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Ask the Wizard #127
- Blackjack dealer makes a mistake in your favor. Do you point it out? Do you tip?
- The etiquette of challenging the dealer where you think he made a mistake in favor of the house against you.
- You wrongfully challenge the dealer, is anything more than an apology expected?
All three have happened to me within the last month. I am a small time bettor so the correction of a win or loss is not significant to me. I'd prefer not jeopardize the dealer's job.
This is a delicate question. Personally I just keep my mouth shut. Once in Atlantic City I saw another player correct the dealer for an overpayment and neither the dealer nor pit boss thanked the player for his honesty. If the casino doesn’t seem to care then why should I? I also view making the correct payment as part of a game. Also, no I do not tip. Sometimes crooked dealers will deliberately overpay players hoping to get tipped in return. This is highly illegal and at least in Nevada they treat cheating as a comparable crime to bank robbery. So I wouldn’t want anyone, including the dealer, to think I was colluding on a mistake-for-tip scheme. Another reason to not say anything is that the dealer will have to call the pit boss over and confess his mistake. Anyone can make a mistake once in a while but if the dealer is known to be mistake prone already then, yes, it could put his job in jeopardy.
Note: See my Jan. 9 column for a dealer's answer to this question.
The number of combinations for a three pair without the joker is combin(13,3)*10*combin(4,2)^3*4/combin(52,7) = 2,471,040. The number of combinations of a three pair with the joker being used to complete a pair of aces is 23776. The number of combinations of a three pair with the joker as the singleton is 61776. So the total combinations are 2556592. Out of total combin(53,7)=154,143,080 possible the probability of a three pair is 1.659%. So changing a three pair from a loss to a win of 1 to 1 decreases the house edge by 3.32%. Assuming the standard pay table on the other hands this would sway the odds in the player's favor with 3 or more other players.
Assuming you are right that they don’t take your double/split bet on a dealer blackjack then make no changes to the U.S. basic strategy.
How can I refuse after you buttered me up so nicely? First there are combin(52,7) = 133,784,560 ways to choose 7 cards out of 52, without regard to order. There are 8 possible spans for a 7-card straight (the lowest card could be A to 8). If we had 7 different ranks there are 47 = 16384 ways to arrange the suits. Note that this includes all the same suit, which would form a straight flush. So the probability is 8*16,384/133,784,560 = 1 in 1020.6952.
The probability is (4/52)*(3/51)*(2/50)*(1/49)*(4/48) = 1 in 3,248,700.
There is 1 way with 0 toppings, 5 ways with 1 topping, 10 ways with 2 toppings, 10 ways with 3 toppings, 5 ways with 4 toppings, and 1 way with 5 toppings. So the answer is 1+5+10+10+5+1 = 32. Another way to solve is either topping can be used or not. So the total is 25 = 32.