Q

Unless there is some anomality in payout structure this statement usually holds true. But of course, if someone has 1 chip and if you bust him from tournament your minimal payout increases, winning this 1 chip from this particular player is very valuable and losing 1 chip to another player is not so valuable.

So busting a player with stack of X chips is not the same as winning X chips from big stack, for example.

I think you are correct. The real question, how exactly to consider POB in such scenario. If we win, we get a lot of push possibilities with low bust probability. If we fold, we continue to get pushed at and at some point we will have to make a call with high bust probability.

Soo.. why not now? If we wait a few hands, our double up will get us back to medium stack and won't grant us chances to make +EV pushes with low bust probability as big stack, thats for sure.

I wrote an article about related problem here: http://www.icmpoker.com/en/articles/icm-poker-and-ultimate-difference-between-call-and-push-spots/

Ben, ICM based analysis of single hand doesn't really consider bust probability and its implications. They can be achieved through some serious mental modeling only.

When you call there is a ~50% chance that tournament ends right here, and upcoming hands won't give you any opportunity to continue making +EV decisions hand after hand. In another 50% of cases you double up and continue tournament in a new scenario - as a big stack where chips flow in your direction. 

When you shove bust probability is much lower pretty much always, so by continiously pushing you can accumulate +EV hands one by one and improve your tournament result. 

This dynamic is pretty much outside of ICM single-handed scope, but it has to be considered when you are contemplating a ~0% EV call.

For example, in HU sng if opponent pushes first hand and you make a slightly +EV call, tournament can end immediately and you will be negative cause of rake being > than +EV call you made. So you can choose to pass some scenarios which have high probability of bust scenario in order to even have a chance to accumulate enough +EV decisions during tournament to beat rake.

In such scenario when you have a medium stack very few hands are actually just slightly -EV, most are very -EV, so this doesn't change much in calling ranges. ICM pressure is very high and (big stack push range % / medium stack call range %) ratio is simply huge.