The prevailing wisdom is that when making a call decision, a fold always has 0 EV. Clearly with a fold you do not invest any more money, so there is no further money of yours at risk. And, by the way, money you may have already invested in the hand, is no longer yours – in economic terms, such money is a sunk cost. In poker terms, your prior bets are now up for grabs for all players still in the hand. I have no problem with this theory.

Now, consider the following argument.

Jake loves to play poker, not to win money, although that would be nice, but primarily for the camaraderie and banter that goes on in the chat boxes or live. Of course, he doesn’t want to lose either. So, since he has heard that folding is 0 EV, he adapts a strategy of folding every hand so that he gets to play a few hours each day with no long term loss. After trying this for a several days, Jake is confused as to why his bankroll is diminishing. What happened to the 0 EV theory?

So, where’s the contradiction, if there is one?

Well, I don’t think there is a contradiction. When you do an EV analysis, you do it with respect to the decision to be made at that time. For deciding to call a particular bet in a particular hand, folding clearly will not entail any more risk on your part so it is 0 EV. We will call this a tactical poker decision.

However, Jake was making a strategic poker decision. When you do an EV analysis relative to deciding to fold every hand, for example, then that strategy decision does involve a risk on your part. That risk, of course, is the blind and/or ante you have to pay to sit at the table. In any hold’em round, for example, you must invest a minimum of 1.5 big blinds, so for an n-player game, each hand involves a risk of 1.5/n big blinds. Therefore, if Jake were to play 60 hands of 6-max per hour, his always-fold strategy has EV = -60*1.5/6 bb per hour or -15 bb per hour.

So, to answer the question, folding does not always have 0 EV, but when it doesn’t, it’s because a strategic decision is being made rather than a tactical one.

I think the problem here is the comparison of absolute vs relative EV.

When we talk about the EV of a move we are really talking about the relative EV between the available options. When a bet has been made we can fold, call or raise. It's convenient to set one of these to 0ev and calculate the rest relative to that. It turns out it's easiest if you say fold=0 and calculate the rest relative to that.

Another option is to calculate your stack size before and after the hand. You can calculate the differences in stack size before/after for each of your options and calculate the relative differences from any point. It comes out exactly the same.

In an absolute sense, folding is always -ev if you have more than 0% equity. It's just that it can be +ev relative to calling.

I agree that EV is best used by comparing it for each of the possible decisions you make, including checking if that is an option.

I don’t know if I agree with your stack size analogy. Consider two cases. A player in middle position holding 72o folds to a raise. His stack size after the pot is identical to that before the pot, so his EV =0, as I think it should be. Now suppose the big blind had the 72o and he folds. His stack size difference is 1 bb less. Ignoring the positional aspect, why should the two EV’s be different? Doesn’t using stack size violate the ‘sunk cost’ aspect of proper EV analysis?

I didn't real the whole post, but yeah, folding is 0EV.

Folding is 0EV and paying the blinds is -EV, if you do nothing else, you'll lose money.

You need to have +EV actions to make up for the blind's -EV. If you fold every hand, you don't have any.

Their EV is different using EV(fold)=0 and more conventional analysis also. There is nothing invalidated, if you're careful.

Let's assume for a second that we have 2 choices - get all in HU with a guy who has AA, or fold. We've either already put in 1bb, or we have not. We have 100bb before starting the hand in both cases. Our equity is 11.8%. For simplicity lets say our opponent has us covered.

Situation 1: we have put in no money yet. There is 1.5bb in the pot.
11.8% of the time our stack will be 201.5bb in it, 88.2% of the time, it will be 0. On average our stack will be 23.777 if we call, and 100 if we fold.
From the point of view of our stack we have -0 when we fold and -76.233 when we call so
Difference: -76.223

Using the more conventional method of EV(fold)=0, then we say EV(call) = .118*101.5 - .882*100 = -76.233

Situation 2: we have put in 1bb of the 1.5bb in blinds. We have 99bb left.
11.8% of the time, we'll end up at 200.5, 88.2% of the time we end up at 0. This averages out to -76.341.
From the point of view of our stack we have -1 when we fold and -76.341 when we call so
Difference: -75.341

Using the more conventional method, EV(call) = .118*101.5 - .882*99 = -75.341

I guess I misintepreted your use of stack size. Sure, for a given player in a given situation, you can get EV through stack size difference or directly. It's basically equivalent to adding and subtracting a constant to the EV equation.

I thought you were suggesting that stack size difference would be the same for two different positions given the same situation. As your example shows, that is not the case for the player in the blind is starting out with a penalty if you will.

Right. So I hope you see, folding isn't 0ev.

When you're comparing 2 or more outcomes, though, the "EV" of each is best expressed by setting one point to a constant and comparing all the other points to that. The idea of "EV of folding is 0" is just setting a reference point. You could just as easily say "The EV of folding is negative (whatever you put in the pot)" as long as you keep everything straight.

There's a subtle psychological thing at play here too though - it most closely expresses how decisions are scored in poker. You score each decision from the point of view (in time) of that position. From that point of view, the EV of folding is 0.

folding is negative e.v. even if it didn't cost you anything. It's theoretically a loss because it was a opportunity that has passed.

This example too easy. There are many posts on this forum like:
100 in the pot i have to call 30 and my EQ=33%
And answer always: EV= 0.33*100 - 0.67*30= +12.9$
Right call! you gain money!
---------------------------------------------------------------
So EV(abs)= -35 + 12.9 = -22.1$ (heads-up pot)
OK.It makes sense.
http://forumserver.twoplustwo.com/15...called-966182/
The first post.When we make EV(fold)=0 if we try to compensate something relative?
There's something to think about... Does EV=+1$ good compensation for higher variance in some cases? We often see marginal calls.
Anyway in all the books i've read they always talk about good pot odds and profitable calls... But don't say relatively profitable

Any time someone says a call is profitable, they mean it's more profitable than the alternative, folding.

Folding is only 0 EV if you are playing a no blind, no ante game and you avoid the bring in for an infinite number of hands. But that ain't gonna happen.

Folding is 0EV. Posting the blinds is -EV.

Since all Jake is doing is taking a lot of 0EV actions and a few -EV decisions you will lose money.

Unfortunately if Jake wants to experience the camaraderie and banter he is going to have to post the blinds. Or he could go make some friends and banter with them away from the poker table.



It's easier this way.

Folding causes you to win 0 and lose 0 with a hundred percent probability, so the expected value for folding is 100%*0-100%*0 which is indeed 0.
If you disagree, read up on the definition of expected value until you agree.

So you fold the small blind..... 0 EV?

Yes. Your stack before folding is x, and your stack after folding is still, with 100% certainty, exactly x. The difference is 0. The expected value is 0.

I did read the OP, and the answer to the "paradox" is that the act of posting a blind is -EV. If you have chosen to play with a 0%VPIP style (and open-folding BB when limped to), the act of posting SB has an EV of -0,5bb, and the act of posting BB has an EV of -1bb. The folds themselves cost nothing, it's the blind bets that lose Jake his money.
Seems Lego said the exact same thing already, but hey here you have it seconded and with different phrasing

Rusty hits it better, imo.

people are frequently confused by this

Folding is 0 Ev by convention, not any mathematical necessity.

You can discuss the overall Ev of a hand keeping track of all the money players put in as negative expectation if they fold or lose, and the amount their stack increases as the positive expectation for the winner, and it will give you the same bottom line as doing it the more conventional way -- it's just usually much harder to do.


you put $10 into a pot, the pot is now $40, and it's $10 to call. You're a 5-1 dog to win:

The conventional "fold=0" math says you'll spend $50 calling 5 times to win $40 once, so the play has (-$50 + $40)/5 = -$2 expectation per hand.

doing it the messy way, you lose $20 4 times and gain $30 once in 5 trials. ((-$20*4)+($30*1))/5 = -$12, compared to -$10 from folding, for -$2 per hand eV.


---- edit: what I mean is, "what rusty said"

When I was saying this I so had the image in my head of Will Hunting. There's the scene where he interrupts the math professor who is going on about some way to do something and Will says something like: No, look, I wrote it down .... it's easier this way.

The actual scene is better.

Nobody claimed it would improve your game.

I agree with you that basically nothing in this forum will improve your game. Try the relevant strategy forum for the game that you play.

First, why you take 5 trials if he 5 to 1 dog (and (-$20*4)+($30*1))/5 = -$10).
Second, have look how "your not messy" way makes some mess in the head of the topic-starter
http://forumserver.twoplustwo.com/15...ing-me-982659/
He really believes that the guy with eq=50% is a big winner.

posting sleepy.

we've put $10 in, it's another $10 to call for a $30 pot as a 4:1 dog

calling will cost us 4*$10 = $40 for every time we win $30. That will take 5 hands on average. -$10/5 = -$2/hand
OR

4 times we lose $20, one time we gain $20. (4*-$20)+(1*$20) = -$60 per 5 hands, or -$12. compare that to -$10 from folding

Folding is +EV if you do it to avoid losing chips. The only trouble is, you may never know what cards your opponent had. But if you're good enough, you can guess, and if you guess correctly most of the time then you will know when the fold is the correct play, and is therefore +EV because over time you will stand to win more money than if you lost some by making a bad call or raise (instead of folding).

I Google "folding + 0EV + strategy" and end up here, how odd. Could you go into more detail on the difference between strategic and tactical decisions?

honestly, who cares?