[JNash]

IF my hypothesis is correct..(and I will need to post it in the theory forum to get more comments), I believe that for a big stack there are two opposing forces at work:

1) Part 1 of the hypothesis is that the relationship between chip count and fair value (FV) of those chips (I'll call this the "payoff function") is concave for big stacks, and convex for small stacks, and the payoff function has its inflection point (switching from convex to concave)at the average chip count.

Incidentally, saying that the payoff function is concave is the same as saying that each chip you win is worth less than each chip you lose. (A commonly accepted statement). Saying that the payoff function is convex is the same as saying that each chip you win is worth MORE than each chip you lose. I claim that this is the case for short stacks. (This latter statement is, I believe, more controversial.)

If this is true, then a 50/50 situation (with a chip-EV of zero for both sides) will have a negative EV as measured in fair value terms for the big stack, and a positive one for the small stack. The implication is that short stacks should seek out chip-EV coinflips, while big stacks should avoid them. Or, to put it differently, short stacks can be correct from a FV-EV perspective to play hands that have negative chip-EVs. (Just how negative it can be and still be justified depends on how convex the payoff function is). [This is also the part of this post that relates to the original subject of the Negreanu thread--i.e. why and when it might make sense to go for big pots when you're seemingly getting the worst of it.]

2) The second part of the hypothesis is that big stacks have an a priori (i.e. before the cards are dealt) higher probability of winning the next hand than a small stack. That's because they get more respect, and so their bluffs and blind-steals have a higher probability of being successful.

If this is true, then big stacks can and should play more aggressively (open-raise pre-flop, bluff-raise or semi-bluff raise, etc.) and are actually correct (in the sense of having positive chip-EV) even though a short stack in the same situation might have a negative chip-EV.

These two forces point in opposite directions: avoiding 50/50 bets sounds like a "conservative" thing to do, while playing more hands (and raising them aggressively) sounds like a more "aggressive/loose" way to play.

While these two forces seem at odds, they can actually co-exist. If the big stack has a higher probability of being successful with bluffs and aggressive plays, then the big stack can enter more pots (i.e. situations that might have been negative chip-EV for a short stack become positive EV for the big stack.) As a result, the big stack is correct to play looser and more aggressively.

Now in situations where the big stack's clout has no value (e.g. when calling an allin bet from a short stack), the only thing that matters are the objective odds based on the cards. In this case, the concavity of the payoff function for the big stack (and the convexity of the function for the short stack) says that a 50/50 situation (with zero chip-EV expectation for both sides) are bad for the big stack and good for the short stack.

So while the two forces go in opposite directions, they do not contradict each other. Hope that helps...