Quote:
Originally Posted by Game Theory Man
Ok, so to get %BB folds given SB folds, do I just need to write down the % BB would fold if it was folded to him after BT opened? Or do I need to make it like equation 2) where BB fold% * SB fold% is 'BB fold given SB folds'?
Not sure I understand your question.
Assume you have the following history of 100 hands when the button opened:
70 hands where SB folded and 30 hands where SB called
Of the 70 folded hands by SB, BB called 35 times, folded 35 times.
Of the 30 hands where SB called, BB called 10 times, folded 20 times.
Then,
Pr (SB folds) = 70/100 = 70%
Pr(BB folds | SB folds) = 35/70 = 50%
Also,
Pr(BB folds | SB calls) = 20/30 = 67%
Pr(SB and BB fold) = P(SB folds) * Pr(BB folds | SB folds) = 70%* 50%= 35%
Of course we get this result by just counting the 35 hands where both folded, but I wanted to write an equation consistent with the forms OP used, which was to have a fold probability for each player.
Note the possible dependence here, where BB is more likely to fold if SB calls (67%) compared to the folding chance when SB folds (50%).