Ask the Wizard #184

The probability of exactly 6 correct is combin(10,6)×0.2⁶×0.8⁴ = 0.00550502.

The probability of exactly 7 correct is combin(10,7)×0.2⁷×0.8³ = 0.00078643.

The probability of exactly 8 correct is combin(10,8)×0.2⁸×0.8² = 0.00007373.

The probability of exactly 9 correct is combin(10,9)×0.2⁹×0.8¹ = 0.00000410.

The probability of exactly 10 correct is 0.2¹⁰ = 0.00000010.

Adding the probabilities for 6 to 10 correct, the probability of at least six correct is 0.00636938.

No.

I’m not an attorney, so I’ll refrain from giving an opinion on the legality. For practical purposes checks from Internet casinos and sports books are sent from generic accounts, usually out of Canada. From looking at the checks you wouldn’t know whom they are from. I have never once heard of a bank not honoring such a check (unless it bounced), or anyone being prosecuted for attempting to cash a single check. So, my advice is go ahead and cash it. You should do so inside with a teller, because some banks don’t like foreign checks deposited in an ATM.

I hope you’re happy, my computer spent five days cycling through all 464 billion possible hands in Omaha. Here are tables for both the high and low hand. For the benefit of other readers, in Omaha the player gets four cards to himself and five community cards. He must use exactly two of his own cards and three community cards to make the best high and low hands. For the low hand, straights and flushes do not count against the player, and aces are always low.

I agree with your hypothesis, that they pulled out the Quartermania machines and rolled the progressive jackpot into Wheel of Fortune. It can't be a coincidence.

The reason the strategy changes, according to the number of cards in your hand, as shown in appendix 18, is that every card that leaves the deck changes the probabilities of every card left to be played. A good example is the single-deck basic strategy says to surrender 7,7 against a 10; but for any other 14 you should hit. The reason you should surrender is half the sevens have already been removed from the deck. You need another seven to make 21, the only hand that will beat a dealer 20. So the shortage of sevens lowers the expected value of hitting to under half a bet, making surrender the better play.

In an eight-deck shoe there are 416 cards. That may seem like a lot, but 16 against a 10 is such a borderline hand that removal of just one card can making standing a better play. The rule is that for eight or fewer decks if your 16 is composed of three or more cards, and the dealer has a 10, then you should stand. In a two-card 16 the average points per card is 8, with a 3-card 16 the average is 5.33. With more small cards out of the deck in the 3-card hand the remaining deck becomes more large card rich, making hitting more dangerous, swaying the odds in favor of standing.

$10,000. A cash transaction of more than $10,000, whether in sports or not, will necessitate a CTR (cash transaction report). You may also ask to be paid in chips, although the same CTR would be generated if and when you cashed them in.