Message Board : Can calling be -EV but still the correct play?

This is something that has been floating in my head for a little bit that I thought I would throw out her to get all of your opinions on.

Let’s say that with 75BB stacks you 3-bet with AK preflop to 12BB when you are in position and get 4-bet all in.  You calculate your pot odds as (75 + 12 + 1.5 - 1 (for rake):63) 87.5-to-63, or about 1.4-to-1.  This means that you need to win approximately 42% of the time for the call to break even.  You decide that you have about 40% equity, so this means that a call is -EV, correct?  Specifically, the EV breaks down as:

(.40)*(87.5) + (.60)(-63) = 35 - 37.8 =  -2.8 BB

However, you already have 12BB invested in the pot.  If you are to fold right now, you will have lost 12BB in the hand.  Therefore, the EV of the entire hand is -12BB for you. This is kinda looping in my head funny, because I always think the the EV of a fold is 0 because it can cost you no more money.  However, it seems that if you are giving up reasonable equity, then folding may not be so good.  This looks to me like even though you are marginally -EV, you should make the call because you will lose less money on avergae.

Is my logic fuzzy anywhere here? 

FWIW, I think there was some material about this in HoH Volume 2.  I’m not for sure though.  However, things seem to sink in when you figure them out for yourselt… or at least it seems to work that way for me.

Anyways, if my logic is accurate here then I think there would be a better way to play this hand so that we aren’t forced to make a -EV call.  I have some ideas, but I’d like to let this brew for a bit first. 

weasel97 said:

Is my logic fuzzy anywhere here? 

---

Yep. 

When you look at pot odds, and assign pot equity, you’re considering that the money in the pot is no longer yours, but if you call, you have some chance to win it.

You’re looking at the expected value of the call only, because the prior action is done, and the money is now property of the pot.  (This overlay is why you no longer need to be a favorite in the hand for this call to be profitable.  It’s also why it can be simultaneously correct for the bettor to push all in, as well as for the caller to call) 

But, by calling folding -12BB, you’re considering that money to still be yours, which is incorrect.  Once bet, that money is property of the pot.

Remember, you’re looking only at the expected value of the call, not of the hand.

I see what you are saying… but iit seems like there might be some holes there.  What I am thinking is that you should look at the EV of the whole hand dependent on your action here.

 I totally agree with what you are saying here, but shouldn’t you be able to look at the EV of the hand as a whole at some point?  I don’t know.

http://en.wikipedia.org/wiki/Sunk_cost

I totally agree with what you are saying here, but shouldn’t you be able to look at the EV of the hand as a whole at some point?  I don’t know.

I see what you’re saying.  Another thought…

I don’t think that any sort of analysis like this is relevant (or possible) while in a hand.  Once you’ve committed chips, you’re looking to make +EV decisions from there on out.  When deciding to call an all-in bet, it’s a pretty straight equity / pot odds computation, like you did before.  That particular decision needs to be +EV.

I think where your line of thinking might have some merit is in meta-game sort of analysis:

3 betting AK preflop is a money loser because you incorrectly assign a 4bet range where calling is correct (even though you never see those hands), or something like that.  Of course, to be statistically valid, you need a pretty darn big sample on stuff like that.

Ie, I think this might be somewhat useful in offline analysis (to look at hands, positions, situations where you lose money, and are thus -EV for the hand),  but I don’t think you can make decisions in a hand based on folding being anything other than 0EV (on that particular decision).  Otherwise, you can come to conclusions like "Calling here is -3BB, but that’s better than the -12BB than if I folded". 

If the expectation of a particular play is negative, you shouldn’t make it (factoring in implied odds, and ignoring the table image effects, etc).