Quote:
Originally Posted by ChrisV
That is super confused thinking. How often villain is bluffing is how you decide between c/c and c/f. You decide between b/f and c/c based on how often he calls worse when you bet vs how often he bluffs when you check. A higher chance of villain bluffing argues for c/c over b/f, once the decision is already made that you cannot fold the hand.
Let's say I tell you villain never bluffs and you decide what to do (either b/f or c/f, obviously never c/c). Now I tell you that actually, villain does bluff some arbitrary % of the time. You're now worried that villain will bluff you. This should NEVER change your decision to a b/f. Sometimes it was a b/f before and stays a b/f, because villain's call range is wide enough that that's still more +EV than c/c. Sometimes it changes your decision to a c/c (from either a b/f or a c/f). But it NEVER changes your decision from one of the other options to a b/f. So "because I thought villain may bluff" is never a reason to b/f, only sometimes a reason not to.
[Emphasis mine]
The bluffing frequency of V (along with some other factors) can turn a c/f into a b/f.
Case 1:
Let's say V has us beaten 50% of the time and bets a PSB. He never bluffs. We always fold to a bet and our EV is 0.5P (the 50% of the time he checks back).
If we bet 1/3 pot, he'll call (or raise) with everything that beats us and fold everything else. EV of betting is 0.5 P - 0.5 * 1/3P = 0.33P.
c/f is the better option.
Case 2:
Now let's increase his bluffing frequency to 25%, still with a PSB. He's now betting 50% + 25% = 75% of the time. The EV of calling the bet is now 0 (50% of the time we lose P, 25% of the time we win 2P).
EV of either c/c or c/f is 0.25P.
As in case 1, if we bet 1/3 P, V will call with all that beat us and fold everything else. EV for that is still 0.33P
b/f is now the better option.
Increasing his bluff frequency has turned our decision from c/f to b/f.
(This was adapted from No Limit Hold 'Em, Theory and Practice by David Sklansky and Ed Miller Concept 4: sometimes you should bluff to stop a bluff, p. 246)