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Cbet Alternative w/ Air
I've been thinking about cbets oop against aggressive villains. http://weaktight.com/444069, for example. I decided to do the math. I figured to work out the math here to let noobies see how the analysis works and FTR regs critique.
Situation: Hero PFR's for 3.5 bb's, gets 1 caller, flops air (8.5 bb pot). Opp has very aggressive flop stats. Hero check/raises.
Question: How often does Hero need a fold to make this +EV?
Assume a 6 bb flop bet from villain and a 15bb raise from Hero. When villain rr's, Hero folds and loses 15bb. When villain calls the c/r, Hero tries to not commit any more chips. He's likely behind, and probably loses 15bb. When villain folds, Hero wins 14.5 bb's. There's a chance villain could check behind, in which case Hero has to play a dog of a hand against what is likely a dog of a hand oop. So that costs a couple bb's.
That math is easy enough - Hero only needs a fold about half the time for it to be +EV if he could guarantee he would never commit more chips after the check/raise attempt failed to end the hand.
But call it two-thirds to have some margin for error. Hero will certainly lose a bit more than he wins when he commits extra chips after a check behind or bet/call from villain (position + no hand).
But from a game theory perspective, it's not enough for an action to be +EV. It must be higher EV than all other +EV actions. Well, the only other alternative is for Hero to cbet (or check/fold every time he misses a flop oop). Against aggressive villains, the auto-cbet will induce a fold when Hero is ahead and get a call/raise only when villain is ahead. The cbet encourages/rewards good play from villain. It does have the advantage of being less expensive, but it's probably only +EV because players are so bad at 10nl.
So my final analysis is this. If I can check/raise successfully about 2 out of 3 times, I'm ++EV even if I commit a few chips after being called every now and then.
The villains don't really pay attention at my level. If they ever did start paying attention, I would need to mix things up by playing some 2 pair/set hands this way for balance.
So, I'm liking this. I've tried it about 20 times in the last two weeks, and I've been successful on 16 or 17 of them. If I can pick spots that successfully, then I've got a nice alternative for when I have aggressive players to my left. I use this with small pp's and 2-3 overs and when I have 2 overs. The key is a super-aggressive villain. In the HH link above, villain's flop aggression factor was 16 (bets/raises 16 times more often than he calls). So I'm pretty certain he'll rr/shove when he's ahead, and fold weak one pair hands and worse.
Sorry if this wasn't very clear. I'm tired. I played my 500 hands, did my studying, and posted this. So I'm off to get some sleep. Hopefully it makes enough sense for someone to benefit. I did.
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