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villain did open raise, but i don't find it as risky because of the runner runner. I heavily discount a flush here. When one hits the turn, and the straight lands on the river, I see lots of solo flush draws chasing one more bet only to hit the inconspicuous straight on the river. But, I see your point.
I am still going to work the math because I haven't tried this in a long time and I think it's close, but have no idea if it really is. So, here we go....
I am assuming villain in my hand is running 50/8/.6, but have no real idea....only that he was loose passive and tended to go to showdown when I glanced at his stats during the hand after SB folded out. Also, being in the BB, I will widen him out to start at 60% vpip, but could argue even more crap like 74s or 94s that doesn't show up in PStove.
After my flop bet, I assume he drops very little. Any clubs come, any pair comes, and I can't see him folding a pp. I don't think he raises a set...yet, or two pair....given his AF metrics. And, most passives wait for the turn to c/r 2pr+ anyway. So, I have his range at: QQ-22,AQs-A2s,KcQc,KcJc,KTs,Kc9c,Kc8c,Kc7c,Kc6c,K5s,Kc4c,Kc3 c,Kc2c,QcJc,QTs,Qc9c,Qc8c,Qc7c,Qc6c,Q5s,Qc4c,Qc3c, Qc2c,JTs,Jc9c,Jc8c,Jc7c,Jc6c,J5s,Jc4c,Jc3c,Jc2c,T3 s+,9c8c,9c7c,9c6c,95s,8c7c,8c6c,85s,7c6c,75s,7c4c, 65s,6c4c,54s,AQo-A2o,K8o+,K5o,Q9o+,Q5o,J9o+,T7o+. Obviously, I have this range crushed.
On the turn, I see a lot c/r'ing me. Yes, a lot of the bigger stuff is afraid to since the flush card hit, but I think we can rule some stuff out. I fold out some stuff like J5cc and AJ and TJ and sets because I think all of these holdings c/r me. And, I fold off pure crap now like K8o, etc. I can see alot of other stuff sticking around, especially hands like Q9o or even K9 with a club. Surprisingly to me, I still have this range crushed with the flush hitting because we know that any pair isn't going to fold and that brings along all the AX, TX, 5X combos of off-suited hands that took a flop. I just didn't think it would be that wide a margin.....82/18 fave.
River sucks for me. I am still way ahead, but this is where I think the hand gets most interesting. I drop to a 66/33 fave over the range that c/c'd a turn bet. It looks like a b/f scenario, but I just want to know what happens when I bet and get folds, bet and get raised, and bet and get called vs. checking behind.
If I check behind, I risk no raise and just either take the pot or save a BB. We are ahead of his range 66% to 33%. The pot is 6 BBs. We win 6 BBs 66% of the time for a net gain of 4 BBs. We lose 2.5 BBs 33% of the time, net loss of 2.5 X .33 = -.83 BBs. 4 BBs - .83 BBs = 3.17 BBs to the positive. Now, let's weigh that against b/f....
If I bet, I win when called by: Ahi pairs, 2pr, sets and some stupid shit...~170 combos
If I bet, I lose when called/raised by: Q's (including QQ), non-nut flushes (I was forgetting how many combos are affected by the A, J, and T of clubs being on board....significantly cuts flush combos)...~84 combos
If I bet, I fold off some weak pairs... ~84 combos
Taking all that into consideration, we have 338 total combos of hands in his range. 84 of which we lose to, which makes up 25% of the time. We invest a total of 3.5 BB's into the pot, multiply by 25% and we have a negative EV of -.87 BBs. 50% of the time we will win 7 BBs when called...EV +3.5. And, 25% of the time we will fold weak stuff off, and win 6BBs....EV +1.5. Combine those EVs and we have 3.5 + 1.5 - .87 = 4.13 BBs positive expectation on b/f.
Clearly, b/f was better, and it wasn't even close, if I did my math correctly....which I probably didn't.
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