EV Question

So Musky Boy and I have been having a conversation, that he - missing the crux of the argument - posted to ITH forums. Now I'm fine with ITH forums, although really, it's all about 2+2. Regardless, here's the heart of the argument.

In a SNG type game. You have 5 players left. You have average to slightly lower than average chip stack. Some of the other players at the table are very agressive, although you're better than they are overall. You figure you have about 7-10 hands before the blinds double, and start to really eat into your stack. If you double up, you are the chip leader.

Now you get into a big hand, heads up against someone with about the same, or more chips than you have. For an example, lets say you have AQo, and the flop is KQr. You bet, he raises. Now, given that this guy is aggressive, it's almost as likely that he's raising after pairing the rag with literally any kicker.

But still, you're probably a dog in this situation. The question here becomes, what is the EV of pushing all your chips in the pot? For the sake of verbosity alone, let's assume an 8 man tourney with paid finishes of $100/$40/$20 for the top 3.

By doubling up, you dramatically increase your chances of winning. If you lose, you are, for all intents and purposes, eliminated out of the money. Without actually doing the math, I think it's obvious that the EV is positive when you are the favorite. But, is the EV positive even when you are a dog?

For purposes of simplifying the math, let's assume that you effectively eliminate the other player by getting him all in. Before, your EV was $26(less than 1/5 of each position paid - $17 + $6 + $3). If you double up, your EV goes up radically $64(more than 1/4 of each $40 + $18 + $6. When you are on the bubble with a chip lead, that gives you a significant adgantage - maybe I'm overstating that a little.

Now, he could also fold, which would increase slightly your EV. But, you could also lose, which brings your EV to 0. So, at what level does your EV change from positive to negative? Let's see. Becuase I'm not smart enough to do the math, I'm going to assume the opponent never folds.

So over 100 hands, if you are 50/50, you EV would be $3,200 (50 wins @ $64). If you don't play that hand, your EV is 100 * $26 or $2,600. Clearly you should play that hand. Now, with that wide a differential, I think it's clear you should also play the hand as a dog too. How many wins (% dog) would you need to break even?

Turns out it's 40 - of course assuming that all this above math and the related assumption are correct.