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 Originally Posted by MadMojoMonkey
OK, so here I've got 3 ranges for Villain's response to 3-bet.
b/b 2.56% { QQ+,AKs,AKo }
b/c 17.8% { JJ-22,AQs-A2s,KTs+,QTs+,JTs,AQo-ATo,KTo+,QTo+,JTo }
b/f 5.73% { K9s-K8s,Q9s,J9s,A9o-A8o,T9o,98o,87o }
total betting range is 26.09%
FT3 = 5.73% / 26.09% = 22%
Call3 = 17.8% / 26.09% = 68%
4-bet = 2.56% / 26.09% = 10%
From here, I'm not really sure how to best go about determining exactly what hands to place in our ranges, and with what frequency we should be taking each action.
Given he 4bets such a tight range, and isn't bluffing, we need ~45% equity to shove over a 4bet, which only KK/AA has against his stackoff range. Shown by this math:
Ev[shove] = (equity)(total pot) - (amount shoved)
0 = X(201.5) - 91
91 = 201.5X
X = 0.45
So while 3betting hands like QQ/AK will be incredibly profitable given how often villain calls with worse, shoving those against villain's narrow 4betting range would be incorrect.
Since we know our 5b shoving range {KK+}, we should try to find out what hands we can profitably 3bet. Now this is where I have no real clue on how to do the math. My best guess is something like:
Villain folds 22% of the time, we win the 4.5bb pot = 0.22 * 4.5 = 0.99
Villain 4bets 10% of the time, we lose our 3bet = 0.10 * -9 = -0.9
Villain calls 68% of the time (anyway to actually calculate this?)
So:
Ev[3bet] = (%fold)(Evfold) + (%4bet)(Ev4bet) + (%call)(Evcall)
0 = (0.22)(4.5) + (0.10)(-9) + (0.68)([X](19.5) - 9)
0 = 0.99 - 0.9 + 13.26X - 6.12
6.03 = 13.26X
X = 45.5% equity
But see, this is where the above feels irrelevant. That 45.5% equity number would be the needed pot equity if we were to 3bet, and then it gets checked down everytime. And doesn't take into profitable bluffs we can make postflop, valuebets we can make, etc. So the overall hand could be +EV even if we had less than 45.5% equity, if we made up for that slightly -EV decision on a later street. For instance, we could 3bet with 0% equity if villain was check/folding 100% of the time postflop, and the hand still be profitable. Just like we can cbet the flop knowing villain never folds, knowing that the fold equity we have on the turn to a double barrel makes up for the flop "mistake".
But, looking at his calling range of 17.8%, and looking at the hands that have at minimum 45.5% equity, it does include most of the hands I would choose to 3bet with.
Putting it into Equilab, we can see that against his 17.8% call range, the range {44+, A3s+, KTs+, QJs, A8o+, KJo+} has 45.5% equity or better. I would definitely be 3betting hands like AT/KQ/KJ/KTs/99/TT/etc for value against this villain. I would probably opt to call hands that play well postflop like 44/55/QJs.
How he plays postflop could help you determine what other hands you can profitably 3bet. If say he's really fit/fold postflop, you could 3bet hands with less pot equity, as your flop cbet fold equity would make up for the lack of pot equity. And so on.
So yeah, the above could also be wrong. Anyone know how to do it correctly?
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