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Ask the Wizard #8

I started playing poker with my friends once a week (five-card draw, stud, seven-card stud). We have seven players at the table. It seems to me the probability of getting the hands would be reduced dramatically due to the numbers of players being allocated cards from a 52 card deck. Do you have a mathematical formula that could direct me in the proper direction?

Tim from Santa Rosa, California

No, the probability of getting any given hand is the same regardless of how many other players are at the table. An unseen card is an unseen card, it doesn't matter if another player has it or it is still in the deck.

Great site! I am interested in your thoughts on card clumping. The theories I have read seem to have some merit in regard to the method dealers now use to pick up cards (naturals first, then breaks, and finally standing hands), and then insufficient shuffling of 8-deck shoes to fully mathematically randomize. This would seem to lead to a reduced probability of dealer busting, thus breaking down the Basic Strategy odds. Keep up the great work!

Bob from Hooksett, New Hampsire

I haven't studied card clumping, but in my opinion it is not a legitimate advantage play. I have never known a professional gambler or writer I respect to give card clumping any respect.

I noticed on your page for Three Card Poker you advise to stay with Q/6/4. A dealer in Tunica told me Q/J. Why the difference and is the Q/6/4 suggestion based on actual computer generated odds? Seems a pretty good game with low house odds, no skill involved. What do you think?

Weintraut

I have no doubt that Q/6/4 is the optimal strategy for three card poker. Stanley Ko independently came up with the same advice. This strategy is based on a computer program which analyzes all 22,100 possible combinations of the player’s three cards and for each one the remaining 18,424 possible combinations of the dealer's three cards.

If you follow the dealer's strategy, then you will be folding on some hands which have an expected return of more than -1 (the return by folding). Overall, however, it shoudn't make a big difference.