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Originally Posted by jesse8888
Doesn't all this "math" ignore the fact that when I'm behind (and pretty much exactly when I'm behind) more bets are going to go in? It's sure starting to "feel" pretty close to me.
At some level, yes. At another level, not quite. It all depends on how you see things playing out. As the hand ranges get smaller, small changes in assumptions can have significant impacts on the calculations involved. And depending on how optimistic or pessimistic those assumptions are, you can get vastly different conclusions.
Let's say you cold-call the turn. There are basically two primary scenarios you're thinking about.
C1) UTG calls. River action is check-bet-call.
C2) UTG 3-bets. Expected action is call-call, bet-call-call.
I think turn capping is pretty rare, so I'm not really giving it much consideration.
If you 3-bet the turn, there are another two scenarios that you're thinking about.
R1) Someone caps. It doesn't matter how this plays out. One bet is going in on the river.
R2) Nobody caps. You're also getting one bet on the river.
So with these four scenarios:
C1 -- You win with high probability.
C2 -- You win with moderate probability.
R1 -- You win with moderate probability.
R2 -- You win with high probability
Now let's look at how many bets are going into the pot on the big streets:
C1 -- 9 BB
C2 -- 12 BB
R1 -- 15 BB
R2 -- 12 BB
At this point, it's impossible to proceed precisely unless you have exact winning probabilities.
But intuitively, If calling/raising both led you to the same winning frequency at showdown, raising is clearly better because you win bigger pots on average and you win at the same rate.
So the question is how less frequently you win when you 3-bet. Including *ALL* sets gives you something like a 36% win. Excluding baby sets gives you something like a 60% win. Your calling win% is probably closer to 60%, but how far off does it drop if you 3-bet? Down to 50%? 40%?
To take this to the next level, you can calculate the two-variable EV for both calling and raising based on assumed win percentages. You can then see how the balance of the probabilities impacts the EV.
Quote:
So yes on the whole I feel like I'm in good shape until exactly one more raise goes in, at which point I am in pretty bad shape.
Maybe try coming up with numbers for C1, C2, R1, and R2 above. Who knows whether or not they're real, but it would at least give you a concrete number to play with.
My intuition (which could easily be wrong) is that I do better driving the action on the turn (bigger pot size, slightly smaller win %) than I do calling on the turn and watching UTG shut down (smaller pot size, slightly larger win %).