Thought experiment: value vs equity denial
Here is a thought experiment looking at the competing factors of value and equity denial when betting against draws.
Hero: K♠ Q♠
Villain: A♥ T♥
Turn: (100 bb) K♥ 4♥ 5♦ 7♣
Both hands are face-up.
Villain says "I will call any bet of X bb or less".
Assume that both stacks are infinitely deep.
Q1) What is Hero's optimal strategy for various values of X?
Q2) How does the answer to Q1 change as we give villain different hands with more or less equity (e.g. A♣8♣, T♣T♦, A♥6♥, A♣K♣)?
2 Replies
Good thought experiment! I asked myself the same questions in the context of this 3way hand:
Spoiler
Hero (SB): 227 BB
BB: 200 BB
UTG: 182.8 BB
UTG+1: 200 BB
MP: 51.8 BB
CO: 119 BB
BTN: 153.2 BB
7 players post ante of 0.4 BB, Hero posts SB 0.4 BB, BB posts BB 1 BB, CO posts penalty blind 1 BB
Pre Flop: (pot: 5.2 BB) Hero has Q♣ Q♥
fold, fold, MP calls 1 BB, CO checks, fold, Hero raises to 8 BB, BB calls 7 BB, MP calls 7 BB, fold
Flop: (27.8 BB, 3 players) 3♣ 3♦ 5♦
Hero bets 15.6 BB, BB calls 15.6 BB, MP raises to 43.4 BB and is all-in, Hero ?
My hand is strong enough to play for stacks. What line does maximize my ev? The options I see are: 1) call, 2) minraise and 3) shove. I mainly give BB weaker overpairs 66-TT and ♦ flush draws that he could continue to play with. His overpairs are virtually drawing dead and the flush draws have robust equity.
My best guess is that shoving gives BB bad pot odds and he will basically just fold everything ==> his equity gets denied and he doesn't make a mistake in the sense of a -ev play. Should I choose a smaller raisesize for this reason eg minraise? This gives villain's flushdraws a better prize, possibly a +ev call, but at the same time he may be forced to continue playing his weaker overpairs.
With reference to the thought experiment, the essential question is whether I should deny equity or rather find some raise size that maximizes value extraction?
If everyone's face-up then the correct bet size is any that's bigger than the break-even point for him to call.
Nice replies, thanks for the engagement!
I find it interesting that all of your answers have something in common - they start by considering the EV of our opponent's actions. This probably jumps out to me because I was expecting the opposite. I hadn't actually considered that our point of indifference will necessarily also be our opponent's point of indifference!
For me, this prompts a natural follow-up question. Consider two approaches to poker, one which focuses on minimising our opponent's EV,
That these approaches are identical is a product of the fact this is a zero sum game and your loss is his profit and vice-versa. It is not just co-incidence. Money you save losing the minimum may feel like it spends differently to money you've earnt my maximising value, but they spend the same.
