8 Folds to the SB

[Gunther S.]

In a 10 handed game, if 8 players fold, do the chances that the SB has a good hand improve? If I were playing the BB in this situation, should I fear a raise more than at a short handed table?

[Lexander]

Depends on the players, but generally that the chances the SB has a better hand does improve in some way after 8 folds. Whether the improvement has any significance is something I am not prepared to say.

Assuming your opponents are not completely insane or just having a bad day, you have gained some information. For example, you can be fairly sure none of the players who folded has a hand such as AA,KK,QQ,AK.

If we define A as the probability that the SB has a certain set of good hands, and B as the set of hands in which 8 people fold, we can derive the conditional probability:

P(A|B) = P(A AND B)/P(B)

Now, the matter at hand is to determine if P(A|B) > P(A).

I might work backwords, and start with the probability that 8 people fold given the SB has a good hand, and use the simple form of Bayes Theorem:

P(A|B) = P(A)*P(B|A)/P(B)

So,

P(A|B) > P(A) if (P(B|A)/P(B) > 1)

Now, I am pretty sure that the probability 8 people fold is greater under the condition that the SB has a good hand. After all, if the SB has a good hand, there is less 'wealth' in the other hands and that should cause them to fold more.

Therefore P(B|A)/P(B) > 1, and P(A|B) > P(A).

Now, the only problem is how much info you gained. The SB has a higher chance of having a premium hand, but he might also be adjusting for the situation and your signal-to-noise ratio might be pretty low.

- Lex

[Gunther S.]

Interesting. I'd had a completely different concept in mind, but still can't figure out if it applies...

It comes from a statistics exercise illustrated in the old game show Let's Make a Deal. There were three curtains each with a prize. One of the curtains had a jackpot prize. Monty (the host) would ask a contestant which curtain they would like to choose. After making a decision, Monty would then reveal what was behind one of the two remaining curtains. The item revealed would not be the jackpot prize, but rather one of the two lesser items. Then the question was asked of the contestant: Would you like to stay with the curtain you originally chose, or switch?

What should the contestant do?

If you know this problem, then you know the answer. Otherwise I won't give it away.

But does the same principal apply if 8 people fold to the SB? I can't quite get my head around it?