My friend Mike and I were having a discussion about this last night as we battled heads up at the end of a single table tournament in my home. We had two contrasting schools of thought. I won't say what I think because I am really interested in an honest answer from the rest of you.

Assume for starters that we are talking about a situation where, at the end of a tournament, you have at least twice as many chips as the other guy. Let's say there are 30,000 chips in play so you have 20,000 (at least) and he has 10,000 (at most). How aggressive can you afford to be about putting him all in? How much does that change as he becomes more and more short-stacked?

Let's actually look at two somewhat different situations. In situation 1, you have 20,000 and he has 10,000. In situation 2, you have 25,000 and he has 5,000. So obviously if the other player doubles up once in situation 1, he moves ahead of you; in situation 2 he would have to double up twice to move ahead, and a single double up still gives him only half your chips.

Does this affect the kind of percentages you need to make a call? If he goes all in, or for you to put him all in? For argument's sake let's say you know for sure you're about 40% likely to win the hand - either you have a decent draw on the flop, or it's pre-flop and you hold a slight dog like K9 vs. his AT. With a 40% chance of winning, would you call his all in if you had twice his chips? If you had five times his chips?