In a game with 8 players where 6 fold, two players went all in pre flop, one had JJ and the other had KJ. I know JJ means that you are ahead before the cards are played and the probability of winning is around 66%, I am wondering though whether this probability should differ at all given that there were 6 other hands dealt out? That is, does the 66% figure refer to a heads up situation, or is it independent of the number of cards left in the deck?
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The question is depended on game type, I guess your talking about hold'em however the answer would be very different for stud poker.– JonCommented Nov 21, 2014 at 21:52
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Probability is a measure of information. All that matters is which cards are known and which are unknown. Their physical locations, whether they are dealt or undealt, etc., doesn't matter.– Lee Daniel CrockerCommented Dec 9, 2014 at 8:28
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2 Answers
Assuming you know nothing about the cards dealt, they don't matter, so the 66% holds up. In most calculations we would just ignore the folded cards since we don't have any definite information about them. If you want to factor them in, you can no longer calculate your exact pot equity, since you don't know how often your opponents are folding hands like Ax, KT, and K9, (and this would also depend how the betting played out preflop).
You can infer that the probability of any of your opponents having had hands like AA, KK, QQ, AK, AQ is slim, so you can expect there to be a very slightly increased probability of A's, K's, and Q's appearing on the board than you would expect if you had no additional information. This means that the KJ has a slightly increased chance of hitting a straight, however this will have a pretty small impact on your probability of winning with JJ. In fact, hitting his straight will allow you to chop if he has paired his K, so the improvement to his hand by factoring in the folded cards is even smaller.
It is almost always the case that factoring in the folded cards will have a very small impact on your pot equity, and it is impossible to measure exactly unless your opponents are playing like robots and you know their exact hand ranges. For these reasons, it is usually impractical to do so.
The short answer is that the other cards don't matter? Why, because the cards are just as likely to have been folded, as they are to still be in the stub of cards to be dealt out. You can't differentiate the cards in that way, so you don't need to account for them in any special way.
