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Just to add a few more random though apropos the last post I made, it made me think about how Savy advised me in another thread to think more clearly about having a plan for 3bet/4bet/5bet spots.
So I thought, given the ranges I gave above, how vulnerable could I be to having my 3bet frequency exploited by someone who 4bets a lot on the BTN, and if someone does 4bet a lot on the button, how light can I stack off?
Ref question 1, if someone starts 4betting a lot, there's no way I want to play 4bet pots OOP, so I'm never going to be calling. So lets assume when faced with a 4bet, I'll either shove or fold.
Let's say he starts 4betting me one time in 4 that I 3bet him.
So if he was opening 35% of hands for a steal, he's going to be 4betting me with 8.75% of hands. Something like [88+, ATs+, KTs+, QTs+, JTs, KQo, AQo+].
If I've got any fold equity after he 4bets, then we'll say he 4bet-folds with [88-99, JTs, QTs+, KTs-KJs] which leaves 6.5% of hands he'll stack off with, and he folds to my shove after 4betting 26% of the time, getting it in the other 74% of the time.
If he 4bets to 22bb, when he 4bet-folds, I win 26.5bb. So my total EV (ignoring the SB and any other dead money, for ease of calculation) is:
EV = (0.26 * 26.5bb) + (0.74 * EQ * 100.5bb) + (0.74 * (1-EQ) * 100bb)
Where EQ is the preflop equity of my hand.
Tidying up, to break even:
0 = (0.26 * 26.5bb) + (0.74 * EQ * 100) - (0.74 * (1-EQ) * 100bb)
0 = 6.89 + 74EQ - 74(1-EQ)
0 = 6.89 + 74EQ - 74 + 74EQ
0 = -67.11 + 148EQ
148EQ = 67.11
EQ = 0.45
I'd need 45% pot equity to shove.
Against his putative stacking-off range of [TT+, ATs+, KQs, KQo, AQo+], I have 45% equity with something like: [88+, A2s+, KQs, KQo, AJo+]
What about if he starts 4betting me one third of the time that I 3bet him?
That gives him 12% of hands, say [99+, A8s+, K9s+, Q9s+, J9s+, T9s, KQo, ATo+].
If he 4bet folds about a quarter of that range again (to keep the required equity at 45% and save redoing the long-ass calculation above) then he continues with something like [TT+, ATs+, KTs+, QTs+, JTs, KQo, AJo+].
then I can stack off with [22-AA, ATs+, KTs+, QTs+, JTs, QJo, KTo+, ATo+].
I'm going to say that again (because it surprised me) - a light 4bettor who 4bets me one third of the time after he opens the button with a typical range and I defend my blind is creating so much dead money that I can stack off with any pair, any suited broadway and almost all unsuited broadways.
To give the opposite, straightforward end of the spectrum, the sample is quite small but in my database, of hands where the BTN has opened and I have 3bet from the blinds, there have been 32 occasions out of 395 when the BTN has then 4bet. So a typical BTN opening 35% of hands is going to click it back 8% of the time when I 3bet him with 3% of total starting hands, or [QQ+, AQs+, AKo].
In my database, of those 395 hands where I 3bet the BB vs a BTN open, 222 times the BTN folded to the 3bet. That's 56% of the time. So his calling range was [3%-23%], something like [66-JJ, A2s-AJs, K7s+, Q8s+, J9s+, T9s, JTo, QTo+, K9o+, A8o+] so (to me at least) a surprisingly wide and weak range.
So he 4bets me 8% of the time, and it's always with a hand he is willing to stack off with (not an unreasonable assumption I think against an unknown or a "typical" player at 25NL)
Let's do an EV calculation, based on his 56% folding frequency when 3bet, and completely ignoring the times he calls and we play postflop by saying that when he does call, we lose our 3bet and just c/f the flop every single time.
EV = (0.56 * 4.5bb) - (0.44 * 10bb) = -1.88bb so worse than folding the BB
So lets do a simplified postflop analysis. I can only be bothered to do this over one street or it'll get unreasonably complex and speculative - the flop pot is 14.5bb
If we pot the flop every time our 3bet is called, we're risking another 14.5bb
If we want to break even vs. just folding the BB, we can set EV=-1bb and see what X makes:
-1 = (0.56 * 4.5bb) - (0.44 * (1-X) * 24.5bb) + (0.44 * X * 14.5bb)
-1 = 2.52 - 10.78 + 10.78X + 6.38X
7.26 = 17.16X
X = 0.42
So if we just potted every flop when called, we'd need 42% folds to break even with just folding the BB.
To get to the -30bb/100 mentioned earlier in the thread (a minimized BB loss-rate), we'd need:
-0.3 = 2.52 - 10.78 + 10.78X + 6.38X
7.96 = 17.16X
X = 0.46
46% folds.
If we bet 10bb instead of potting it, we'd need:
-0.3 = 2.52 - 8.8 + 8.8X + 6.38X
5.98 = 15.18X
X = 0.39
39% folds required.
With the wide, weak calling range identified earlier, that doesn't sound unachievable. Easy to say that when you suck and are losing 47bb/100 from the BB eh?
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