Last Updated: Oct. 13, 2014

Blackjack Side Bets - Analyzed

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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*n2. 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)-n2). 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)-n2)/combin(52×n,2).

The probability of a royal match is 4×n2/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 0.4751n. 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


Palms casino, Managua

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.
The following table shows the proper basic strategy assuming the maximum side bet is played and the rules above.

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.

Here is another version that has been seen at Internet casinos using Cryptologic software. The game uses eight decks of cards.

Progressive Blackjack — Cryptologic Version

Hand Pays Permutations Probability Return
Four suited aces Jackpot 6720 0.00000023 ?
Three suited aces 2500 516096 0.00001748 0.043710
Four aces unsuited 1500 856320 0.00002901 0.043515
Three aces unsuited 250 10911744 0.00036966 0.092415
Two suited aces 100 35524608 0.00120348 0.120348
Two aces 25 121798656 0.00412620 0.103155
All other 0 29348718336 0.99425394 0.000000
Total 29518332480 1.00000000 0.403142 + ?

Based on a $1 bet, this bet becomes break-even at $2,621,763.29. The general formula for the return is 0.403142 + jackpot/4,392,609.

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

Winners Option web site.

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.

  1. Player makes a blackjack and poker bet.
  2. 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.
  3. 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.
  4. The poker hand shall pay according to the return table below.
  5. If the player does not bust, then the poker bet will push.
  6. 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.

Six-Deck Poker Probabilities by First CardExpand

Poker Hand A up 2 up 3 up 4 up 5 up 6 up 7 up 8 up 9 up 10 up J up Q up K up
Five of a kind 0.000023 0.000023 0.000023 0.000023 0.000023 0.000023 0.000023 0.000023 0.000023 0.000023 0.000023 0.000023 0.000023
Royal flush 0.000003 0 0 0 0 0 0 0 0 0.000003 0.000003 0.000003 0.000003
Straight flush 0.000003 0.000007 0.00001 0.000014 0.000017 0.000017 0.000017 0.000017 0.000017 0.000014 0.00001 0.000007 0.000003
Four of a kind 0.001668 0.001668 0.001668 0.001668 0.001668 0.001668 0.001668 0.001668 0.001668 0.001668 0.001668 0.001668 0.001668
Full house 0.003653 0.003653 0.003653 0.003653 0.003653 0.003653 0.003653 0.003653 0.003653 0.003653 0.003653 0.003653 0.003653
Flush 0.003516 0.003516 0.003516 0.003516 0.003516 0.003516 0.003516 0.003516 0.003516 0.003516 0.003516 0.003516 0.003516
Straight 0.001729 0.001729 0.002593 0.003458 0.004322 0.004322 0.004322 0.004322 0.004322 0.004322 0.003458 0.002593 0.001729
Three of a kind 0.041826 0.041826 0.041826 0.041826 0.041826 0.041826 0.041826 0.041826 0.041826 0.041826 0.041826 0.041826 0.041826
Two pair 0.065558 0.065558 0.065558 0.065558 0.065558 0.065558 0.065558 0.065558 0.065558 0.065558 0.065558 0.065558 0.065558
Jacks or better 0.25072 0.091171 0.091171 0.091171 0.091171 0.091171 0.091171 0.091171 0.091171 0.091171 0.25072 0.25072 0.25072
All other 0.6313 0.790849 0.789982 0.789114 0.788246 0.788246 0.788246 0.788246 0.788246 0.788246 0.629565 0.630432 0.6313
Total 1 1 1 1 1 1 1 1 1 1 1 1 1

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
This is another obviously countable side bet. I'll leave that details of that to you.

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.

  1. The game is based on conventional blackjack rules.
  2. 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

  3. 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.
  4. 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.

  1. The game is based on conventional blackjack rules.
  2. 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.
  3. 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 is a side bet that came out in 2003 with several placements. The bet seemed to fade away but in December 2012 I noticed it at the Gold Coast. It is a pair of side bets, one on the player and one on the dealer. Each wins if the first two cards form 20 points, including a soft 20. I would think that any casino offering this side bet would put it on a continuous shuffer.

The following return table is for six decks and shows a house edge of 18.06%.

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



Palms casino, Managua

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.

Triple Sevens



Triple Sevens is a $1 progressive blackjack side bet found at Internet casinos using Microgaming software. I believe it is available only in the download version. The number of decks used is five and the player gets an opportunity to draw a third card because the dealer follows the European "no peek" rule. The three sevens must all be part of the original hand.

The following table assumes the player always hits two sevens for a third card. This will cause some strategy errors where the player should split instead, increasing the house edge of the base game.

Triple Sevens — Five Decks

Event Pays Probability Return
7-7-7 in diamonds Jackpot 0.000003 ?
7-7-7 suited 1000 0.000010 0.010360
7-7-7 mixed suits 250 0.000380 0.094971
7-7 suited 50 0.001105 0.055256
7-7 mixed suits 25 0.004144 0.103605
7 5 0.071280 0.356400

The return of the game is 62.06% plus 3.453% for every $10,000 in the meter. The break-even point is $109,862.

More information is available at Casino Listings.



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:

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