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Continuing my previous example
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I wanted to point out a few things about our potential c-bet here. What does this bet accomplish, specifically versus each part of villain's range? Ceteris paribus:
A range: will never fold
B range: not likely to fold, but still might; we'd be folding a better hand
C range: the top half of the C range will fold with some (probably low) frequency - and again we'd be folding better. Some hands in the lower half are behind ours (the A-high gutshots and 76) and we'd be folding worse.
D range: mostly behind our range; we'd be folding worse.
We learn very early on that there are three reasons for betting. One, to get value from worse hands; two, to get better hands to fold; and three, to capitalize on the dead money in the pot (i.e. getting our villain to give up their equity). It's also said that the third reason - capitalization of dead money - is never proper justification for a bet on its own, but rather a sweetener that makes up for the thinness of one of the previous two reasons.
C-bets generally rely on this third reason as an extension of betting to 'fold better'. But in situations such as the hand in question, our hand actually has some very weak showdown value that might be relevant in a small-pot scenario such as this... So where is the utility in betting?
We've already shown that the majority of our villain's range is behind ours, all else being equal. Accordingly, we can assume that the times our c-bet is "successful" -- i.e. the villain folds to it -- we are likely just having our opponent fold a worse hand. But we aren't betting to fold worse hands, are we?
What's worse, by betting now we forgo the opportunity to induce any sort of bluff on the turn or river from the air range of our villain that, regardless of whether our AJ high is ahead, will likely fold to continued aggression i.e. a call on the turn and then betting when checked to on the river.
What it all boils down to here is that our c-bet is mainly designed to force some marginally better holdings to fold. Given the board texture, these holdings consist largely of better aces (AK, AQ only), some weird low-pair aces (A4, A3), and low pocket pairs (88 and under, excluding 44/33); and all this is assuming that these holdings would actually fold to a c-bet. All we have to gain from folding out the "worse" portions of our opponent's range here is the equity in the pot that is sacrificed when they release their hand, which isn't really significant, especially when we can either win at showdown or even sometimes induce a bluff from worse if we check behind on this street.
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Math of a c-bet
We need our c-bet to work (Bet / Bet + Pot) % of the time in order for it to be profitable. Assuming a 2/3 pot c-bet, we have:
[(2/3) / 1+(2/3)] = 40%
This is all well and good. How does this compare to the proportion of our villain's range that may fold to a c-bet, and how often are we actually folding worse?
A: 99(3), 44(3), 33(3) = 9 combos
B: JJ(3), TT(6), A9(9), K9s(3), Q9s(3), J9s(3), T9s(3), 98s(3), 65s(4) = 37 combos
C: 88-55(24), 22(6); A4s(2), A3s(2), A5s(3), A2s(3), 76s(4), AK(12) = 56 combos
D: All else -- AQs-ATs(8),A8s-A6s(9),KTs+(11),QTs+(7),JTs(3),87s(4),AQo-ATo(25),KTo+(33),QTo+(28) = 128 combos
Total = 230 combos
A never folds; B folds only with a very low frequency (say 15% rounded to 6 combos); C will fold say 32 of 56 combos (all but the pocket pairs from 88 to 55); and D will fold the majority of the time, occasionally floating some overs - for the purpose of this example we'll say about 85% of the time or 110 combos.
So under these assumptions, our c-bet folds 148 of our villain's 230 combos for a success rate of about 64.3%.
How many of these 148 combos are actually better than ours, though?
We have 6 combos from the B range that we said would fold (but even this seems overly generous), as well as 22 combos from the C range (we said 88-55 would call, so the only 'better' hands that are folding are 22, A4, A3 and AK). From the D range, all that's better than us here is AQ for a total of 12 combos.
Based on this, we fold 6+22+12 = 40 combos that are better than A , J . So, when our villain folds to our c-bet, he is folding worse 73% of the time.
(As an aside, I'd like to point out that I don't think folding worse is some kind of cardinal sin that should be avoided at all costs. Of course we gain when our opponent forfeits his equity in the pot, and each of the "worse" combos at least have some equity to speak for. I'm really just trying to illustrate the point that folding worse is not the primary intention of a c-bet.)
This probably seems like a very long-winded way of saying that it makes little sense to c-bet a dry board with high cards when you're typically way ahead of your opponent's range. But there are other factors that work into this as well.
We worked out that our c-bet is successful 64% of the time assuming our villain never bluffs. But what if he does bluff here, with some frequency - or what if he calls our c-bet, and then leads out for a 1/2 or 2/3 pot-sized bet on the turn?
Clearly, we cannot continue to a raise on the flop (I feel we would need reads to 'play back' at our villain, otherwise we'd be re-raising simply for the sake of doing so), and we will likely fold on most turns when he leads out.
Note that earlier, I said that we could get value out of our villain by getting him to bet worse holdings on the turn, and I'm now saying that we would fold to his turn bet unimproved. The difference between the two situations is that his range would be much stronger if he first called our c-bet rather than if we simply checked behind and he decided to bet any turn.
Given the board texture, a thinking opponent will probably bluff raise or otherwise continue some percentage of the time. We needed our bet to be successful 40% of the time, and based purely on combinations we found that he would fold over 64%.
Let's add in another assumption to keep things (hopefully) simple. If our opponent plays straightforwardly with the A and B portions of his range (and still folds 10% of his B-range as stated earlier), and now decides to bluff raise 1/4th and float another 1/4th of his garbage.
Our calculation is now:
74 / 230 = 32%
and our c-bet is unprofitable. Some of the time when our villain floats, we'll improve to top pair and we may or may not end up winning a larger pot, so this percentage is offset somewhat; but likely still not often enough to make it a profitable play.
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So, therein lies the argument for forgoing a c-bet. I seem to have gone off on a bit of a tangent, and I doubt anyone is actually going to read all this but I felt it was a worth exercise.
I'll continue analysis of this hand -- with <gasp> a turn, and possibly a river card to come -- at a later date.
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OP: 25NL to life
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Originally Posted by XxStacksxX
($1.60, 2 players)
