# Blackjack - FAQ

- Positional advantage is very important. When you are last to act is the best time to take chances with big bets.
- Bide your time at the beginning. Sometimes on a cold table everyone else will burn themselves out while you coast to first place at your table.
- The second half of the round take big chances to get in first place.
- If competing against one other player you want to bet with him when ahead, and contrary to him when behind.
- Pay attention to the maximum bet allowed. If the maximum bet is small compared to the player stacks you should get aggressive early.

Blackjack tournaments are not my strong subject. For advice on that I would highly recommend Casino Tournament Strategy by Stanford Wong. Wong says that if you are behind to bet opposite of the leader, small when he bets big, and big when he bets small. If you are in the lead then you should bet with the second highest player. The book gets into much more detail. Speaking of supporting my site, it helps to click through my Amazon links when buying books there.

My question relates to what has come to be known in certain blackjack circles as The Flaw. In a nutshell it says that the original creators of basic strategy programmed a flaw into their calculations which has been recreated over and over again by other mathematicians when they’ve come up with their basic strategy. As one proponent of ’The Flaw’ proclaims, "only 3 others that know post on this board. One is the recently retired IBM type, who confirms that to find the Flaw a computer simulation would have to be programmed to do so-therefore prior knowledge is REQUIRED. The math boyz are certain that they are right; but Thorp can’t figure why so few win. One percent says it all."

So, what is The Flaw, and is there any truth to it? Or is it theoretically BS? I know it’s easy to dismiss the nay sayers out of hand, but I’m intrigued.

It is a Nevada state law that an electronic game with representations of cards or dice must be based on fair odds. So the game should be fair with odds the same as in a hand dealt game having the same rules.

I have some questions on tipping etiquette...

Blackjack: Can I double, split or take insurance for the dealer?

Caribbean Stud Poker: Can I (or do I have to) raise also for the dealer?

Let It Ride Poker: Can I place more than one bet for the dealer (what happens if I decide to take back one of my bets and there was a tip)?

Craps: Can I play a tip everywhere I can play (odds and props included)?

Roulette: Can I play on numbers for him?

As a general rule, you can make any bet for the dealer in any game. In general you should tell the dealer which bets are his, except blackjack where its common practice that any bet outside the betting circle is for the dealer.

Blackjack: Yes to all three. The usual way to bet for the dealer in blackjack is to put the tip on the edge of the betting circle. If you split or double most people also split or double the dealer’s bet, although it is not required.

Caribbean Stud Poker: I asked a dealer and he said raising for the dealer is optional. I haven't studied it but I think this would result in the tip having an advantage.

Let it Ride: I'm told that the player should put out three tips initially but must pull them back in the same manner that they pull back their own bets. Bets that are pulled back go to the player, not the dealer.

Craps: Yes, you can make any bet for the dealer. The most common ones are the yo-11 and the hard ways. If you make a line bet for the dealers and back it up with the odds it is implied the odds are a tip too.

Roulette: As in craps you can make any bet for the dealer. Just tell them in advance.

[Bluejay adds: Every video blackjack game I’ve seen pays only even money on naturals, which significantly increases the house edge.]

### Soft 18 Vs Ace Combinatorial Analysis

Player cards |
Conditional Probability |
Hit EV |
Stand EV |
Hit Return |
Stand Return |

A7 | 0.621139169 | -0.100359 | -0.100502 | -0.062336906 | -0.062425729 |

A6A | 0.036728229 | -0.11202 | -0.116009 | -0.004114296 | -0.004260805 |

A52 | 0.146912917 | -0.111299 | -0.103382 | -0.016351261 | -0.015188151 |

A43 | 0.146912917 | -0.114804 | -0.103721 | -0.01686619 | -0.015237955 |

A5AA | 0.001827682 | -0.111395 | -0.105122 | -0.000203595 | -0.00019213 |

A42A | 0.016814677 | -0.116975 | -0.108233 | -0.001966897 | -0.001819903 |

A33A | 0.007356421 | -0.132142 | -0.107256 | -0.000972092 | -0.00078902 |

A322 | 0.020470041 | -0.134229 | -0.11004 | -0.002747673 | -0.002252523 |

A4AAA | 0.000073486 | -0.117554 | -0.110984 | -0.000008639 | -0.000008156 |

A32AA | 0.001028802 | -0.134775 | -0.112433 | -0.000138657 | -0.000115671 |

A222A | 0.000709873 | -0.136788 | -0.114993 | -0.000097102 | -0.00008163 |

A3AAAA | 0.000002238 | -0.135313 | -0.114821 | -0.000000303 | -0.000000257 |

A22AAA | 0.000023502 | -0.137312 | -0.117376 | -0.000003227 | -0.000002759 |

A2AAAAA | 0.000000046 | -0.137859 | -0.119823 | -0.000000006 | -0.000000006 |

Total | 1 | -0.105806844 | -0.102374694 |

Explanation of column titles

Player cards:Cards in player’s hand

Conditional probability: Given that the player has a soft 18 against a dealer ace the probability of the given hand composition.

Hit EV:Expected value by hitting

Stand EV:Expected value by standing

Hit Return:Product of probability and hit expected value

Stand Return:Product of probability and stand expected value

The right two cells of the bottom row show that overall the expected value of hitting is -0.105807 and for standing is -0.102375. So, the table shows the odds favor standing by 0.00343.

To confirm these results I ran two simulations under the rules in question, one simulation hitting and one standing on this play. I counted only hands where soft 18 against a dealer ace happened at any time during play. Here are my results.

### Soft 18 Vs Ace Simulation

Soft 17 | Hands Played |
Total Win |
Expected Value |

Stand | 3857490 | -396224 | -0.102715 |

Hit | 3208390 | -337572 | -0.105215 |

So, the simulation shows the odds favor standing by 0.0025 over all possible scenarios where this hand turns up. Thus, for practical purposes of playing all hands, the best play is to stand, contrary to what my basic strategy chart says.

- Free Food & Beverage
- Free Lodging
- One of those high roller suites
- Free golf at Wynn
- A new car
- Free airfare.

### Average Dealer Total in Blackjack

Decks | Stand Soft 17 | Hit Soft 17 |

1 | 18.840371 | 18.880098 |

2 | 18.842648 | 18.882868 |

3 | 18.843415 | 18.883798 |

4 | 18.843826 | 18.884288 |

5 | 18.844053 | 18.884564 |

6 | 18.844205 | 18.884720 |

7 | 18.844292 | 18.884880 |

8 | 18.844370 | 18.884981 |

To answer your second question, I used a brute force combinatorial program in C++ to cycle through all the possible combinations of dealer hands.

6 decks

Dealer stands on soft 17

Double on any first two cards allowed

Double after split allowed

Late surrender allowed

Player may re-split to four hands, including aces

Cut card used

First, I had both players follow correct total-dependent basic strategy. Over almost 1.6 billion rounds, the loss of the first player to act was 0.289%, and the second player to act of 0.288%.

Second, I had the first player follow the same correct strategy, and the second player follow the same correct strategy except:

Always hit 12 to 16

Always double 9 to 11

Split any pair

Never surrender

Never soft double

In a simulation of 1.05 billion hands the loss of the first player was 0.282%, and the second player was 11.260%. So the house edge of the basic strategy playing first player was almost the same, regardless of whether the second player played correctly or wildly incorrectly. I hope this puts and end the third baseman myth, but I doubt it. As I have said many times, the more ridiculous a belief is, the more tenaciously it tends to be held.

Thanks for an awesome site! I get lost in your odds calculations sometimes, but it’s just so damn informative!

I think your odds are best with the big Table Master units with big video screens housing attractive dealers. These are getting easier and easier to find, but I don’t know of any specific list of them. Your odds of finding them will be better in low-roller casinos. Some pay 3 to 2 on blackjack, and some only pay 6 to 5. An an example, the unit at the Riviera has the following rules:

- 6 decks (shuffled after four decks)
- Blackjack pays 3 to 2
- Dealer hits soft 17
- Double after split allowed
- Double on any two cards allowed
- Surrender allowed
- Split to two hands only
- Seven Card Charlie (un-busted hands of 7 cards automatically win)
- Bet range: $2-$200

The house edge under these rules is 0.68%. If you play an even-money game, the house edge will be 1.4% to 2.0%, depending on the other rules. Be sure to use a player card to earn whatever cash, free play, or comps the casino offers.

The picture below shows one of these products.

### Cost of Blackjack Errors

Location | Cost of Errors | Margin of Error |

Atlantic City | 1.13% | 0.12% |

Las Vegas | 1.67% | 0.17% |

Reno | 1.48% | 0.19% |

Lake Tahoe | 1.39% | 0.54% |

Total | 1.41% | 0.10% |

In my opinion, play has improved a lot in the 23 years since the study. If forced to guess, I think the cost due to errors is about 0.5% now. I would agree with Griffin that Atlantic City players are more skilled than Vegas players.

This question was raised and discussed in the forum of my companion site Wizard of Vegas.

After this column first appeared, I heard from gaming consultant Bill Zender. He offered to let me post his article How Poor are Blackjack Players (PDF 147K), from Gaming Operations magazine. There is says his own research showed the cost of player mistakes to be about 0.83%.

- 8 decks.
- Cards shuffled after every hand.
- Blackjack pays 2 to 1.
- Dealer hits on soft 17.
- No doubling down.
- Split pairs once only.
- No surrender.

Using my blackjack house edge calculator, I get a house edge of 0.82%, before factoring the 2-1 on blackjacks and no doubling. 2-1 on blackjacks is worth 2.26% to the player. No doubling is worth 1.37% to the dealer.

So I show the player edge is 0.82% -2.26% + 1.37% = 0.07%.

This question was raised and discussed in the forum of my companion site Wizard of Vegas.

To me, the key clue is this sentence from the article, "'They also agreed to discount 20 percent of his blackjack losses as an incentive to get him to play,' he said." With liberal blackjack rules, a well-financed player can easily have a strong advantage with a 20% rebate.

The proper strategy is to quit when you have either achieved a huge win or a moderate loss, whichever comes first. For example, winning $1,000,000 or losing $100,000. Most of the time you will lose, so it takes a big bankroll to weather the ups and downs. Fortunately for the player, he was properly financed to take advantage of such offers. Besides having an advantage, he may also have exceeded expectations since December. I salute him for his success.

You are correct. In June the Barona sadly removed their single-deck game, which allowed doubling on any two cards, double after splitting, and surrender. The basic strategy house edge was 0.01%. According to the Current Blackjack Newsletter, that was the best game in America.

So, who rises to fill the top position? According to my own Las Vegas rule survey, the best game is now at the Hacienda casino, near Hoover Dam. However, I don't keep track of anything outside of the greater Vegas area, so I checked the Current Blackjack Newsletter, which monitors the entire U.S. and Canada. They indicate the Hacienda game is not only best in Vegas but the best anywhere in the U.S. and Canada. So, I congratulate the Hacienda for rising to the number one spot!

The rules of said game are:

- Single deck
- Blackjack pays 3-2 (of course)
- Dealer hits soft 17
- Double any first two cards
- Double after split
- Re-splitting aces allowed
- No surrender
- Table limits: $2-$200
- Game not always open

Based on my blackjack house edge calculator, the house edge is 0.02%, assuming basic strategy and no cut card. To get this figure, take the "realistic house edge" and subtract 0.11%, what the cut-card effect otherwise costs the player in a single-deck game. Al Rogers, with the Current Blackjack Newsletter, tells me that both the Hacienda and the Peppermill casinos, mentioned below, do not use a cut card, in favor of dealing a specified number of rounds per deck. Single-deck games usually follow the rule of six, which means the number of rounds per deck is equal to max(2,6-p), where p is the number of players.

For players who want to bet over $200 in single-deck games, Al suggested I put in an honorable mention for the Peppermill group of casinos (Peppermill, Montego Bay, and Rainbow) in Wendover, Nevada. They have the same rules, except no double after a split, for a house edge of 0.16%, again assuming basic strategy and no cut card. That is probably the best single-deck game that is open 24-hours and doesn't mind large bets.

Shameless Plug: The Current Blackjack Newsletter lists the rules and card-counting conditions for every legitimate casino with table games in the U.S. and Canada. The monthly reports are $15 each, $30 per quarter, or $99 per year. I've been using it as an invaluable resource for over a decade.

This question was raised and discussed in the forum of my companion site Wizard of Vegas.

Okay, how about this "Extra Simple Strategy." Follow the first rule that applies.

- Split eights and aces.
- Double 10 and 11.
- Hit hard 9 or less.
- Hit hard 12 to 16 against a 7 to ace.
- Hit soft 17 or less.
- Otherwise, stand.

That is just 30 words, counting the numbers as words. The cost due in errors relative to the full basic strategy is 0.44%. That is a lot more than the 0.14% of my full Simple Strategy, but is still about half the cost of errors made by the average blackjack player.

This question was raised and discussed in the forum of my companion site Wizard of Vegas.

The following table shows the effect on the player's expected return by removing one card from a six-deck shoe, according to whether the dealer hits or stands on a soft 17. For example, if the dealer stands on soft 17, and the burn card is a five, then the house edge drops by 0.146%.

### Effect of Removal in Blackjack

Card | Stand Soft 17 |
Hit Soft 17 |
---|---|---|

2 | 0.069% | 0.071% |

2 | 0.070% | 0.072% |

3 | 0.084% | 0.089% |

4 | 0.114% | 0.122% |

5 | 0.146% | 0.148% |

6 | 0.079% | 0.085% |

7 | 0.041% | 0.038% |

8 | -0.010% | -0.012% |

9 | -0.041% | -0.046% |

10 | -0.092% | -0.098% |

Ace | -0.101% | -0.091% |

The table above assumes otherwise "liberal Strip rules," which allow double after split, late surrender, and re-splitting pairs (including aces) up to three times. The table was created using the Composition Dependent Combinatorial Analyzer at bjstrat.net.

This question was raised and discussed in my forum at Wizard of Vegas.

I think casinos that shuffle the cards early in a good count are cheating. I'm going to file a formal complaint with the Gaming Control Board against the Stratosphere for doing this to me. No particular question, I just wanted to vent.

Shuffling early, as a defense against card counters, has been part of game for 50 years. I would say that if casinos were using computers to tell the dealer when the count was good, as a hint to shuffle, that would be cheating. I also think if the dealer counted himself and shuffled early on recreational players, that too would be cheating. However, if the dealer is doing it when you raise your bets, well, that is just the way the game is played. If you won your case with Gaming, the casinos would ruin the game for counters, like they did in Atlantic City over the Ken Uston lawsuit. The next thing you would see is every game on a continuous shuffler. Both sides would be better off to leave the cat and mouse game as it is.

This question is raised and discussed in my forum at Wizard of Vegas.

Your task is to get from square 0 to square 19. You may not take a path of the same color twice in a row. In other words, at every square you must change to a path of another color. No u-turns. What is the solution?

Puzzle by David Pleacher.

I encourage my readers to solve this for themselves. However, if you give up, you may click the solution button below.

Here is one possible solution: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 17, 18, 12, 11, 18, 17, 9, 8, 7, 6, 5, 4, 3, 2, 1, 15, 14, 13, 19.

The key is to notice that you can make a u-turn in the 11-12-18 triangle. The solution is to go the whole way around the outside circle, in a counter-clockwise rotation until you get back to 1. Then take the inner circle clockwise to 18. Then make a u-turn and get back to 18. Then retrace your steps back to 1. Then it is an easy path to 19 from there.