# Ask the Wizard #127

Three questions of etiquette and ethics.

- 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.

Nathan W.

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.

At the Trump Casino in Gary, Indiana (near Chicago) the fortune bonus in Pai Gow Poker pays out the regular bonuses for a 3 of a kind or better, but also pays 1 to 1 for 3-pair. Statistically speaking, how will this increase your chances of winning on the bonus? What percentage of the time will a player have 3-pair in their hand?

Anonymous

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.

What is the probability of a blackjack for n decks?

Anonymous

2*(4/13)*(4n/(52n-1))

In San Juan, Puerto Rico, at blackjack, a number of casinos do not deal the dealers "hole card" until after the players have taken their cards. I am reasonably sure that they don’t take your doubled/split bet if they get a blackjack. What changes, if any should be made to basic strategy.

Anonymous

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.

Dear awesome Mr. Wizard of Odds, I am in complete and utter awe of your statistical acumen. Would you by chance be able to calculate for me the probability of a seven card straight - i.e. A,2,3,4,5,6,7 or 2,3,4,5,6,7,8 or 7,8,9,10,jack,queen,king in a seven card stud. We recognize this is not a real poker hand; however it came up when we were playing and we were wondering if it had a lower probability than a normal full house in seven card stud. Cheers, oh knowledgeable one.

Anonymous

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 4^{7} = 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.

I am a blackjack dealer and last night I amazed my table on a single-deck blackjack game (the horrible 6 to 5). My hand consisted of an Ace up, Ace in the hole and then I drew the other 2 Aces and then a 7 for 21! What are the odds of this happening and I am especially interested in knowing the math. Thanks!

Anonymous

The probability is (4/52)*(3/51)*(2/50)*(1/49)*(4/48) = 1 in 3,248,700.

With five different toppings to choose from, how many different pizzas can you make, with any number of toppings?

Anonymous

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 2^{5} = 32.