This situation was one a friend of mine was in the other day (this was also posted in my journal, but I wanted some more opinions on it. I've given my friend's explanation in the journal. I'm curious what people think about this).

He was playing in a satellite to the main event of the World Series. Top 2 players got the seat and some spending money while 3rd got $900. His total investment was $3.

They were down to 3 and the situation was like this:

Chip Leader 200k+
Player 1 (my friend) 5.4k
Player 2 (other opponent) 1k

Blinds were 2k/4k with an ante (I don't remember the ante). Player 2 is the button, Chip leader is the SB and my friend is the BB.

After posting blind and ante, my friend is down to 1.3k. Button folds and Chip leader does the minimum raise to put my friend all in.

What do you do? You have AQs.

(As far as a dynamic, you can make a valid assumption the chip leader will always put the players all in - which is how the situation ended up like this)

fold assuming the chip leader will be all in with both of you the next hand. Your friend will have more chips than the other guy and both be all in for the blinds. Therefore, as long as the bb doesn't win that hand, you get your seat. so you have a 2/3 chance to win if you wait. Even against a hand like AJ, you aren't really better than that. Since there's no point going for a win, fold and hope for a 2 on 1 to get 2nd.

I call and expect to win.

Call and win (66.2%): 11k in chips v 200k+ v 900 chips.
Call and lose (33.8%): $900
Fold: 1.3k chips v 200k+ chips v 900 chips

If you call and win, assume there is a 90% chance that your friend comes first or second. $12,000 x 0.90 x 0.662 = $7,149.6 EV in calling.
If you call and lose, there is a 100% chance you come third. $900 x 0.338 = $304.2 EV in calling.

Total $EV in calling = $7,453.8

If you fold, assume that the next hand will be a 3way all in (i can't see how the bigstack would fold from the button here). Bri is right in saying that if you OR the button win this hand, you will get second at least and get the seat. Therefore there is a 66.67% chance of getting the seat. $12,000 x 0.667 = $8,004 EV in folding.

If you fold and lose the 3-way all in, you will come third. $900 x 0.33 = $297 EV in folding.

Now assume that the shortstack wins the hand but you have the second best hand, here's where the math gets fuzzy and i'm not sure if i can say this but there's a 33% chance the shortstack wins and IF he wins, there's a 50% chance that you will come second, having some chips remaining (600). The probability of this is 0.33 x 0.50 = 0.165 or 16.5%. Now in this case, the next hand will have the bigstack in the SB and the shortstack still all-in in the BB as he would've only tripled up to 3,000 (900x3 + 100x3). You fold on the button and the bigstack calls the shorty allin. If the bigstack wins which is a 50% chance, you have the seat. $12,000 x 0.165 x 0.5 = $990 EV in folding.

Total $EV in folding = $9,291

You should fold.

Even if you assume a 100% chance of winning if you call and win, your total calling $EV only goes up to $8,248.2 which is still less than what it would be if you folded. The 66.2% chance of winning I assumed is if you're up against a random hand. If you put the opponents range to be tighter, such as any PP, Axs, Kxs and Qxs, you're less of a favourite and this further proves that folding is more profitable.

This is a pretty good example of why you gotta run the numbers ahead of time, huh? I thought through all the potential holes in the above argument I could think of, and there aren't any real ones. 90% chance to win if you take the first allin is actually conservative, I'd guess it is around 93%, and it really doesn't make a bit of difference. Clear fold.

If you want to be even sicker about it, fold the next hand 3way if you have a crap hand like 23o.. and you even further increase your odds. I'm not talking about folding 67o or anything.. just the absolute bottom barrel hands. I suspect that would even further make it ridiculously profitable to fold.