When playing against opponent, the board comes for example J99, on turn is another J, then we assume that the opponent has lower chance he's holding J because it came also on turn so he probably doesnt have J, which is good. Why do we assume that, how to rationalize that? Thanks.
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1The turn would be the 3rd J. If a 4th J comes up on the river you can be sure they don't hold one.– paparazzoApr 18, 2016 at 16:21
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3 Answers
Before the flop, there were 47 cards you didn't know the location of, three of which were jacks. On that information and nothing else, the probability that your opponent holds a jack is about 12.5%. When the jack turns, there are now 46 unknown cards, two of which are jacks. On that new information, the probability that he has a jack goes down to 8.6%.
But that's just a good first guess given no other information. If he calls the flop and raises you on the turn, I would increase your estimate quickly. :-)
answered Apr 20, 2016 at 20:59
Actually, you cannot say "there is a second J on the board, so the probability that the opponent holds a J is lower". If you're saying so you're doing poker wrong. Mathematically speaking, out of the context - yes, the probability is lower than before seeing the J. But unfortunately when you play poker you cannot build your probability estimations only on the cards you see. You must go deeper.
According on the opponent profile and the preflop and flop actions you estimate the range of hands he plays. A good example: the opponent is very tight, he's the initial aggressor preflop, he misses his cbet and calls your bet vs missed cbet. Before you see the turn you can say that his range includes QQ+ and all the well kicked jacks.
The exact probability that the opponent holds a jack is rather irrelevant at this point in the hand, without considering things like how the hand has gone down to this point. If the player had just cautiously called a bet on the flop then check raises the turn you can give him a higher probability of holding a jack for example.
The fact that two of the jacks are on board of course means there are less jacks for player to hold, but that is really not a consideration when your trying to figure out if an opponent holds a jack.
