Hi all,

How to defend vs midstack 3bet in general (positions, sizes, stats known but it should be done for general case).

1) We can calculate the EV for hands that we want to 4bet/call, and we stack off all hands which are +EV.

2) But, what about hands that are playable but not good enough to stack off? how to calculate this EV for call 3bet, or if not calculate how to approximate it?


I will try to answer the 1) and for 2) I have no idea how


1)
EV_4bet_call = fold_vs_4bet * dead_money + (1 - fold_vs_4bet) * (equity * total_pot - remaining_stack)

Here, dead_money is the money in the pot before we 4bet, and equity is our hand equity vs all in range from villian, and total_pot is the total pot when we both go all in, and remaining_stack is hero's all in stack - open_raise_size.

Note that this EV calculation is identical as it would be when we directly go all in, instead of 4bet/call, because we calculate EV for the hands that we know we will 4bet/call, so it is like shoving vs 3bet, but with difference that when we 4bet we can add range that 4bet/fold, and villain can make mistake by shoving too light, or flatting too wide.

Example:
SB midstack 3bets us 6bb vs BU 2bb open raise. He 3bets 20% depolarized range, and folds vs 4bet 35%. Our hand is AA, and vs his stack off range of 13% we have with AA 84% equity. We have 50bb effective stack size.
In this case, remaining_stack = 48bb, total_pot = 101bb, dead_money = 9bb

EV_4bet_call = 0.35 * 9bb + 0.65 * (0.84 * 101bb - 48bb) = 27bb

So AA is +EV to stack off. Now we can in similar way calculate for any hand the equity vs his range and EV and decide to stack off or not.