Discount outs for prob of others holding cards?

[eyeski]

Technically, don't you have to discount outs by the probability of the cards being out already?

[EnderFFX]

Only if you have a correct read on an opponent and know what he has. If you do not know what an opponent has you cannot discount outs because you think there are probably some outs in other peoples hands.

[Veloso]

If you're in a situation where you are almost certain what your opponent has, then you do have to discount some of your outs. Here's a heads-up HE example. Before the river, if you have Ax off, the ace matching three suited cards on the board, then there are 9 suited cards that can give you the flush on the river out of 46 unaccounted for cards. Probability of hitting is 9/46, odds are 1 to 4.1111.

But if you have a confident read that your opponent has a made lower flush, then you can no longer count two of those nine outs. Keep in mind, though, that this means there are only 44 cards unaccounted for from your point of view. Your probability of hitting becomes 7/44, or 1 to 5.2857.

If you've got no idea what your opponent is holding, then, no, you don't discount outs by the probability of the cards being out already. This is because the mere fact that your opponent holds two cards doesn't give you any information. If you don't believe that, do this thought experiment: Take your opponent's two cards, put them back into the deck of 44 cards, and shuffle them all together. Now deal two cards back into your opponent's hand. Since you didn't know what he had before, you don't know what he has now, the odds of you hitting an out now are the same as they were before. You can reshuffle as many times as you want, but the situation remains the same. There are 46 random cards, 9 of them help you, so there's a 9/46 chance that the card on top of the deck helps you.

[Shawsy]

Technically, yes. But this is difficult to do because you usually don't have complete information.
There are a few situations where this could come up though. Say you hold A[img]/images/graemlins/heart.gif[/img] and some other card that is not a heart, but there are three [img]/images/graemlins/heart.gif[/img]s on the board. If you are certain that your opponent has a made flush, then you could discount your outs to 7 rather than 9 to make the nut flush.
Of course, your opponent (or someone else in the pot) could have a set, so what do you do when you catch your flush but the board pairs?? Incomplete information makes it tough to accurately discount outs, but you will see some discussion of discounting outs, or fractions of outs, to take into account situations where you make your hand but still lose.

[eyeski]

I guess I'm talking more about Bayes Theorem kind of stuff. If you have all ten people in a pot, there is a probablity that one or more will hold an A (or any other card for that matter), so if you think you have 3 outs to hit an A, in reality it's less than that since the probability of someone else holding one of your outs is more than zero.

[DPCondit]

[ QUOTE ]
I guess I'm talking more about Bayes Theorem kind of stuff. If you have all ten people in a pot, there is a probablity that one or more will hold an A (or any other card for that matter), so if you think you have 3 outs to hit an A, in reality it's less than that since the probability of someone else holding one of your outs is more than zero.

[/ QUOTE ]

You are saying that they are more likely to hold an ace "or any other card for that matter". If they are just as likely to be holding any other card as to be holding an ace, then that tells you nothing about what they are holding. If you know nothing about what they are holding, then it has no impact on your outs, it is the same as if the cards were still in the stub. If 9 tight opponents are seeing the flop this hand, that is quite different (and would be pretty rare), and that would tell you something about your outs, but if they are just as likely to be holding any random cards, then it has no impact whatsoever on your outs.

Unless you have very specific information about what kind of hands your opponents play, and unless there is a significant deviation from the normal number of callers, or you are against an opponent, and you know exactly what he has, then your outs are unchanged and unaffected.

Don