[AleoMagus]

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...he's consistently making -CEV moves... By doing so (folding), he is *by definition*, increasing his opponent (aggressor) $EV, and by that reducing his own. Another point (that really complicates it, IMO), is that we can no longer assume all players have equal ability, if Hero is making a consistent CEV mistake against his opponents.

if all opponenets are equally skilled, Hero should take ANY +CEV opportunity he has, since he hasn't got any skill advantage. Not taking even the slightest +CEV opportunity is, according to our "equally skilled" assumption, a mistake. Therefore - our Hero should call all-in even if he's less than a coin-flip, if the pot-odds justify it.

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From what I can tell, these and a few other points seem to confuse two issues that are not directly related.

Chip EV (CEV) and Dollar EV ($EV)

Making consistent -CEV plays in a tournament does not 'by definition' imply an increase in opponent $EV and does not imply an decrease in one's own $EV. Extending this, I think it is safe to say that even though equally skilled, we should not be inclined to take ANY +CEV edge we can get if $EV is what we are really concerned about.

$EV is a kind of a strange thing to even talk about in the context of a single play though I and others attempt to do it all the time. It would seem though (strange as it is) that -CEV plays can be +$EV in the context of tournament play.

Imagine for example a four handed situation like this

You (BB) have t3600
SB has t3600
Button has t400
UTG has t400

Blinds are 200/400 and antes are 50. After UTG and button pass, SB pushes all-in. You hold TT. SB is not a wild player, but is certainly capable of a push in this situation with less than premium hands. In fact, lets just assume you know his hand is JQo.

This is clearly a +CEV call, and may even be a +CEV situation for both you AND the SB even after you have called.

Strangely though, the two small stacks experience a major boost in $EV if the two of you collide and one of you is eliminated here. What this does imply is that despite your +CEV situation, both you and the SB have just lost $EV by getting into this big confrontation.

This actually brings me to an interesting thought. On any all-in steal on the bubble, the move itself does not seem to have a $EV independent of your opponent's reaction. If, for example, you are stealing with A7s and your opponent calls with KJo, it may be +CEV for both the steal and the call, and may even in some sense be +$EV for the steal and a fold, but if your opponent decides to call anyways (playing according to CEV concerns), he effectively lowers BOTH of your actual $EV in the tournament and increases the $EV of the small stacks.

Well, this may be unclear (or simply flawed) so before I ramble anymore, I'll see how this goes over first.

Regards
Brad S

-edit. In rereading this and the previous posts, I think I have noticed something that may be more accurate in describing what I mean. Making -CEV plays may actually increase your opponents $EV, but less than if you called. More importantly, avoiding slight +CEV situations on the bubble when facing elimination, though it will almost certainly lessen your $EV may still be better than making the +CEV play which will lower your $EV by even more.