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.

[Collin Moshman]

Wow, lots of great discussion in this thread!

[ QUOTE ]
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.

[/ QUOTE ]

I'm gonna have to agree with Slim, Kibby, and others who express this sentiment. For those who disagree, I think you are actually taking future action into account, e.g. Pudge's examples (which are very interesting situations, but not ones that qualify given our strict assumptions, IMO.)

Let's see if we can prove the opening quote, using Galwegian's idea of ICM as a chip-to-equity function as our basis. Suppose there are N players left, 2 <= N <= 10. Let the stack sizes at the beginning of the hand be X1, ..., Xn, respectively.

We proceed by contradiction. Suppose there exists a play P that is -cEV and yet +Equity from player J's perspective. (Where +Equity means + for this particular play, and not any future action). J makes the move P, and now the new expected value of the stacks are Y1, ..., Yn.

(Where EV (Xj) is the expected value of the stack size Xj after P has been made by J).

Then by hypothesis, Yj < Xj. (*)

Now let ICM(A, B, C, etc.) have output I(A), I(B), etc. Then plugging in X1...Xn and Y1...Yn we have ICM outputs I(X1)...I(Xn) and I(Y1)...I(Yn). Then:
ICM(Y1,...,Yn) = I(Y1),I(Y2), etc and same with the Xi.

Then (*) and the convexity of ICM => I(Yj) > I(Xj), which contradicts our initial hypothesis that P was +Equity.

QED...?

Best Regards,
Collin

[Austiger]

[ QUOTE ]
Wow, lots of great discussion in this thread!

[ QUOTE ]
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.

[/ QUOTE ]

I'm gonna have to agree with Slim, Kibby, and others who express this sentiment. For those who disagree, I think you are actually taking future action into account, e.g. Pudge's examples (which are very interesting situations, but not ones that qualify given our strict assumptions, IMO.)

Let's see if we can prove the opening quote, using Galwegian's idea of ICM as a chip-to-equity function as our basis. Suppose there are N players left, 2 <= N <= 10. Let the stack sizes at the beginning of the hand be X1, ..., Xn, respectively.

We proceed by contradiction. Suppose there exists a play P that is -cEV and yet +Equity from player J's perspective. (Where +Equity means + for this particular play, and not any future action). J makes the move P, and now the new expected value of the stacks are Y1, ..., Yn.

(Where EV (Xj) is the expected value of the stack size Xj after P has been made by J).

Then by hypothesis, Yj < Xj. (*)

Now let ICM(A, B, C, etc.) have output I(A), I(B), etc. Then plugging in X1...Xn and Y1...Yn we have ICM outputs I(X1)...I(Xn) and I(Y1)...I(Yn). Then:
ICM(Y1,...,Yn) = I(Y1),I(Y2), etc and same with the Xi.

Then (*) and the convexity of ICM => I(Yj) > I(Xj), which contradicts our initial hypothesis that P was +Equity.

QED...?

Best Regards,
Collin

[/ QUOTE ]

O RLY?

[Slim Pickens]

[ QUOTE ]
[ QUOTE ]
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.

[/ QUOTE ]

I'm gonna have to agree with Slim, Kibby, and others who express this sentiment. For those who disagree, I think you are actually taking future action into account, e.g. Pudge's examples (which are very interesting situations, but not ones that qualify given our strict assumptions, IMO.)

[/ QUOTE ]

Eh, I was wrong about it the first time. The "folding AA on the BB when everyone else is all-in on the first hand" example seems to work just fine. Most of the other scenarios do give +$EV plays that are also -cEV, but seem to violate some of the ICM assumptions in ways that make sense to us as poker players.

Is your aim to answer this question on a theoretical level or a practical level? I'm sure the Poker Theory people are (duh) better with theory than STTF, but that's because we're too busy shipping da moniez to worry about impractical exceptions to an otherwise useful tool. [img]/images/graemlins/wink.gif[/img]

Dealing with theoreticians is fun and scary. On one hand, they are usually the best pure thinkers in the world. On the other, they'll argue a point indefinitely until you at least concede there's some validity to it, long after anyone except them has stopped caring.

[Collin Moshman]

[ QUOTE ]
Is your aim to answer this question on a theoretical level or a practical level? I'm sure the Poker Theory people are (duh) better with theory than STTF, but that's because we're too busy shipping da moniez to worry about impractical exceptions to an otherwise useful tool. [img]/images/graemlins/wink.gif[/img]

Dealing with theoreticians is fun and scary. On one hand, they are usually the best pure thinkers in the world. On the other, they'll argue a point indefinitely until you at least concede there's some validity to it, long after anyone except them has stopped caring.

[/ QUOTE ]

LOL I guess in part I'm just trying to relive my math days with threads like these. For sure this discussion is theoretical, in that actual hands could be given to show existence, but at the tables, proving/disproving abstract concepts probably won't up your ROI much [img]/images/graemlins/smile.gif[/img]

In the meanwhile I have a lot to do with the book, but will definitely check out the threads linked to by Durron, the Giga threads, etc. I will also try to look at the many hand examples that have been thoughtfully posted by you STTF guys -- thanks to everyone who has contributed so far.

Also, for the casual player just trying to win $, this type of analysis goes a bit beyond what you need in your toolbox....

Lastly, the Gus/Daniel example was meant to be in an MTT context, but I'd have to imagine these guys could do pretty well at SNGs if they wanted to switch gears. I guess that's a topic for another thread though.

Best Regards,
Collin

[HighEV]

Collin,

I hope I'm not misinterpreting your notation, but I don't think I can high five your QED because it looks like, to me, you're cranking expected stack sizes in. When using ICM, we can't plug expected stack sizes in; instead, we have to plug the stack sizes from every possible outcome and weigh the ICM monetary equity from each outcome according to the probability of each outcome. The results obtained using ICM by plugging in expected stack sizes are wrong (I wish they were correct, because they take a lot less work to get). It's precisely because ICM isn't a function of expected stack sizes that I initially hypothesized the existence of plays that are -cEV yet +Equity.
-------
Two Plus Two Forum,

My sincere apologies to anyone who objected to me putting my website in my posts. I spend a lot of my time these days promoting myself, so I sometimes forget to tone it down at times. My schedule gets really busy, and I don't have a lot of history on 2+2, but it's clearly a great place with lots of great minds to debate poker with, so I hope we can put it behind us [img]/images/graemlins/smile.gif[/img] Great thread guys!

Tony Guerrera

[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.