Probability Falicy

[PITTM]

It seems to me like many use odds incorrectly when playing poker. If one finds the odds of someone having an ace high flush over their king high flush with 4 of a suit on the board in hold em for example, on thinks, well, there are 46 cards i havent seen and so there is a small chance that he has the ace, but if he didnt have the ace would your opponent be playing at all? There may be a 1/23(2/46) chance that they have the ace, but if theyre betting hard late with an obvious flush on the board, the probabilities seem to go out the window a bit, am i correct? Of course the probability is a guideline for the frequency of a given card to come up, but your opponents play must factor in much more largely than those 1/23 odds that he has the ace he needs. Can anyone agree/disagree/set me straight on this one?

rj

[Im Just A Bill]

I would tend to agree. Poker play is only partly mathematical. Probabilities should (IMO) only be used as a guidline for understanding what is likely or unlikely to occur. With this said, it is at least as important, if not more so, to understand your opponent.

Still, if you are into numbers, it is still fun to talk about the odds whether it actually gets you anywhere or not.

[pzhon]

[ QUOTE ]
There may be a 1/23(2/46) chance that they have the ace, but if theyre betting hard late with an obvious flush on the board, the probabilities seem to go out the window a bit, am i correct?

[/ QUOTE ]

It sounds like you want conditional probability.

[img]/images/graemlins/spade.gif[/img] Start with a probability distribution.
[img]/images/graemlins/heart.gif[/img] Reweight the possibilities based on the information observed. For example, throw out hands that would never play that way. Decrease the probabilities of hands according to how unlikely it would be for that hand to have the observed actions, e.g., not folding preflop.
[img]/images/graemlins/diamond.gif[/img] Renormalize to get a conditional distribution.

If someone represents a big hand, you could consider all of the possible hands, and estimate a probability that someone in that position would play the hand as you have observed.

Suppose you are playing no-limit hold'em with deep stacks. UTG limps, you raise as UTG+1 with KK, and everyone folds to UTG who reraises all-in, 10 times your bet.

[img]/images/graemlins/spade.gif[/img] A priori, AA and QQ are equally likely. Another KK is only 1/6 as likely a priori, since you hold two of the kings, eliminating 5/6 of the possible pairs of kings.

[img]/images/graemlins/heart.gif[/img] Would AA limp preflop UTG? Sure, depending on the player and game. Maybe you feel it would happen 70% (made up) of the time at that table, as opposed to raising. Would QQ limp? That is much less likely, as QQ wants to avoid letting Ax and Kx see the flop. Maybe you feel it would happen 10% of the time.

Would AA respond to your raise that way? Would QQ? Each may have more profitable actions; suppose QQ is twice as unlikely to reraise all-in.

[img]/images/graemlins/diamond.gif[/img] Put together, you may estimate that it is 14 times more likely that the limp-reraise all-in was AA than QQ.

The mathematics agrees with common sense. It is useful to know how likely there is an Axs out there (step [img]/images/graemlins/spade.gif[/img]), and this is just one step in estimating a distribution of potential hands. Information from later betting should be combined with the prior distribution rather than replace it.

[PITTM]

So tonight i'm big blind with KD-9D at my house game, which is no limit. The flop is 2d-4d-6d. I check to see where everyone is at, everyone checks, the turn is a 7c. There are 4 of us still in the hand, the small blind goes in, i think hes bluffing (what are the ODDS he has AD-XD?) so i reraise all in(i had about 12 bucks, he had about 7), next guy folds, next guy calls, and lays down AD-10D for the nut flush, the odds blew it and i was too busy reading the wrong guy to think about that. The 1st all in had the high pair with no kicker, so at least i got the side pot(the winner started with 6 dollars) not that bad, but a lapse in concentration and an overemphasis on odds blew it for me.

rj

[daryn]

the guy will not have the A high flush often enough to make it not profitable i think. he could have a set, or could be on a bluff with just the naked ace. you have to call this i think.