Existence of -cEV yet +Equity Plays?

[Collin Moshman]

Hi Guys,

My Caltech buddy Tony Guerrera (whose book Killer Poker by the Numbers I will be reviewing in Books/Publications next week) were discussing an interesting topic, so I thought I'd bring it here.

The question: Does there exist a play that is -cEV, yet is +Equity?

As Tony points out, there are many examples if you switch the plus/minus signs so that the question reads "+cEV yet -Equity." I gave one such example of this latter category of hand in a recent thread:

Blinds: 200-400
On the bubble. CO has 350, button has 270, you have 3500 in the big blind, and the reckless small blind has the rest (about 9.5k). CO and button fold, SB pushes, you hold A2o. If you call, you have a +cEV (because you are ahead of a LAG's < 10 BB pushing range with your ace-high), yet
-Equity situation.

This sort of situation is common. But -cEV yet +Equity? So I came back and said OK, how about this:

"Suppose you are playing a winner-take-all MTT or SNG. It is down to the final three, you guys are playing deep, and you assess that your competition is vastly better than you. (E.g., you are an online qualifier used to playing pre-flop poker are now facing Gus Hansen and Daniel N., each having M's of around 50) Then if you could get all your chips in pre-flop by making a slightly -cEV call, then this would increase your tournament equity relative to folding. This is because seizing a guaranteed near coin-flip would be your best chance against much better players."

It is a rare situation, to be sure, but I thought it fit the criteria. Then Tony replied and said, "OK, what if we now make all the ICM assumptions such as equal-skilled players. Then is there still an example?"

My initial thoughts are: No. I.e., suppose you exclude factors such as skill, relative positions, and metagame considerations (e.g., raising during Level I with a weak hand to establish a loose reputation, or anytime your opponents react in subsequent hands to how you have played previous hands). Then with those assumptions there are no situations where you will lose chips on average, yet gain equity.

What do you guys think?

Best Regards,
Collin

[PattdownManiac]

I think this is what gigabet's block theory is about. You can make calls that are marginally -cEV because if you lose nothing will change regarding your stack position (i.e. mid stack 5-handed) but if you win you will jump up to say, being chip leader on the bubble.

[Slim Pickens]

There is no way to get a -cEV action to be +$EV using the assumptions used in the ICM and without attempting to predict future action.

[HighEV]

Tony Guerrera here. Collin...thanks for tossing this up on the forum! My intuitive response to this issue was "hell no!" and I'm still sticking with it; however, my general approach to such things is to be open-minded, especially since statements of non-existence are typically much harder to prove than statements of existence, and since not being open-minded is a surefire way to become a stagnant player.

I agree that there's no way that this can happen when considering calling versus folding. I just have to figure out how to justify it in a way that the general public will understand (gotta maximize my audience to maximize my writing EV).

The one potentially interesting situation I've thought of with respect to aggressive play on the -cEV +Equity front is a squeeze play situation with lots of dead chips in the pot. Most likely, even scenarios like these with lots of skewed stack sizes or unconventional payout structures will end up being +cEV and +Equity or -cEV and -Equity, with the potential of some +cEV -Equity situations.

With all of that being said, anyone here who DOES come up with some really unique situation that's -cEV yet +Equity will get a crazy shout out in my third book, Tournament Killer Poker By The Numbers.

May Your Monetary EV Always Be Positive!

Tony Guerrera

edited by durron597:

please don't use this forum to advertise your site, thanks

[Pudge714]

There are potentially metagame plays. Apathy made a thread in HSNL awhile ago and the OP was "Should you mkae money on your bluffs?"
There are spots were taking a -EV play is better than taking future more -EV plays. Like minraising allin UTG with Q8s, which is clearly -CEV, but also clearly the best play.

[Kibby]

We typically refer to EV in this forum in terms of prize pool equity based on ICM calculations as everyone who's reading this I'm sure knows. ICM is just a mathematical model that is accepted and that model will not allow a -cEV calc to turn in to +$EV. That being said, if someone used a different model that made assumptions about certain plays that sacrifice chips to blah blah blah, then you could say that it could exist assuming that model is true. I think what we're hearing is that such a model isn't known to those in this forum.

[HighEV]

Ugh...have to pick up my girlfriend soon...just when some interesting discussion is developing. I'll put something really detailed up here in a few hours. For now, I'll just say that assuming everyone is equally skilled, ICM is not just an "accepted mathematical model." Granted, it assumes that everyone is equally skilled, but given the push or fold end game of most tournaments...especially STTs...that assumption is highly valid, and proving the general formula isn't too bad (writing it down, on the other hand, is a notational nightmare, and I'm not sure I can do it on this forum without Equation Editor).

Really quickly, I agree that early tourney decisions that are slightly -cEV can be +Equity, especially when thinking about having to make a slight -cEV play to avoid a more -cEV play later to preserve equity. I'll be honest in saying I should have phrased the problem more precisely, since I was really focusing on the short-stacked tourney end game.

However, since we're talking about earlier tourney considerations, one interesting ICM calculation for this discussion would be limping with a small pocket pair with about 10BB (insufficient implied odds across all possible lines of play) with the intention of continuing only when flopping a set.

Have a monster night at the tables everyone...be back in a few hours!

Tony Guerrera

[rvg72]

Might be a little bit of a tangent but there are lots of ICM -$ev plays that are +$ev in terms of real $.

ICM does not measure things like fold equity, position, impending blind increase, likely action of future hands based on your push/fold (largely due to above factors) etc so there are lots of plays where the ICM model would tell you folding is the best option but in actual fact pushing is much better and vice versa.

Regarding -cev but +$ev (as calculated by ICM and with no meta game included) I have to think there are real examples of this when deciding to make a small call vs multiple short stack all-ins around the bubble. I'm too lazy to try and do math or simulate the scenario but if there was one I would suspect it would be in this type of situation.

rvg

[Slim Pickens]

[ QUOTE ]
Regarding -cev but +$ev (as calculated by ICM and with no meta game included) I have to think there are real examples of this when deciding to make a small call vs multiple short stack all-ins around the bubble. I'm too lazy to try and do math or simulate the scenario but if there was one I would suspect it would be in this type of situation.

[/ QUOTE ]

I worry that as soon as you found this type of situation, pundits would cry foul that the assumptions of ICM had been violated by the presence of short stack. The error introduced by shorty might be enough to make the play not definitively +$EV.

[dode]

If I'm BB with AA on the first hand of a SNG and everyone goes all in I fold. I think that's a +$ev fold.