[pzhon]

A slight modification of my satellite example produces a non-satellite example. Of course this is contrived, and assumes your opponents' hands are face up.

SNG paying 50%-30%-20%
Villain 1: Started with 1600 chips, A[img]/images/graemlins/heart.gif[/img] A[img]/images/graemlins/diamond.gif[/img]
Villain 2: Started with 1000 chips, Q[img]/images/graemlins/spade.gif[/img] J[img]/images/graemlins/spade.gif[/img]
You: started with 7,400 chips, K[img]/images/graemlins/spade.gif[/img] 2[img]/images/graemlins/spade.gif[/img]
Turn (3200, 3 players, 1 all-in): A[img]/images/graemlins/spade.gif[/img] 7[img]/images/graemlins/diamond.gif[/img] 6[img]/images/graemlins/heart.gif[/img] 4[img]/images/graemlins/spade.gif[/img]
Villain 1 bets his last 500, Villain 2 is all-in, call or fold?

You are getting 3700:500, and you have 5 outs in 42 cards, so this is EChip-neutral.

If you call, 5/42 of the time, you win the tournament, and 37/42 of the time, you are heads-up against Villain 1 leading 5800-4200. That has the same average value as leading 6300-3700, 42.6% of the prize pool.

If you fold, 5/42 of the time, Villain 2 catches a spade that does not pair the board, and you lead 6300-700-3000. 37/42 of the time, you lead 6300-3700 when no spade comes. On average, that is worse than leading 6300-3700, since 6300-700-3000 is worse than 6300-3700, worth only 42.1% of the prize pool. In this situation, the ICM says you should be more eager to call than the chip counts.

A slight perturbation of this example, making your call larger, produces an example of a +E$ call that is -EChips:


SNG paying 50%-30%-20%
Villain 1: Started with 1601 chips, A[img]/images/graemlins/heart.gif[/img] A[img]/images/graemlins/diamond.gif[/img]
Villain 2: Started with 1000 chips, Q[img]/images/graemlins/spade.gif[/img] J[img]/images/graemlins/spade.gif[/img]
You: Started with 7,399 chips, K[img]/images/graemlins/spade.gif[/img] 2[img]/images/graemlins/spade.gif[/img]
Turn (3200, 3 players, 1 all-in): A[img]/images/graemlins/spade.gif[/img] 7[img]/images/graemlins/diamond.gif[/img] 6[img]/images/graemlins/heart.gif[/img] 4[img]/images/graemlins/spade.gif[/img]
Villain 1 bets his last 501, Villain 2 is all-in, call or fold?

Calling is worth 447263/1050000 = 42.5965% of the prize pool.
Folding is worth 38762514601/91130200000 = 42.5353% of the prize pool.
Calling is right by 0.061% of the prize pool despite costing 16/21 of a chip on average.

Side note: In this example, it would be right to call an extra 43.7 chips (costing 33.3 chips, 1/300 of the total chips in play) in this situation to ensure the elimination of Villain 2. This is a lot less than people think it is worth paying. Part of the reason is that Villain 2 is likely to be eliminated anyway. The other part is that it's just not worth much to eliminate a player, as the small total value is shared by all of the other players. The ICM also doesn't see that you could push the middle stack around when there is a short stack.