Pot odds when all-in

[slapdash]

I've been reading the "Harrington on Hold 'em" books. For anybody who hasn't seen these, they are about tournament play, and I really like the style, with plenty of example hands given in detail. One thing I wondered about, though, was that he talks a lot about pot odds, even when the decision is whether to go all-in. For example, you have $1000, there's $1000 in the pot, and the only other player remaining in the hand bets $1000. So if you call, you get pot odds of 2/1. But since this is a tournament and not a cash game, if you call and lose then you're out and if you call and win then you're still in with a stack of $3000. If you fold then you're still in with a stack of $1000. For the pot odds calculation to be relevant, having a stack of $3000 would have to be three times as good as having a stack of $1000. How accurate is this? If your stack is three times as big, do you have roughly three times the chance of winning the tournament? Received wisdom is that in rebuy tournaments it's generally right to rebuy, because you're getting good odds. This suggests people think that small stacks are proportionately more valuable, so a stack of $3000 is less than three times as good as a stack of $1000. There's one very artificial situation where it's possible to calculate this exactly. This is where there are two players remaining and the blinds are so big that the small blind is bigger than the total number of chips (so both players are automatically all-in on every hand and there are no decisions to make ... I did say that this was a very artificial situation!). In this case, your chance of winning is exactly proportional to the size of your stack. But it's not at all clear to me what happens in more realistic situations.