Hi!

I figured yesterday I dont even know what's right about the following, after years of poker! Super shame.

Hero and Villain are at the flop. There is 10 in the pot, Villain just bet 5, has 10 left. Hero has 15 left. If Hero goes allin, we assume Villain will call. Hero has x% chance of winning a showdown.

How big should x be for Hero to go allin?

So here is what bugs me: do you just have to compute the pot odds? Suddenly, it seems to me it's not enough. You may have to compare 2 losses. The loss by folding, the loss by going allin.

First, the pot odds. Hero has to put 15 to win 2x15+10, so he needs x at least 37.5%. Now, if we consider the flop pot, if we compare the allin break-even outcome to the folding outcome, the difference is +7.5. So suddenly, I'm like, does Hero lose/win more by going allin instead of folding if he has x at 36.5%?

So alright, what's the right thing to do? )

The loss you have by folding is zero - the money is already in the pot, it's not yours. You just need to work out whether you have the odds (so 15:25) are sufficient given your cards and his range

Does villain never fold?

OP you need to know your equity % in the hand and also the % of the time villain is folding to run the numbers here. And there’s no calculus here, just algebra.


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Villain never folds

Let say numbers are 15:15 and I have 49.9% of winning at showdown. Should I fold (mathematically)?

The way I see it is, if I go allin, I'll lose 0.01% of 30$ and if I fold I'll lose 7$ -- 50% of the pot, the break-even point.

If my equity is 0%, Im drawing dead, if I go allin, I'll lose 15$ = (0%-50%)x30$, whereas if I fold I lose 7$.

So in between, there is a x% that's not the pot odds (assuming villain never folds).

Super roughly.

pot is 10,

both vill/hero are putting in 15

15/(15+15+10)= 15/40 = 37.5%

hero needs =>37.5% equity vs. villain's calling range.

I'll be very surprised Hero has to give up the entire pot if he has only 37.499% versus Villain's range.

If Hero has 37.499% equity versus villain's range, it means that overall the pot gonna split, and Hero gonna loss pennies sometimes. If Hero folds, he gives up the entire pot, losing the 37.499% of it that are his.

It's something like, if you go allin, your expected value is 37.499% of the pot at an additional cost of C, and C must be <= 37.499% of the pot to be the less worse decision.

no.

Damn, you are right.

Say the pot is 10, hero has 10 left and 49.99% chance of winning at showdown. If hero fold he ends up with a 10$ stack, if he calls, he ends up with a 49.99% * 20$ stack which is below 10. Fold is better.

you described the situation wrong an therefore are confusing yourself. If villian never folds after betting 5, he is effectively just shoving 15 into 10, and that is the only calculation you need to make. If he is shoving 10 into 10, you only need 33,3...% equity.

Im super happy with the final answer actually. It means that if you're not quite ahead in terms of odds relative to perceived Villain's range, it's a full-stop no-go. Easy decision (still assuming Villain never folds). Thank you everybody.

No.

You’re confusing yourself and take another step back with every post you make. Let’s go all the way back to the basics:

10 in the pot, villain bets 10, hero has 10 left. If hero folds, he still has 10. If hero calls, he has 49.99% of 10+10+10 = ~.5*30 = 15.

If you are trying to solve examples where villain never folds and you never call, just assume villain bets all-in and go from there. Makes the math significantly easier.

Just to make sure: No, again.

There’s only one situation in poker where you don’t have the odds to call with 49.99% equity and that is a game with blinds like a $1 BB while stacks are >~10000.

Other than that, the dead money in the pot makes calling always the right play with that close to 50% equity. (absent other considerations)

Just to make things clear, in this example, Ive changed things. Villain is allin already, total pot is 10, hero has 10 left (say its HU preflop). Sorry for the confusion.

edit: ok the math doesnt add up with 49.99%. Whatever, maths are pot-odds versus equity. Got it. Thanks!

Yes, thanks