Edge

Decks | Return |
---|---|

8 | -0.224693 |

6 | -0.231637 |

5 | -0.2372 |

4 | -0.245555 |

2 | -0.28754 |

## Perfect Charlie

"Perfect Charlie" is a side bet seen at the Fort McDowell casino in Arizona. Here are the rules:

- Six decks.
- Pays based on the player's first 3 to 5 cards on his initial hand.
- All winning pays must start with the first card.
- The player is only eligible for the highest qualifying win.
- Busting does not void any win.
- All pays are on a "for one" basis, meaning the player does not keep his original bet, even if he wins.
- The bet is only available for 25 or 50 cents.

### Perfect Charlie — Six Decks

Event | Pays | Permutations | Probability | Return |
---|---|---|---|---|

2,3,4,5,7 suited in order | 300000 | 31104 | 0.0000000109 | 0.0032595048 |

2,3,4,5 suited in order | 80000 | 1565568 | 0.0000005469 | 0.0437497978 |

2,3,4,5,7 suited any order | 40000 | 3701376 | 0.0000012929 | 0.0517174762 |

2,3,4,5,7 unsuited in order | 20000 | 7838208 | 0.000002738 | 0.0547596807 |

2,3,4,5 suited any order | 4000 | 36008064 | 0.0000125781 | 0.0503122675 |

2,3,4 suited in order | 2000 | 80227584 | 0.0000280245 | 0.0560489959 |

2,3,4,5 unsuited in order | 1000 | 88335360 | 0.0000308566 | 0.0308566455 |

2,3,4 suited any order | 300 | 403004160 | 0.0001407744 | 0.0422323172 |

2,3,4,5,7 unsuited any order | 200 | 937039104 | 0.0003273195 | 0.0654638944 |

2,3,4 unsuited in order | 150 | 1130163840 | 0.0003947804 | 0.0592170535 |

2,3,4,5 unsuited any order | 100 | 2111215104 | 0.0007374738 | 0.0737473826 |

2,3,4 unsuited any order | 40 | 5650819200 | 0.0019739018 | 0.0789560713 |

Loser | 0 | 2852316197568 | 0.9963497023 | 0 |

Total | 2862766146240 | 1 | 0.6103210873 |

The lower right cell shows a return of 61.03%, for a house edge of 38.97% (ouch!).

## In Between

"In Between" is a side bet asked about at my companion site Wizard of Vegas. A reader wrote me that it was seen at the Sandia Resort & Casino in Albuquerque, New Mexico in April 2011.

The side bet plays like Red Dog. Here are the specific rules.

- Unknown number of decks. My analysis below is based on six decks.
- Player may make a side wager that the dealer's up card will fall between the ranks of the player's first two cards.
- For purposes of the side bet, aces are high only.
- If player's first two cards and dealer's up card form a three of a kind, then player wins 30 to 1.
- If the player wins with a spread of 1 (one rank between player's two ranks), then player will win 12 to 1.
- If the player wins with a spread of 2, then player will win 6 to 1.
- If the player wins with a spread of 3, then player will win 4 to 1.
- If the player wins with a spread of 4 or more, then player will win 1 to 1.
- Otherwise, the player will lose.

The following table shows a house edge of 3.40% with six decks.

### In Between — Six Decks

Event | Pays | Permutations | Probability | Return |
---|---|---|---|---|

Trips | 30 | 157872 | 0.005248 | 0.157453 |

Spread 1 | 12 | 304128 | 0.010111 | 0.121328 |

Spread 2 | 6 | 552960 | 0.018383 | 0.110298 |

Spread 3 | 4 | 746496 | 0.024817 | 0.099268 |

Spread 4+ | 1 | 6303744 | 0.209567 | 0.209567 |

Loss | -1 | 22014720 | 0.731874 | -0.731874 |

Total | 30079920 | 1 | -0.033961 |

The next table shows the house edge according to the number of decks.

### In Between — House Edge

Decks | House Edge |
---|---|

1 | 8.34% |

2 | 5.70% |

4 | 4.01% |

5 | 3.64% |

6 | 3.40% |

8 | 3.08% |

Another analysis of this bet, based on eight decks, can be found at miplet's blackjack side bet docs.

## 3 Card Hard Hand

The 3 Card Hard Hand is a side bet I noticed at the Boulder Station in Las Vegas on September 16, 2010. Much like the Lucky Lucky, it pays based on the player's first two cards and the dealer's up card. Aces may count as 1 or 11 points. The following table shows the pay table, probability of each win, and contribution to the total return, based on a six-deck game. The lower right cell shows a house edge of 4.27%.

### 3 Card Hard Hand — Six Decks

Event | Pays | Permutations | Probability | Return |
---|---|---|---|---|

Suited 21 | 25 | 27,512 | 0.005488 | 0.137200 |

Unsuited 21 | 2 | 421,200 | 0.084016 | 0.168032 |

17-20 | 1 | 1,410,056 | 0.281262 | 0.281262 |

Loser | -1 | 3,154,552 | 0.629234 | -0.629234 |

Total | 5,013,320 | 1.000000 | -0.042740 |

The next table shows the house edge according to the number of decks.

### 3 Card Hard Hand — House Edge

Decks | House Edge |
---|---|

1 | 3.87% |

2 | 4.13% |

3 | 4.21% |

4 | 4.24% |

5 | 4.26% |

6 | 4.27% |

7 | 4.28% |

8 | 4.29% |

## Block

The Block bet is based on the player's first two cards and the dealer's up card. As of this writing (Nov. 2010) it can be found in South Africa, Egypt, Latvia, Estonia, Ireland, and Morocco. The bet wins if the dealer's up card matches the suit of one of the player's cards, and the player's card is higher. There are higher pays if the player's cards are a pair, suited, or both. Here is how the various winning hands are defined.

- Ultimate Block®: A Block consisting of two cards both of the same rank, both higher than and both of same suit as the dealer's card.
- Pair Block®: A Block consisting of two cards of the same rank, both higher than, and one of them the same suit as, the dealer's card.
- Flush Block®: A Block consisting of two cards of the same suit and one/both cards are higher and in the same suit as the dealer's card.
- Normal Block®: A Block consisting of one card higher and in the same suit as the dealer's card.
- Push: If one of the Player's cards matches the Dealer's card in both rank and suit, then is a push.

Here are return tables for 2, 6, and 8 decks. The pay tables were provided to me by the game maker.

### Block — Two Decks

Event | Pays | Permutations | Probability | Return |
---|---|---|---|---|

Ultimate Block® | 60 | 1,248 | 0.001142 | 0.068532 |

Pair Block® | 10 | 14,976 | 0.013706 | 0.137065 |

Flush Block® | 5 | 39,104 | 0.035789 | 0.178945 |

Normal Block® | 2 | 179,712 | 0.164477 | 0.328955 |

Push | 0 | 18,720 | 0.017133 | 0.000000 |

Loser | -1 | 838,864 | 0.767752 | -0.767752 |

Total | 1,092,624 | 1.000000 | -0.054255 |

### Block — Six Decks

Event | Pays | Permutations | Probability | Return |
---|---|---|---|---|

Ultimate Block® | 35 | 56,160 | 0.001867 | 0.065346 |

Pair Block® | 10 | 404,352 | 0.013443 | 0.134426 |

Flush Block® | 5 | 1,100,736 | 0.036594 | 0.182969 |

Normal Block® | 2 | 4,852,224 | 0.161311 | 0.322622 |

Push | 0 | 848,640 | 0.028213 | 0.000000 |

Loser | -1 | 22,817,808 | 0.758573 | -0.758573 |

Total | 30,079,920 | 1.000000 | -0.053210 |

### Block — Eight Decks

Event | Pays | Permutations | Probability | Return |
---|---|---|---|---|

Ultimate Block® | 35 | 139,776 | 0.001956 | 0.068448 |

Pair Block® | 10 | 958,464 | 0.013410 | 0.134102 |

Flush Block® | 5 | 2,622,464 | 0.036692 | 0.183458 |

Normal Block® | 2 | 11,501,568 | 0.160922 | 0.321844 |

Push | 0 | 2,114,112 | 0.029579 | 0.000000 |

Loser | -1 | 54,136,576 | 0.757441 | -0.757441 |

Total | 71,472,960 | 1.000000 | -0.049590 |

The next table shows the pay tables available for 1 to 8 decks and the house edge.

### Block — Eight Decks

Decks | Normal Block | Flush Block | Pair Block | Ultimate Block | House Edge |
---|---|---|---|---|---|

1 | 2 to 1 | 5 to 1 | 15 to 1 | N/A | 5.88% |

2 | 2 to 1 | 5 to 1 | 10 to 1 | 60 to 1 | 5.43% |

3 | 2 to 1 | 5 to 1 | 10 to 1 | 50 to 1 | 4.52% |

4 | 2 to 1 | 5 to 1 | 10 to 1 | 40 to 1 | 5.21% |

5 | 2 to 1 | 5 to 1 | 10 to 1 | 35 to 1 | 5.61% |

6 | 2 to 1 | 5 to 1 | 10 to 1 | 35 to 1 | 5.32% |

7 | 2 to 1 | 5 to 1 | 10 to 1 | 35 to 1 | 5.11% |

8 | 2 to 1 | 5 to 1 | 10 to 1 | 35 to 1 | 4.96% |

More information is available about this bet at the casinoholdempoker.com.

## Hit and Run

The Hit and Run is a progressive side bet I first noticed at the Suncoast in Las Vegas on November 3, 2011. It is a $1 bet that pays if the dealer gets a blackjack or at least five cards. For purposes of the total dealer cards, all cards count, including a bust card, if there was one.

To analyze this bet I first looked at the probability of each possible event, by the number of decks. The following two tables show those probabilities, according to whether the dealer hits or stands on a soft 17.

### Hit and Run Probabilities — Dealer Hits on Soft 17

Event | 1 deck | 2 decks | 4 decks | 5 decks | 6 decks | 8 decks |
---|---|---|---|---|---|---|

8+ cards | 0.00000553 | 0.00001250 | 0.00001759 | 0.00001875 | 0.00001956 | 0.00002060 |

7 cards | 0.00019242 | 0.00028462 | 0.00033818 | 0.00034948 | 0.00035712 | 0.00036680 |

6 cards | 0.00345798 | 0.00408065 | 0.00439796 | 0.00446180 | 0.00450443 | 0.00455777 |

5 cards | 0.03434820 | 0.03581484 | 0.03652738 | 0.03666828 | 0.03676193 | 0.03687865 |

BJ | 0.04826546 | 0.04779686 | 0.04756596 | 0.04752005 | 0.04748949 | 0.04745134 |

Loss | 0.91373042 | 0.91201053 | 0.91115293 | 0.91098163 | 0.91086748 | 0.91072483 |

### Hit and Run Probabilities — Dealer Stands on Soft 17

Event | 1 deck | 2 decks | 4 decks | 5 decks | 6 decks | 8 decks |
---|---|---|---|---|---|---|

8+ cards | 0.00000399 | 0.00000882 | 0.00001238 | 0.00001320 | 0.00001377 | 0.00001451 |

7 cards | 0.00015154 | 0.00022623 | 0.00027019 | 0.00027951 | 0.00028582 | 0.00029381 |

6 cards | 0.00298450 | 0.00354247 | 0.00382789 | 0.00388539 | 0.00392379 | 0.00397187 |

5 cards | 0.03168991 | 0.03307633 | 0.03375033 | 0.03388366 | 0.03397228 | 0.03408275 |

BJ | 0.04826546 | 0.04779686 | 0.04756596 | 0.04752005 | 0.04748949 | 0.04745134 |

Loss | 0.91690461 | 0.91534928 | 0.91457324 | 0.91441819 | 0.91431485 | 0.91418571 |

The next two tables show the returns for all non-progressive wins. All wins are on a "for one" basis, meaning the player does not keep his original bet if he wins. The table below shows, for example, that in a two-deck game, where the dealer hits a soft 17, the non-progressive wins return 57.24%.

### Hit and Run Returns — Dealer Hits on Soft 17

Event | Pays | 1 deck | 2 decks | 4 decks | 5 decks | 6 decks | 8 decks |
---|---|---|---|---|---|---|---|

7 cards | 100 | 0.01924185 | 0.02846213 | 0.03381830 | 0.03494830 | 0.03571243 | 0.03667967 |

6 cards | 25 | 0.08644947 | 0.10201621 | 0.10994908 | 0.11154508 | 0.11261064 | 0.11394429 |

5 cards | 7 | 0.24043741 | 0.25070388 | 0.25569165 | 0.25667798 | 0.25733348 | 0.25815057 |

BJ | 4 | 0.19306184 | 0.19118745 | 0.19026384 | 0.19008019 | 0.18995795 | 0.18980538 |

Loss | 0 | 0.00000000 | 0.00000000 | 0.00000000 | 0.00000000 | 0.00000000 | 0.00000000 |

Total | 0.53919057 | 0.57236967 | 0.58972287 | 0.59325155 | 0.59561450 | 0.59857990 |

### Hit and Run Returns — Dealer Stands on Soft 17

Event | Pays | 1 deck | 2 decks | 4 decks | 5 decks | 6 decks | 8 decks |
---|---|---|---|---|---|---|---|

7 cards | 100 | 0.01515360 | 0.02262332 | 0.02701911 | 0.02795094 | 0.02858187 | 0.02938144 |

6 cards | 25 | 0.07461250 | 0.08856179 | 0.09569721 | 0.09713469 | 0.09809477 | 0.09929678 |

5 cards | 7 | 0.22182935 | 0.23153433 | 0.23625234 | 0.23718563 | 0.23780594 | 0.23857923 |

BJ | 4 | 0.19306184 | 0.19118745 | 0.19026384 | 0.19008019 | 0.18995795 | 0.18980538 |

Loss | 0 | 0.00000000 | 0.00000000 | 0.00000000 | 0.00000000 | 0.00000000 | 0.00000000 |

Total | 0.50465729 | 0.53390689 | 0.54923250 | 0.55235145 | 0.55444054 | 0.55706282 |

The next two tables show how much the return increases per $10,000 in the meter, as well as the "breakeven-point," which is how high the meter would need to reach to have a 100% return, for a statistically fair bet.

### Hit and Run Value per $10,000 in Meter and Breakeven Point — Dealer Hit on Soft 17

Metric | 1 deck | 2 decks | 4 decks | 5 decks | 6 decks | 8 decks |
---|---|---|---|---|---|---|

Return per $10000 in meter | 0.05526440 | 0.12496464 | 0.17587273 | 0.18753475 | 0.19559878 | 0.206010727 |

Breakeven | $83,382.68 | $34,220.11 | $23,328.07 | $21,689.23 | $20,674.23 | $19,485.40 |

### Hit and Run Value per $10,000 in Meter and Breakeven Point — Dealer Stands on Soft 17

Metric | 1 deck | 2 decks | 4 decks | 5 decks | 6 decks | 8 decks |
---|---|---|---|---|---|---|

Return per $10000 in meter | 0.03989356 | 0.08816667 | 0.12381517 | 0.13203645 | 0.13773304 | 0.145102266 |

Breakeven | $124,166.07 | $52,865.00 | $36,406.48 | $33,903.41 | $32,349.50 | $30,525.86 |

When I saw this bet at the Suncoast it was on a two-deck game, where the dealer hits a soft 17. The meter on November 3, 2011 was at $8,888.44. Thus, the return at the time was 0.53919057 + (8888.44/10000)×0.124964643 = 68.34%.

## Bet the Bust

Bet the Bust is a side bet I noticed at the Palace Station on December 29, 2011. The bet is offered after the initial two cards are dealt to each player and the dealer, with one dealer up card exposed, as usual. If the dealer's exposed card is a 10 or ace the dealer checks for blackjack before offering the Bet the Bust wager.

The Bet the Bust pays if the dealer busts. The probability of the dealer busting depends on his up card, thus so do the odds.

At the Palace Station the table with this side bet used six decks and the dealer hit a soft 17. The following table shows what the Bet the Bust paid, the probability of winning, and the expected return, according to the dealer's up card. The right column shows the lowest house edge is on the 8 at 2.52%.

### Bet the Bust — Six Decks — Dealer Hits Soft 17

Up Card | Pays | Probability | Expected Return |
---|---|---|---|

A | 3.5 | 0.201281 | -0.094236 |

2 | 1.5 | 0.356661 | -0.108348 |

3 | 1.5 | 0.376958 | -0.057605 |

4 | 1 | 0.398470 | -0.203060 |

5 | 1 | 0.419632 | -0.160736 |

6 | 1 | 0.439259 | -0.121482 |

7 | 2.5 | 0.261936 | -0.083224 |

8 | 3 | 0.243693 | -0.025228 |

9 | 3 | 0.229242 | -0.083032 |

10 | 3 | 0.230239 | -0.079044 |

The next table shows the probability of the dealer busting according to the number of decks, assuming the dealer **hits** on a soft 17.

### Dealer Bust Probability — Dealer Hits on Soft 17

Up Card | 1 Deck | 2 Decks | 3 Decks | 4 Decks | 5 Decks | 6 Decks | 7 Decks | 8 Decks |
---|---|---|---|---|---|---|---|---|

A | 0.204574 | 0.202556 | 0.201912 | 0.201595 | 0.201406 | 0.201281 | 0.201192 | 0.201125 |

2 | 0.356345 | 0.356527 | 0.356593 | 0.356627 | 0.356647 | 0.356661 | 0.356670 | 0.356677 |

3 | 0.378075 | 0.377460 | 0.377218 | 0.377090 | 0.377011 | 0.376958 | 0.376920 | 0.376891 |

4 | 0.405796 | 0.401328 | 0.399887 | 0.399176 | 0.398751 | 0.398470 | 0.398269 | 0.398119 |

5 | 0.429961 | 0.423668 | 0.421634 | 0.420629 | 0.420030 | 0.419632 | 0.419348 | 0.419136 |

6 | 0.437756 | 0.438754 | 0.439022 | 0.439144 | 0.439214 | 0.439259 | 0.439291 | 0.439314 |

7 | 0.259854 | 0.261143 | 0.261546 | 0.261742 | 0.261859 | 0.261936 | 0.261990 | 0.262031 |

8 | 0.238627 | 0.241630 | 0.242656 | 0.243173 | 0.243485 | 0.243693 | 0.243842 | 0.243954 |

9 | 0.233442 | 0.230898 | 0.230066 | 0.229653 | 0.229406 | 0.229242 | 0.229125 | 0.229037 |

10 | 0.232499 | 0.231144 | 0.230692 | 0.230465 | 0.230329 | 0.230239 | 0.230174 | 0.230125 |

The next table shows the expected return according to the number of decks, assuming the dealer **hits** on a soft 17, and the same pay table as at the Palace Station, indicated above.

### Expected Return — Dealer Hits on Soft 17

Up Card | 1 Deck | 2 Decks | 3 Decks | 4 Decks | 5 Decks | 6 Decks | 7 Decks | 8 Decks |
---|---|---|---|---|---|---|---|---|

A | -0.079417 | -0.088498 | -0.091396 | -0.092823 | -0.093673 | -0.094236 | -0.094636 | -0.094938 |

2 | -0.109138 | -0.108683 | -0.108518 | -0.108433 | -0.108383 | -0.108348 | -0.108325 | -0.108308 |

3 | -0.054813 | -0.056350 | -0.056955 | -0.057275 | -0.057473 | -0.057605 | -0.057700 | -0.057773 |

4 | -0.188408 | -0.197344 | -0.200226 | -0.201648 | -0.202498 | -0.203060 | -0.203462 | -0.203762 |

5 | -0.140078 | -0.152664 | -0.156732 | -0.158742 | -0.159940 | -0.160736 | -0.161304 | -0.161728 |

6 | -0.124488 | -0.122492 | -0.121956 | -0.121712 | -0.121572 | -0.121482 | -0.121418 | -0.121372 |

7 | -0.090511 | -0.086000 | -0.084589 | -0.083903 | -0.083494 | -0.083224 | -0.083035 | -0.082891 |

8 | -0.045492 | -0.033480 | -0.029376 | -0.027308 | -0.026060 | -0.025228 | -0.024632 | -0.024184 |

9 | -0.066232 | -0.076408 | -0.079736 | -0.081388 | -0.082376 | -0.083032 | -0.083500 | -0.083852 |

10 | -0.070004 | -0.075424 | -0.077232 | -0.078140 | -0.078684 | -0.079044 | -0.079304 | -0.079500 |

It is not difficult to see that this side bet would be very countable. However, for now, you're on your own with that.

## Bust Me

I have an unconfirmed report that this side bet was seen at Freddie's Club in Fife, Washington in February, 2012. It is a side bet that the player will bust on the next card. The bet may be made on player totals of 12 to 16. The odds a winning bet pays depends on the player's total as shown in the table below.

The following table shows the pertinent information for Bust Me, based on a two deck game. This table assumes the player makes this bet only on his original two cards.

### Bust Me — Two Decks

Player Total | Pays | Probability | Expected Return |
---|---|---|---|

12 | 2 | 0.308453 | -0.074642 |

13 | 1.5 | 0.385154 | -0.037115 |

14 | 1 | 0.461451 | -0.077099 |

15 | 0.5 | 0.537582 | -0.193627 |

16 | 0.5 | 0.607843 | -0.088235 |

The next table shows the house edge according to the player's total and number of decks.

### Bust Me — House Edge for One to Eight Decks

Player Total | 1 Deck | 2 Decks | 4 Decks | 5 Decks | 6 Decks | 8 Decks |
---|---|---|---|---|---|---|

12 | 7.25% | 7.46% | 7.58% | 7.60% | 7.61% | 7.63% |

13 | 3.57% | 3.71% | 3.78% | 3.79% | 3.80% | 3.81% |

14 | 7.76% | 7.71% | 7.70% | 7.70% | 7.69% | 7.69% |

15 | 19.50% | 19.36% | 19.30% | 19.28% | 19.27% | 19.26% |

16 | 10.00% | 8.82% | 8.25% | 8.14% | 8.06% | 7.97% |

It is not difficult to see that this side bet would be vulnerable to card counters. I'll leave that as an exercise for the readers (I hate it when people say that!).

## Cowboys & Cowgirls

I noticed this side bet at Arizona Charlie's on Decatur on February 23, 2012. It is a pair of bets, mostly paying based on the color of the dealer's up card. However, there are exceptions for kings, queens, and threes. The following two return tables show the odds of all possible outcomes. The number of decks does not matter.

### Cowboys

Event | Pays | Cards | Probability | Expected Return |
---|---|---|---|---|

Red Queen or King | 1.5 | 4 | 0.076923 | 0.115385 |

Any other red, except 3 | 1 | 20 | 0.384615 | 0.384615 |

Black or 3 | -1 | 28 | 0.538462 | -0.538462 |

Total | 52 | 1.000000 | -0.038462 |

### Cowgirls

Event | Pays | Cards | Probability | Expected Return |
---|---|---|---|---|

Black King or Queen | 1.5 | 4 | 0.076923 | 0.115385 |

Any other black, except 3 | 1 | 20 | 0.384615 | 0.384615 |

Red or 3 | -1 | 28 | 0.538462 | -0.538462 |

Total | 52 | 1.000000 | -0.038462 |

## Red Flex

The Red Flex is a blackjack side bet reported to be seen at the Lake Elsinore Hotel and Casino in California. It is based on the number of consecutive red cards in the dealer's hand, starting with the first one, and including the bust card, if there was one. If every player busts, then the dealer will continue drawing cards as necessary to adjudicate the side bet.

I'm told they use five decks and the dealer hits a soft 17 where this side bet appears. The following table shows the return under these rules. The lower right cell reflects a house edge of 5.47%.

### Red Flex — Five Decks — Dealer Hits Soft 17

Reds | Pays | Probability | Return |
---|---|---|---|

7 or more | 200 | 0.00000230011 | 0.00046002216 |

6 | 100 | 0.00006438572 | 0.00643857156 |

5 | 50 | 0.00115421980 | 0.05771099013 |

4 | 10 | 0.01220995252 | 0.12209952522 |

3 | 5 | 0.06849517726 | 0.34247588632 |

2 | 1 | 0.16710871362 | 0.16710871362 |

1 or less | -1 | 0.75096525097 | -0.75096525097 |

Total | 1.00000000000 | -0.05467154196 |

If you find this side bet, with the same pay table, with any other number of decks, or where the dealer stands on soft 17, you can use the following table to get the expected return.

### Red Flex — Expected Return

Decks | Stand Soft 17 | Hit Soft 17 |
---|---|---|

1 | -0.114336 | -0.102910 |

2 | -0.085823 | -0.073163 |

3 | -0.076052 | -0.062951 |

4 | -0.071114 | -0.057788 |

5 | -0.068136 | -0.054672 |

6 | -0.066143 | -0.052586 |

7 | -0.064716 | -0.051093 |

8 | -0.063644 | -0.049971 |

## Dealer Bust 21

Dealer Bust 21 is a side bet I noticed at the Tropicana on September 13, 2012. I am also told it can be found at the Fiesta Henderson. The wins pay according to the dealer's up card, as follows.

### Dealer Bust 21 Pay Table

Up Card | Tropicana | Fiesta Henderson |
---|---|---|

Ace | 2 | 10 |

10 to King | 2 | 4 |

7 to 9 | 2 | 2 |

2 to 6 | 2 | 1 |

To begin my analysis, the following two tables show the probability of the dealer busting according to the number of decks, up card, and whether the dealer hits or stands on soft 17.

### Dealer Bust Probability — Dealer Stands on Soft 17

Up Card | 1 Deck | 2 Decks | 4 Decks | 5 Decks | 6 Decks | 8 Decks |
---|---|---|---|---|---|---|

Ace | 0.116540 | 0.115872 | 0.115569 | 0.115511 | 0.115473 | 0.115426 |

2 | 0.352973 | 0.353291 | 0.353451 | 0.353483 | 0.353504 | 0.353530 |

3 | 0.375588 | 0.374794 | 0.374349 | 0.374256 | 0.374194 | 0.374115 |

4 | 0.402803 | 0.398540 | 0.396481 | 0.396075 | 0.395805 | 0.395469 |

5 | 0.428905 | 0.422505 | 0.419419 | 0.418810 | 0.418406 | 0.417902 |

6 | 0.420823 | 0.422132 | 0.422676 | 0.422776 | 0.422842 | 0.422922 |

7 | 0.259854 | 0.261143 | 0.261742 | 0.261859 | 0.261936 | 0.262031 |

8 | 0.238627 | 0.241630 | 0.243173 | 0.243485 | 0.243693 | 0.243954 |

9 | 0.233442 | 0.230898 | 0.229653 | 0.229406 | 0.229242 | 0.229037 |

10 | 0.214264 | 0.213191 | 0.212651 | 0.212543 | 0.212471 | 0.212381 |

Average | 0.283585 | 0.282582 | 0.282086 | 0.281987 | 0.281921 | 0.281839 |

### Dealer Bust Probability — Dealer Hits on Soft 17

Up Card | 1 Deck | 2 Decks | 4 Decks | 5 Decks | 6 Decks | 8 Decks |
---|---|---|---|---|---|---|

Ace | 0.140394 | 0.139626 | 0.139266 | 0.139196 | 0.139149 | 0.139091 |

2 | 0.356345 | 0.356527 | 0.356627 | 0.356647 | 0.356661 | 0.356677 |

3 | 0.378075 | 0.377460 | 0.377090 | 0.377011 | 0.376958 | 0.376891 |

4 | 0.405796 | 0.401328 | 0.399176 | 0.398751 | 0.398470 | 0.398119 |

5 | 0.429961 | 0.423668 | 0.420629 | 0.420030 | 0.419632 | 0.419136 |

6 | 0.437756 | 0.438754 | 0.439144 | 0.439214 | 0.439259 | 0.439314 |

7 | 0.259854 | 0.261143 | 0.261742 | 0.261859 | 0.261936 | 0.262031 |

8 | 0.238627 | 0.241630 | 0.243173 | 0.243485 | 0.243693 | 0.243954 |

9 | 0.233442 | 0.230898 | 0.229653 | 0.229406 | 0.229242 | 0.229037 |

10 | 0.214264 | 0.213191 | 0.212651 | 0.212543 | 0.212471 | 0.212381 |

Average | 0.287485 | 0.286446 | 0.285931 | 0.285829 | 0.285760 | 0.285675 |

The next table shows the house edge according to the number of decks and whether the dealer hits or stands on soft 17 under the Tropicana rules where all wins pay 2 to 1.

### Dealer Bust 21 House Edge — Tropicana Rules

Decks | Dealer Stands Soft 17 |
Dealer Hits Soft 17 |
---|---|---|

1 | 14.92% | 13.75% |

2 | 15.23% | 14.07% |

4 | 15.37% | 14.22% |

5 | 15.40% | 14.25% |

6 | 15.42% | 14.27% |

8 | 15.45% | 14.30% |

The next table shows the house edge according to the number of decks and whether the dealer hits or stands on soft 17 under the Fiesta Henderson rules.

### Dealer Bust 21 House Edge — Fiesta Henderson Rules

Decks | Dealer Stands Soft 17 |
Dealer Hits Soft 17 |
---|---|---|

1 | 9.81% | 7.38% |

2 | 10.14% | 7.72% |

4 | 10.30% | 7.89% |

5 | 10.33% | 7.93% |

6 | 10.36% | 7.95% |

8 | 10.38% | 7.98% |

## House Money 21

House Money 21 is a side bet by game inventor Roger Snow of Shufflemaster. As of this writing (September 2012), it is reported to be at the Pala Casino near San Diego, the Siena in Reno, and the Drift On Inn in Washington.

The thrust of this one is that the side bet wins if the player's first two cards form a pair, straight, or straight flush. The twist is that the player may choose to take down his original bet and winnings, or add them to his blackjack wager. Normally capping a bet is a serious offense in Vegas, but this game offers a chance to do it safely. Here are the complete rules.

- The game is based on conventional blackjack rules.
- The House Money side bet pays according to the following pay table.
### House Money 21 Pay Table

Player Hand Pays Ace-king suited 9 to 1 All other straight flush 4 to 1 Pair 3 to 1 Straight 1 to 1 - If the player wins the House Money bet he may choose to (1) take down his original wager and winnings, or (2) add both to his blackjack wager.
- The blackjack hand will be played out according to standard blackjack rules.

For my analysis I'm going to assume the following blackjack rules:

- Six decks
- Dealer hits soft 17
- Blackjack pays 3 to 2
- Double after split allowed
- Player may re-split any pair (including aces) up to four times.

**Strategy**

The following table shows when the player should parlay his win on the blackjack wager.

From there, the strategy is the same as the same basic strategy that applies to blackjack. Keep in mind when making the wager, that this will sometimes call for putting out more of your own money when splitting. If you're not comfortable doing that, don't make the House Money bet in the first place.

**House Edge**

My analysis shows the player will have a paying two-card hand 22.83% of the time. From there, the player will parlay the win on his blackjack wager 46.92% of the time. Overall, the house edge on the House Money 21 bet is 2.79%. This is defined as ratio of the expected loss from the House Money bet to the initial House Money bet itself.

**Outside Links**

Discount Gambling also has an analysis of House Money, including a look at the vulnerability to card counters. Stephen puts the house edge at little lower than I do at 2.6%, based on the same rules.

## Wild Aces

Wild Aces is a side bet I heard started at the Golden Nugget in October, 2012. Here are the rules.

- The game is based on conventional blackjack rules.
- If the player's first card is an ace then he may make the Wild Aces side bet, for up to his blackjack wager or $100, whichever is less.
- If the player's second card is any 10-point card then the Wild Aces bet will pay 2 to 1. Otherwise it loses.

In other words, it is mathematically the same as Insurance. Here is the probability of winning and expected return according to the number of decks.

### Wild Aces

Decks | Probability | Return |
---|---|---|

1 | 0.313725 | -0.058824 |

2 | 0.310680 | -0.067961 |

3 | 0.309677 | -0.070968 |

4 | 0.309179 | -0.072464 |

5 | 0.308880 | -0.073359 |

6 | 0.308682 | -0.073955 |

8 | 0.308434 | -0.074699 |

I'm sure some will be wondering what games they have this on. I hear it is mostly on 6-5 games in the Party Pit and pool, plus one 3-2 game on the main casino floor. None use a continuous shuffler.

## Royal 20's

### Royal 20's — Six Decks

Event | Pays | Combinations | Probability | Return |
---|---|---|---|---|

Suited pair of J-K | 25 | 180 | 0.003710 | 0.092753 |

Suited 20 | 10 | 1,068 | 0.022013 | 0.220134 |

Unsuited 20 | 5 | 3,888 | 0.080139 | 0.400693 |

Loser | -1 | 43,380 | 0.894138 | -0.894138 |

Total | 48,516 | 1.000000 | -0.180559 |

The next table shows just the house edge by number of decks.

### Royal 20's House Edge

Decks | House Edge |
---|---|

8 | 17.57% |

6 | 18.06% |

5 | 18.44% |

4 | 19.03% |

2 | 21.96% |

Here is an article about the side bet, in which I am mentioned as the mathematician: NEVADAN AT WORK: BOBBY FLORENCE, Blackjack dealer — With blackjack patent, ex-UNLV hoops star goes from nets to bets

## Suit 'em Up

I noticed Suit 'em Up at the Red Rock casino in Las Vegas on April 19, 2013. It was on a double-deck table. As long as the player's first two cards are suited he wins, with wins ranging from 2-1 to 60-1.

The following return table is for two decks and shows a house edge of 9.41%.

### Suit 'em Up — Two Decks

Event | Pays | Combinations | Probability | Return |
---|---|---|---|---|

Suited aces | 60 | 4 | 0.000747 | 0.044810 |

Suited blackjack | 10 | 64 | 0.011949 | 0.119492 |

Suited pair | 5 | 48 | 0.008962 | 0.044810 |

Suited 11 | 3 | 64 | 0.011949 | 0.035848 |

Any other suited | 2 | 1120 | 0.209111 | 0.418223 |

Loser | -1 | 4056 | 0.757282 | -0.757282 |

Total | 5356 | 1.000000 | -0.094100 |

The next table is for a hypothetical six deck-game and shows a house edge of 3.41%.

### Suit 'em Up — Six Decks

Event | Pays | Combinations | Probability | Return |
---|---|---|---|---|

Suited aces | 60 | 60 | 0.001237 | 0.074202 |

Suited blackjack | 10 | 576 | 0.011872 | 0.118724 |

Suited pair | 5 | 720 | 0.014840 | 0.074202 |

Suited 11 | 3 | 576 | 0.011872 | 0.035617 |

Any other suited | 2 | 10080 | 0.207767 | 0.415533 |

Loser | -1 | 36504 | 0.752412 | -0.752412 |

Total | 48516 | 1.000000 | -0.034133 |

The next table shows the expected value by various numbers of decks.

### Suit 'em Up Expected Return

Decks | Expected Return |
---|---|

8 | -0.026691 |

6 | -0.034133 |

5 | -0.040095 |

4 | -0.049052 |

2 | -0.094100 |

## 20 Bet

This is a simple bet I noticed at the Palms casino in Managua, Nicaragua, on April 29, 2013. The bet was titled *Apuesta de 20*. It pays 7 to 1 if the total of the dealer's first two cards is 20, including a soft 20. The following table shows the probability of winning and expected return for one to eight decks. The Palms uses six decks, for a house edge of 15.31%.

### 20 Bet

Decks | Pays | Probability | Return |
---|---|---|---|

1 | 7 | 0.102564 | -0.179487 |

2 | 7 | 0.104556 | -0.163555 |

3 | 7 | 0.105211 | -0.158313 |

4 | 7 | 0.105537 | -0.155704 |

5 | 7 | 0.105732 | -0.154143 |

6 | 7 | 0.105862 | -0.153104 |

7 | 7 | 0.105955 | -0.152363 |

8 | 7 | 0.106024 | -0.151807 |

## Dealer Bust — Nicaragua Version

This is a side bet I noticed at the Palms casino in Managua, Nicaragua, on April 29, 2013. The bet was titled *Casa Demasiado*, which means "house too much." The bet wins if the dealer busts. The win depends on what the dealer's up card is, as follows:

- Dealer busts with 2 to 6 up: Pays 1 to 1
- Dealer busts with 7 to 9 up: Pays 2 to 1
- Dealer busts with 10 up: Pays 3 to 1
- Dealer busts with ace up: Pays 7 to 1

Unlike the Dealer Bust 21 bet, the wager may be made after seeing the dealer's up card. The following table shows the expected return according to the dealer's up card and the number of decks, assuming the dealer stands on a soft 17. At the Palms they use six decks.

### Dealer Stands on Soft 17

Up Card | Pays | 1 | 2 | 4 | 5 | 6 | 8 |
---|---|---|---|---|---|---|---|

Ace | 7 | -0.067680 | -0.073024 | -0.075448 | -0.075912 | -0.076216 | -0.076592 |

2 | 1 | -0.294054 | -0.293418 | -0.293098 | -0.293034 | -0.292992 | -0.292940 |

3 | 1 | -0.248824 | -0.250412 | -0.251302 | -0.251488 | -0.251612 | -0.251770 |

4 | 1 | -0.194394 | -0.202920 | -0.207038 | -0.207850 | -0.208390 | -0.209062 |

5 | 1 | -0.142190 | -0.154990 | -0.161162 | -0.162380 | -0.163188 | -0.164196 |

6 | 1 | -0.158354 | -0.155736 | -0.154648 | -0.154448 | -0.154316 | -0.154156 |

7 | 2 | -0.220438 | -0.216571 | -0.214774 | -0.214423 | -0.214192 | -0.213907 |

8 | 2 | -0.284119 | -0.275110 | -0.270481 | -0.269545 | -0.268921 | -0.268138 |

9 | 2 | -0.299674 | -0.307306 | -0.311041 | -0.311782 | -0.312274 | -0.312889 |

10 | 3 | -0.142944 | -0.147236 | -0.149396 | -0.149828 | -0.150116 | -0.150476 |

Here is the same table if the dealer hits a soft 17.

### Dealer Hits on Soft 17

Up Card | Pays | 1 | 2 | 4 | 5 | 6 | 8 |
---|---|---|---|---|---|---|---|

Ace | 7 | 0.123152 | 0.117008 | 0.114128 | 0.113568 | 0.113192 | 0.112728 |

2 | 1 | -0.287310 | -0.286946 | -0.286746 | -0.286706 | -0.286678 | -0.286646 |

3 | 1 | -0.243850 | -0.245080 | -0.245820 | -0.245978 | -0.246084 | -0.246218 |

4 | 1 | -0.188408 | -0.197344 | -0.201648 | -0.202498 | -0.203060 | -0.203762 |

5 | 1 | -0.140078 | -0.152664 | -0.158742 | -0.159940 | -0.160736 | -0.161728 |

6 | 1 | -0.124488 | -0.122492 | -0.121712 | -0.121572 | -0.121482 | -0.121372 |

7 | 2 | -0.220438 | -0.216571 | -0.214774 | -0.214423 | -0.214192 | -0.213907 |

8 | 2 | -0.284119 | -0.275110 | -0.270481 | -0.269545 | -0.268921 | -0.268138 |

9 | 2 | -0.299674 | -0.307306 | -0.311041 | -0.311782 | -0.312274 | -0.312889 |

10 | 3 | -0.142944 | -0.147236 | -0.149396 | -0.149828 | -0.150116 | -0.150476 |

## Roulette

I noticed the roulette bets, or *ruleta* in Spanish, at the Palms casino in Managua, Nicaragua, on April 29, 2013. They are side bets on the next dealer card. Interestingly, they may be made at any point the dealer is about to draw a card. Bets on an ace to 9 pay 10 to 1, and any 10-point card pays 2 to 1.

The house edge is 2/13, or 15.38%, on the ace to 9 bets. On the dealer 10 bet the house edge is 1/13, or 7.69%.

## Dealer Total

This is a set of side bets I noticed at the Palms casino in Managua, Nicaragua, on April 29, 2013. The bets had no name so I'm taking the liberty of calling them the "Dealer Total" bets. There are five bets available on the final dealer total, ranging from 17 to 21. The bets may be made **after** seeing the dealer's up card. However, the player may not bet on the up card plus ten. For example, if the up card is a seven, then the player can't bet on 17. Here is what each total pays.

- Total of 17: Pays 5 to 1
- Total of 18: Pays 6 to 1
- Total of 19: Pays 6 to 1
- Total of 20: Pays 6 to 1
- Total of 21: Pays 7 to 1

The following table shows the expected value of each bet according to the up card, assuming six decks and the dealer stands on soft 17, which are the rules at the Palms in Managua. I'm leaving in the situations the player is not allowed to bet per the "+10 rule," should another casino pick these bets up and be nice enough to not enforce that rule.

### Dealer Total Bets — Expected Value

Up Card | 17 | 18 | 19 | 20 | 21 |
---|---|---|---|---|---|

Ace | -0.219898 | -0.084246 | -0.085842 | -0.083630 | -0.571972 |

2 | -0.162064 | -0.059277 | -0.089860 | -0.131867 | -0.052696 |

3 | -0.194224 | -0.086227 | -0.123418 | -0.154281 | -0.080576 |

4 | -0.216664 | -0.131566 | -0.151096 | -0.184913 | -0.105072 |

5 | -0.268942 | -0.142941 | -0.176975 | -0.217449 | -0.136440 |

6 | -0.005758 | -0.256642 | -0.254983 | -0.289143 | -0.221795 |

7 | 1.215248 | -0.034483 | -0.451004 | -0.449229 | -0.409474 |

8 | -0.226360 | 1.519685 | -0.098939 | -0.515468 | -0.444239 |

9 | -0.278140 | -0.178564 | 1.462978 | -0.157424 | -0.512982 |

10 | -0.328516 | -0.218317 | -0.216385 | 1.380098 | -0.721461 |

If you must make this bet, then the next table shows shows the best bet and expected value for any given up cards.

### Dealer Total — Strategy

Up Card | Best Bet | Expected Value |
---|---|---|

Ace | 20 | -0.083630 |

2 | 21 | -0.052696 |

3 | 21 | -0.080576 |

4 | 21 | -0.105072 |

5 | 21 | -0.136440 |

6 | 17 | -0.005758 |

7 | 18 | -0.098939 |

8 | 19 | -0.157424 |

9 | 20 | -0.157424 |

10 | 19 | -0.216385 |

## Let's Play

I'm not sure if the correct title of this side bet is "Let's Play," "Let's Play AKQJ," or "100K ... Let's Play." Whatever the name, I first saw it at the Eureka Casino in Mesquite NV on January 3, 2014. It usually pays based on the player's first two cards, with the top pay also involving the dealer's first two cards. The following return table, based on two decks, shows all the specifics. The lower right cell shows a house edge of 11.01%.

### Let's Play — Double Deck

Event | Pays | Combinations | Probability | Return |
---|---|---|---|---|

AKQJ suited (player and dealer) | 250 | 384 | 0.000014 | 0.003480 |

Ace-king suited (player only) | 20 | 82,352 | 0.002985 | 0.059700 |

Queen-jack suited (player only) | 15 | 82,352 | 0.002985 | 0.044775 |

Straight flush (player only) | 4 | 906,512 | 0.032858 | 0.131432 |

Flush (player only) | 2 | 5,624,700 | 0.203877 | 0.407753 |

Loser | -1 | 20,892,456 | 0.757282 | -0.757282 |

Total | 27,588,756 | 1.000000 | -0.110142 |

The game's web site, turbogamingllc.com, says that other pay tables are available for other numbers of decks. All I know is the Eureka double-deck pay table, which you see above.

There is discussion about Let's Play, including the vulnerability to card counters, in my forum at Wizard of Vegas.

## Lucky Eights

Lucky Eights is a side bet that was reported to be at the Marina Bay Sands in Singapore in May, 2014. It pays based on the player's first two cards and the dealer's up card. The following return table for six decks shows a house edge of 7.66%.

### Lucky Eights — Six Decks

Event | Pays | Combinations | Probability | Return |
---|---|---|---|---|

Three suited eights | 1,000 | 16 | 0.000011 | 0.010824 |

Three unsuited eights | 100 | 544 | 0.000368 | 0.036800 |

Two suited eights | 10 | 4,608 | 0.003117 | 0.031172 |

Two unsuited eights | 5 | 18,432 | 0.012469 | 0.062344 |

Pair | 3 | 283,200 | 0.191577 | 0.574731 |

All other | -1 | 1,171,456 | 0.792458 | -0.792458 |

Total | 1,478,256 | 1.000000 | -0.076588 |

The next table shows the house edge for variou numbers of decks.

### Lucky Eights — House Edge

Decks | EV |
---|---|

4 | 7.66% |

5 | 6.19% |

6 | 5.21% |

8 | 3.96% |

Card counters will be unhappy to learn they use a continuous shuffler at the Marina Bay Sands. I would keep an eye out for any other casinos that don't.

## Lucky 7

Lucky 7 is a side bet found in the Lucky 7 Blackjack game at Internet casinos using Amaya software, such as InterCasino. Eights decks are used. It wins if the first player card is a seven, and up from there, depending on how many more sevens the player gets in a row, up to three, and whether they are suited.

If the player has two sevens, and the dealer gets a blackjack, then the player will **not** have the opportunity to take a third card.

Assuming the player always draws or splits for a third card with two sevens, which he should, the following table would show the probability and return for each possible outcome. The lower right cell shows a house edge of 49.89%. I think that makes this the worst side bet, in terms of player odds, I've ever seen.

### Lucky 7 — Eight Decks

Event | Pays | Probability | Return |
---|---|---|---|

Three suited sevens | 500 | 0.000018 | 0.008949 |

Three un-suited sevens | 100 | 0.000378 | 0.037844 |

Two suited sevens | 50 | 0.001204 | 0.060219 |

Two unsuited sevens | 25 | 0.004145 | 0.103634 |

One seven | 3 | 0.071177 | 0.213531 |

Zero sevens | -1 | 0.923077 | -0.923077 |

Total | 1.000000 | -0.498900 |

## Lucky Stiff

There is a separate page devoted to Lucky Stiff Blackjack.

Sign seen at the Silver Dollar casino near the Seattle airport in June 2007. It would read "Side-bets are strictly prohibited", if it were spelled correctly.

If you are interested in the analysis of blackjack side bets, please see my Gaming Math course notes on that topic. Here are some links: