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Ask the Wizard #87

Dear Mr. Wizard, How do minimum payback laws affect video poker machines? Can a casino have a VP machine installed if an ideal strategy is not known? Can really stupid players (ones who would discard a paying pair or even a pat royal) sue a casino if their strategy results in payoffs under x%, as mandated by state law? Finally, out of curiosity, what is the lowest return possible on a VP machine, assuming discarding royal flush, keeping all 5 cards of a garbage hand, etc? Thank you for your valuable time in reading and hopefully responding.


Nevada Gaming Control Board regulation 14.040.1(a) states that gaming devices must return at least 75% assuming optimal player strategy. To answer your second question I modified my video poker program to always make the worst possible play. For example, keeping all five cards on a non-paying hand , and tossing part or all of pat hands. Based on 9/6 Jacks or Better this strategy results in a return of 2.72%, or house edge of 97.28%. Following is the complete return table. Such a player would not be able to sue the casino because it was his fault for playing so badly.

Jacks or Better - Worst Possible Player

Hand Payoff Number Probability Return
Royal flush 800 48564 0.000000 0.000002
Straight flush 50 2058000 0.000000 0.000005
4 of a kind 25 38040380 0.000002 0.000048
Full house 9 292922028 0.000015 0.000132
Flush 6 336550092 0.000017 0.000101
Straight 4 6239759724 0.000313 0.001252
3 of a kind 3 12510891616 0.000628 0.001883
Two pair 2 34968642984 0.001754 0.003509
Jacks or better 1 334574728656 0.016785 0.016785
Nothing 0 19544266875156 0.980487 0.000000
Total 19933230517200 1.000000 0.023717

Where I play pai gow poker the commission on a $25 bet is $1, or 4%. How much does this reduce the house edge?


A 4% commission lowers the house edge by 0.29%.

Hey dude I had a random question and I didn’t know who else to ask!! I won 12000 on an online casino. Should I cash it all out at once? Do I have to do anything related to reporting it on my taxes? If I don’t report it will I get in trouble? What would you do in this situation? Thanks for the help!!!


Whether to cash out it all out at once is your decision. Assuming you are a U.S. citizen you are obligated to declare the income on your next tax return. If you don’t you could be charged with tax evasion. However this sort of thing is largely on the honor system. You are also allowed to deduct any gambling losses in the same year against your winnings.

Mr. Wizard, if 50 different people toss a coin in the air 8 different times. What percentage of the 50 people will toss 8 consecutive heads or tails? Thanking you in advance.


The probability of any given person tossing 8 heads or tails is 2*(1/2)8 = 1 in 128. If 50 people did this on average 0.39 of them will get all heads or tails. The probability of at least one person getting all heads or tails is 32.44%.

I recently went to Vegas and had an incredible hand of blackjack... received an ace as first card, split, received another ace, split, received a third ace, split, and got one last ace... Then was dealt blackjack on all 4 hands! No lie! 2 of my friends were witnesses, as was the entire Luxor gaming gods...What are the odds on this? It was a 6 card deck shoe, I was sitting in #3 seat of a 4 person game. Assume a fresh shuffle?


Not too many places allow resplitting aces, so be glad you were playing somewhere that did. Your seat position does not matter. The probability of this is the probability that the first four cards out of the shoe are aces, and the next four are tens, or (combin(24,4)/combin(312,4))*(combin(96,4)/combin(308,4)) = 1 in 4,034,213.

If seven players each get seven cards, what is the probability at least one person will get a 7-card flush?


The probability of a single player getting a 7-card flush is 4*combin(13,7)/combin(52,7) = 1 in 19491. The probability of at least one player out of 7 getting a 7-card flush is about 1 in 2785.

Could you tell me the odds when holding 3 and drawing 2 to a Royal Flush ? My wife and I will often throw away a high pair to draw 2 to a royal.


The probability is 1/combin(47,2) = 1 in 1081. In every game I have studied a high pair is a stronger hand than 3 to a royal, except in the game Chase the Royal.

I play at a local casino that offers a 6 deck, h17, DAS, DOA game. However, they pay 2-1 on a suited blackjack. How much does that reduce the house edge? How would you figure this out mathematically?


The probability of a suited blackjack in a 6-deck game is number of suits * number of aces of given suit * number of tens of given suit / number of 2-card combinations out of 312 = 4*6*24/combin(312,2) = 576/48516 = 1.19%. I assume a blackjack tie is a push, so the probability of a suited blackjack, when the dealer does not have a blackjack is 1.13%. Getting an extra half unit 1.13% of the time cuts the house edge by 0.57%. In this case the house edge goes from 0.62% to 0.05%!