So a friend and I are having an argument, he's a better player then I am and he says I'm thinking wrong here, but I don't get it.. Maybe I am?

Anyway, lets say on the turn my opponent has 8 outs and I have a bluff catcher.

Lets say the pot is 100bb for ease of math.

8/46 times he hits his cards, bets 65bb and I pay him off.

he wins 165bb 8/46 times for 165*17%=28bb

lets say when he misses, he bluffs 65bb 1/3 of the time. so 38/46=82%/3=27%
so 27% of the time I call is bluff and win 165bb for 165*27%=44.5bb

and lets say the other 82%-27%=55% of the time he misses and checks and I check behind and win.

Is it not profitable to check/call a turn bet and let him bluff the river? This is discounting the fact that he could already have a monster and I'm beat in which case he bets 65bb on the river and I pay him off anyway.

But either way, I cannot see why I would raise the turn to get him out of the hand.

Without calculating things in any kind of detail: If you get him to fold on the turn, you win the entire pot. Since villain wins the pot in some instances on the river, your river equity, not counting any value from the betting on the river, is smaller than the pot. So for it to be worth giving him the free card, you have to gain enough from the river betting to offsett this equity loss.

ok I really like this, I haven't thought about it this way, my thinking was more as follows, lets say the hand looks like this:

8,712 games 0.005 secs 1,742,400 games/sec

Board: Tc 7d 3h 3s
Dead:

equity win tie pots won pots tied
Hand 0: 78.260% 78.19% 00.07% 6812 6.00 { JsTs }
Hand 1: 21.740% 21.67% 00.07% 1888 6.00 { A9s-A2s, K7s, Q7s, J7s, T7s, 97s, 87s, 75s+, 63s, 53s, 43s, 32s, A9o-A2o, T7o, 97o, 87o, 75o+, 43o, 32o }


that's the stove vs. his tightest of ranges, this does not include any of his random bluffs like 56, q8, k9 and other random crap that he is capable of showing up with here..

taking those into account, and based on the assumptions, what do you think is the best turn move? Should I just call and let him bet again on the river which I believe he will do at minimum 30% of the time when I've still got him beat on the river, or should I raise which would basically push out all but 89 and his combinations of 3's and will basically have to fold to a river bet.

so roughly 80% of the time I win at showdown, but 30% of that 80% = 24% of the time he will bluff at this river (minimum) and I will call off his bluff..

since the 24%>21% he is to win the hand, doesn't it make sense to check and let him bet the river?

Or is that margin to small? or am i missing something?

Also assume his river bet is also 1/2 pot... with monster and bluff...

ok so going by your statement... and dealing with the 100bb + 65bb river bet...
and the poker stove calcs above...

if I just call the turn and he misses and bluffs 30% of the time I end up winning an extra 39.6bb -> I win about 80% of the time and he bluffs 65bb 30% of 80% = 24%->.24*165 = 39.6

if i just call and he ends up winning which happens 20% of the time for 165*.2=33

I end up making about 6bb more if I check the turn and the action takes places as described.

The question is, is risking the pot worth the extra 6bb.

Now, since by just calling the turn I give up ~20% in pot equity, and based on the calculations I only gain 6bb which is 6% pot equity it is a bad play....

correct?

If he's betting the river that often with nothing when no flush hits, you are ahead overall. But that situation quite artificial. In real play players have a made hand that beats your bluffcatcher more often than 0% when they bet the river. Maybe they're betting the turn to make you pay for flush drawing too.

You aren't risking the pot. You're risking the current pot to win a larger pot, the net result of which will be that you re 6BB richer, already counting the times you lose the pot. Hence it is a good decision.

That's assuming your maths is correct, and the action will take place as described.

Ok so I thought I had it right... assuming all things as described, it's more +ev to check/call the turn and call his river bet...

Thanks!

On the turn, he catches an out 17% and bluffs another 27%, so he's betting 44% of the time.

17% / 44% * +165 = +63.75
27% / 44% * - 65 = -39.89

If you always check/call on the turn, then his strategy will be +EV at that point.

If the turn didn't improve either of your hands, then on the river, if he bets, say, $150 when he hits and bluffs $150 1/3 of the time when he misses:

18% / 46% * +230 = +40.89
28% / 46% * -150 = -42.22

If you always check/call on the river, then he should check the river when he misses.

If you always check/call both the turn and river, then he can devise a +EV game-theory strategy.