Another Ace on the turn

[BruceZ]

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The probability question is controversial and requires a lot of hair-splitting to answer.

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It should be made clear to the OP that as a practical matter, there is no controversy here, and this issue is very, very basic. The probability that you should be using to make your decisions absolutely changes when the ace appears, unless you were 100% sure that your opponent had or did not have an ace on the flop. This comes directly from Bayes' theorem. Those who stated that we should not recompute our probability in light of additional information are completely wrong, and they will lose money to those who do take all additional information into account. There is nothing subjective about that.

The definition of probability issue that Aaron has raised here is a philosophical one that applies to everything that we compute in poker, not just to the type of hand in question. For example, if we have 9 outs on the flop, we say that there is a 9/47 probability that we will make our hand on the turn. The fact that the shuffle has already determined which card will be the turn card does not make the probability 0 or 1 from our point of view. The probability that we calculate always depends on the information that we have when we compute it. This can be different at different times, or for different people at the same time. This raises deep philosophical issues about the definition of probability which has given rise to different branches of statistics, but as interesting as this may be, it has no bearing on the answer to your question regarding whether you need to recompute your probabilities when the ace appears on the turn.


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The only difference in your example is that someone has seen the hand, and you can make additional inferences based on her actions.

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But not the inference that he is a her.


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For example, the fact that she saw the flop raises the chance she has an Ace to maybe 40% (depending on the game and the player, of course) because people are more likely to stay in with Aces than other cards.

If she looked happy and raised after the flop, that's more evidence for having an Ace. It might even cause your belief she has an Ace to increase from 40%, despite the fact that with an unseen hand the Ace on the flop caused the probability of an Ace in the hand to go down.

If she laughs and claps, "A set! I'm all in!" when the turn card comes, that would also influence your estimate (which way depends on how big an idiot the player is).

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5 more times Aaron, just because I complained about it? You are just a grammar terrorist. [img]/images/graemlins/laugh.gif[/img]

[AaronBrown]

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Its no surprise that you ave effectively summarised my dilemna.

I feel that our subjective belief that opponent has an ace might increase/decrease in different cases, as a result of the ace, and the consequent action.

Wud it be fair to claim that without information of the resultant action, we cannot claim any change in our subjective beliefs??

--Is this a question that actually belongs somewhere in the psychology or mebbe poker theory forum?

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To answer the last question first, this belongs in the probability section, it refers to the basic meaning of probability.

For the first question, the nice thing about subjective beliefs is you can change them whenever you want, with or without evidence. But I think the Ace on the turn should definitely influence your estimate of the likelihood of another player holding an Ace.

To simplify a bit, let's assume the player always bets on Ax, any pair and nothing else. You hold KQ. There are 190 Ax hands (including AA) and 66 pairs (not including AA). So there's a 74% chance she has an Ace.

The flop turns up A72. Now there are 135 Ax hands and 60 pairs, so there's a 69% chance she has an Ace.

With the Ace on the turn there are 89 Ax hands and 60 pairs, so there's a 56% chance she has an Ace.

All this ignores any inference from her action on the flop and turn.

[uphigh_downlow]

Many thanks to everyone who gave their input.