IRC Poker Quiz #3

Heads up NLHE, we see our opponent's cards and he doesn't know it. We shove the flop for exactly pot and he has us covered. Under what circumstances are we rooting for a call? For a fold?

when he has under 33% equity we're rooting for a call
when he has over 33% equity we're rooting for a fold

edit*

nevermind

Say there's $10 in the pot. so we shove 10 to win 20.

Ignoring rake, if we have 33% equity, we have oEV when called. If we have 40% equity, we're +EV, but only slightly as we only expect to win $2 on average:
.6(-10) + .4(20) = 2

Compare that to the $10 we get when he folds, and it's clear we're hoping for a fold with even 40% equity.

The breakeven point is done by solving the equation:

(1-eq)-10 + eq(20) = 10, and we get 2/3 equity before we're actually hoping for a call over a fold.

Take home message: When they fold it's risk-free monies & FE is nice.

Originally Posted by iopq

when he has under 33% equity we're rooting for a call
when he has over 33% equity we're rooting for a fold

Not true, whilst in your terms it certainly may be +EV, it is not necessarily the largest positive expectation to have him call with, say, 40% equity.

Originally Posted by killerkebab

Originally Posted by iopq

when he has under 33% equity we're rooting for a call
when he has over 33% equity we're rooting for a fold

Not true, whilst in your terms it certainly may be +EV, it is not necessarily the largest positive expectation to have him call with, say, 40% equity.

Instead of just saying this, you should prove it.

You bet $1 making pot $2. If your opponent folds we walk away with the 2 bucks. If we have 2/3 equity and he calls our hand is worth $2. Obviously if we have more than 2/3 equity we want a call otherwise we're rooting for a fold.

Call: When we have it
Fold: When we don't

Ez game

Originally Posted by Lucothefish

Call: When we have it
Fold: When we don't

Ez game

And it's 50/50 on whether we have it or not.

Originally Posted by XxStacksxX

Originally Posted by Lucothefish

Call: When we have it
Fold: When we don't

Ez game

And it's 50/50 on whether we have it or not.

{Forum Locked} Give yourselves a round of applause. You guys did it. Pretty amazing that you figured the game out.

iopq's answer was correct, but I'm going to prove a more general case with some algebra.

Suppose we go all-in for s into a pot of 1 with x equity against 1 opponent who has us covered. Our EV when our opponent folds is 1, and our EV when our opponent calls is:



So when would we be rooting for a call? When the EV of a call is greater than the EV of a fold, or:



We can play with this equation a bit by isolating our opponent's equity (1-x):

[MATH OH NOES]

[/MATH OH NOES]

When we bet all-in for s into 1, our opponent is calling s in a pot of s+1, so the equity he needs to break even is s/(2s+1). Since 1-x is our opponent's equity, we have shown that we are rooting for a call when our opponent's equity is less than s/(2s+1).

he needs 33% to have the pot odds to call
when he has 40% he's getting the correct odds to call so we'd rather have him fold

Originally Posted by iopq

he needs 33% to have the pot odds to call
when he has 40% he's getting the correct odds to call so we'd rather have him fold

Yeah sorry about that, I read what you wrote wrong and on top of that said something that wasn't right