[kamrann]

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If you double up the first hand, your chances should double exactly, from a theroetical standpoint. If you are tripled up, your chances should triple. What reason in the world is there to say that they haven't tripled?

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Where does this come from? It hasn't been proved beyond doubt that your probability of winning is exactly equal to your stack size as a proportion of the chips in play, has it? That's been used as a reasonable assumption for various models, such as ICM, but I see no reason to take it as fact.

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That's like saying that when you win 100% of the chips you have a 99.2% chance of winning the tournament.

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This does not have to follow, for example if there was an inflexion point in the curve, it could reconverge to a 100% chance of winning at 100% of the chips, right?

Also, on a totally unrelated note:
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Ps = Q(1 +/- ln(e(|S-Q|)/Q)/T
Let's have a look at how this plays out. First of all, notice that when S = Q, Ps evaluates to Q/T

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Forgive me if this is a dumb question, my math is rusty, but if S = Q then surely you are taking the log of zero, which is undefined? It seems you are missing a closing bracket in the formula though, so maybe this is leading to my confusion.