[Nick C]

[ QUOTE ]
I think we can all agree that the best turn line is b/f

if we get called on the turn it leads to a more interesting river decision. the PPs that we can get value from are outweighed by the ton of Ax combinations that a LP can have, plus he will sometimes be slowplaying a monster like trip Ts.

messing around with stove I think we have around 30% equity on a brick river. also I don't expect villain to value bet any of the hands we beat after we check to him. I do think that he'll probably VB every hand that beats up unless he can show up with KK

the pot size will be ~7BB, so if villain is bluffing more than 1/8 of the time (7 times we lose 1BB, 1 time we win 7BB = breakeven) we should be calling. 1/8 is 12.5% of the time.

so if we expect villain to bluff less than 12.5% of the time we should c/f. if we expect him to bluff between 12.5% and 30% of the time we should b/f because we lose less on that river bet. if we expect him to buff more than 30% of the time we should c/c.

does that look right?

[/ QUOTE ]

In this scenario, we have no good options at all (our hand is simply worst too often, and we have no folding equity) and the whole exercise is about limiting the damage. But sometimes that's all you can do, so here goes . . .

In a pot that's 7 BB big after a river bet from Villain (which is about right, especially after taking the rake into account), his theoretically optimal bluffing frequency is to have the best hand 7 out of 8 times that he bets. This means that if he's betting the best hand the full 7 out of 10 times that he has it, he should theoretically bet 1 out of his 3 losers for balance. And if he does this, all we can do is either bet-fold or check-call, depending on how many of those 30 losing hands Villain will actually call with (if he'll call with more than 1/3 of them and will never bluff-raise, then bet-folding is the best play). The reason check-folding is bad (in this scenario) is that the bet we "save" by folding the worst hand those 7 out of 10 times is wiped out by that 1 time in 10 that we fold the pot away, and meanwhile we never win a river bet with a check-fold and also never snap off a bluff.

As Villain's bluffing frequency decreases, bet-folding becomes more attractive (check-calling is now bad), but at some point this play becomes inferior to check-folding. (If Villain would always call with his losing hands, then check-folding would overtake bet-folding when Villain started betting less than roughly 6.67 of his 30 losers. But having him always call with his losing hands does seem unrealistic, so for practical purposes that 6.67 cutoff point must be at least a little higher.)

As Villain's bluffing frequency increases, the case for check-calling starts improving. Nevertheless, if Villain were calling 100 percent if we bet, check-calling would never be superior to betting.

Er, basically, I guess I'm saying you haven't really provided enough information to work out the scenario. We need to know how many of those worse hands Villain will call a bet with.