[LearnedfromTV]

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Now to your points:

I understand what you are saying, but with all due respect it isn't relevant to the points Jman was making. Jman's points were wrong from a clear logical perspective. He was basically saying that by making a move that is -CEV (in his own words) you are increasing your stack size. Later on he agreed that you are increasing it only some percentage of the time, but now the whole "tactic" got into a mess, because clearly the rest of the time you are giving chips to your opponent and (even according to Jman's ideas) you are helping him quite a lot.

I fully understand that there could be models for which "the outcome of interest (probability of winning tournament) is not a linear function of your stack size in a HU match". These ideas were discussed on this forum and elsewhere several times. But again, that wasn't the issue of this discussion at all. Jman was (like most of us here) basing his idea on the simple model in which CEV=$EV for HU (and as an evidence, he even used the ICM [he didn't need to, of course] to illustrate his points), and thus he wasn't at all arguing with it but only making different claims with regard to CEV alone (without any relation to the outcome of the interest), IN this model.

I'm sorry if I sounded patronizing, and I am certainly aware of limitations of EV in many cases. However, I still stand behind the points I've made on this thread.

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J-Man is arguing that the value of having 1100 chips 80% of the time and 595 chips 20% of the time is greater than the value of having 1000 chips 100% of the time. (In reality, by choosing not to push you are folding and leaving yourself with less than 1000 chips but this is accounted for in the EV calculation so we can use the simple example).

So 1100 80% + 595 20% > 1000 100%. Clearly this only works if chip equity and $ equity aren't linear. It seems J-Man is assuming they are by invoking a linear model in his argument. I think this contradiction is resolved as follows:

The reason the 1100/595 80/20 option is better, according to J-Man, is that the 80% of the time you get to 1100, your opponent modifes his hand range calling requirements such that we can push more hands profitably.

I think what most people who are disagreeing are saying is that the standard push/fold model already takes into account changes in the opponents calling range via adjustments in our pushing range. In other words, so long as we properly adjust our pushing requirements when the opponent adjusts his calling requirements, there is no such thing as an opponent making a "bigger" mistake at a given stack size... on every hand we can make an optimal play given his calling requirements so there is no way that having 1100 chips can be more than 1.1 times as valuable as having 1000 chips.

However, I think J-Man is trying to argue that if you are really close to the threshold for pushing any 2 *and* really close to a threshold where your opponent significantly changes his calling requirements and starts folding more, then there can be a nonlinear jump in chip value.

In other words, lets say the blinds and chip stacks are such that you should push any hand but 32 according to the standard model.. You have 32. If your opponent folds, not only do you move into push any two territory, but now he is much more likely to fold than he would have been had you folded and waited until the next hand. In that case the 80% chance of going to 1100 overrides the 20% of falling to 595.

Edited to add: The reason the "push any two" threshold is important is that this is the only point at which you can't fully compensate for an opponent tightening his calling standards by widening your push range. You can't push more than any two, although I'm sure a few here would like to try.

I have no idea if he is right, just my feeble attempt to parse the debate.