[gergery]

Very interesting. Seems like a Markov chain could get at a decent answer.

I dealt this out and played 3 hands for grins, assuming no blinds.

I’d guess that for the first 3-4 opponents you might average a 75-25 advantage for each play, between getting in with dominating hands or picking overcards to undercards where undercards are missing outs.

So on first all-in you’ll lose 25% of the time. Second all-in where you survive, you’ll lose the next two a total of 4.6% (.75*.25*.25), run a couple more and maybe you get to ~35% total loss thru the first 4 or so trials.

The times you haven’t lost then (~65%), you’ll have about a stack of 4 with 6 opponents, and maybe a typical hand advantage of ~65-35% now. So you’ll go bust maybe 5% of the time (.65*.35*.35 * .3 or so you must fact that bigger stack) on each of the next 4 opponent ranges (4 left, 3 left, etc.). Then heads up, assuming you come in with a 8-2 or 9-1 advantage, you will lose 3 in a row (or equivalent amount) around 20% of the time (.5^3 + some lose-lose-win-lose type scenarios).

Add those up, and I get maybe 35+5+5+5+5+20 = 75% chance of losing in aggregate.

Since you need to win ~>20% over the very long run to be EV positive, I’d guess this prop bet is 1) very, very close, and 2) Perhaps slightly EV positive.

But my numbers are obviously extremely rough, and slight changes could make this easily a EV negative bet. In fact, I think 75-25 might be too optimistic an average over the first few trials, so there’s a good chance this is EV negative. And if your friend is smart, I’d say it probably is EV negative 

--Greg