a theoretical question

[gumpzilla]

Some recent posts about Karlsen-Sklansky hand rankings got me thinking about this. Karlsen-Sklansky ranks hands based on how big a stack you can profitably push with face up if folded to in the SB, assuming that the BB is going to call you with and only with hands that are ahead.

Now, it's clear that in a cash game, flipping your cards over in the SB is clearly going to be a losing move, because now your one remaining opponent can always make the best EV decision and in this context your opponent gaining EV corresponds always to you losing EV. So it can only hurt you if you flip your cards over. However, in a tournament setting, while it is still the case that the BB can make his or her optimal EV play, it is not clear that you're getting screwed here. This is because chip EV != $ EV, and changes in the chip position affect the equity of everybody at the table, not just the two blinds in this case. So it is at least theoretically possible that flipping over your cards can help both you and the BB here at the expense of everybody else at the table.

So, my question: can one construct a case where you actually benefit from flipping over your cards, assuming that all players involved are perfect ICM calculators? I've tried constructing a couple of scenarios but haven't come up with anything yet. This question has pretty much no relevance to SNG play, as far as I can tell, but I think it's interesting.