#15
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Re: simple game theory question
With 2 players, there are 5 cards exposed at the river,
you see 2 additional cards in your hand, that leaves 52-7 =45 cards remaining. Your opponent could have one of 45*44/2=990 hands. If only 1 hand is the nuts, You can NEVER bet more than 989 times the pot, else you're guaranteed to be making a negative expectancy bet. 989 is an upper limit. If you have Kxs with a flush, 3 of your suit on board and none is an Ace, there are 7 ways your opponent could have the nut flush- A and any of the 7 remaining cards. In that case, he'll have the nuts 7/990 of the time so you can't bet more than 990/7 = 141 3/7 of the pot or you're guaranteed to be making a negative expectancy bet. If you bet 9 times the pot, and your opponent calls you less than 1/(9+1) of the time, you'll win money by betting anything. If you bet 989 times the pot and your opponent calls you less than 1(989 +1) of the time you'll win money, but he'll have the nuts at least 1/990 of the time if you don't have something like A of the suit to prevent this. If you bet over 1/(141 3/7) of the pot with Kxsuited and 3 of your suit on board, your opponent will call you 1(141 3/7) of the time and you'll lose money. - A. McIntire |
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