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