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Ask the Wizard #87
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
|4 of a kind||25||38040380||0.000002||0.000048|
|3 of a kind||3||12510891616||0.000628||0.001883|
|Jacks or better||1||334574728656||0.016785||0.016785|
A 4% commission lowers the house edge by 0.29%.
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.
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%.
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.
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.
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.
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%!