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OPP pots the river, laying 2-1. I hold a bluff-catching type hand--middle pair or something. I believe OPP's value-betting range that beats me is X, and it contains let's say 40 combinations. As I'm getting 2-1, OPP would need to be bluffing with ~13 combinations (33% of his v-betting range) for me to be indifferent to calling or folding. If, by my estimations, he would bluff less than 13 combinations then I should fold; if I estimate he could be bluffing with more than 13, I should call.
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Close, to make you indifferent between calling and folding he'd need to be bluffing 20 combinations, so that way he'd be betting 60 total combinations, 1/3 of which would be bluffs... you're getting 2:1 odds and you're indifferent between calling/folding when his ratio of value bets to bluffs is also 2:1.
On a bit of a tangent on the application side, even if we pick out 20 hand combinations the opponent may bluff with, usually we wont think that the opponent will bluff those hands every time that he gets them. If there are 40 combinations he'd bluff but he'd only bluff with them half the time then we weight each of those 40 combinations by a half and there are effectively only 20 combinations so we're again indifferent. I examine this more fully in my post here:
http://forumserver.twoplustwo.com/showfl...&PHPSESSID=
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Ah yeah, good point on the 40-20 issue. I guess the simplest way to figure that out at the table is just to divide the v-bet combinations by the first number in pot odds? OPP bets pot with what you think are 60 combinations, then he'd need to bluff with at least 30 to be indifferent (2-1 pot odds). 1/2 pot with 20 v-bet combos is ~6 bluff combos (3-1), etc.
Thanks for the link, I'll check it out.