Texas Hold'em Club's odds
July 30th, 2016 at 11:35:46 AM
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The other night at my local eagles club I called my opponents all in with 9,7 clubs & 2 clubs on flop. My opponent had pocket K's & the K of clubs. There were 8 players playing at that time. The turn was a club that gave me a flush, got trumped by a club on the river. What are the odds with that many people at the table of a club on the river?
July 30th, 2016 at 12:11:39 PM
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We know the values of 8 cards (your two, your opponent's two, and the four up cards); six are clubs (your two, the opponent's one, the two on the flop, and the one on the turn.)
That leaves 44 cards, each of which is equally likely to be the river card; seven of these 44 are clubs.
The probability of a club on the river = 7/44, or slightly worse than 1 in 6. Note that you are more likely to get a club on the river in this case than you are to throw a 5 with two dice (that is, the sum of the dice is 5).
Note that the number of other players is irrelevant; even in heads up, it would still be 7/44. You might be able to make some assumptions as to how many clubs were in the other 12 hole cards based on how they were played, but I chose not to do so.
That leaves 44 cards, each of which is equally likely to be the river card; seven of these 44 are clubs.
The probability of a club on the river = 7/44, or slightly worse than 1 in 6. Note that you are more likely to get a club on the river in this case than you are to throw a 5 with two dice (that is, the sum of the dice is 5).
Note that the number of other players is irrelevant; even in heads up, it would still be 7/44. You might be able to make some assumptions as to how many clubs were in the other 12 hole cards based on how they were played, but I chose not to do so.
