Re: Theory: Gigabet\'s \"bands\" and \"The Finch Formula\" Grand Unificati
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If you were to add all the numbers for everyone in the tournament, would you get 1?
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Can't believe I didn't check that
If you have a stack of 2Q with a field of n players and they all have equal stacks, then they all have (T-2Q)/(N-1) = Q(N-2)/(N-1). Thus, each has a probability of coming in first of
P = Q(1 +/- ln(e(|Q(N-2)/(N-1)-Q|)/Q)/T
= Q/T * (1 - ln(e/(N-1)) = Q/T*ln(N-1)
Thus, the odds that we come in first should be 1-(N-1)Q/T * ln(N-1)
Ps = Q(1 +/- ln(e(|2Q-Q|)/Q)/T
= Q/T * (2+ln(2)).
I think you need to normalize.
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I figured I would. This is just a first cut. There are 3 things I like about it that I'd like to maintain:
1) If S = Q, Ps = Pq
2) It's continuous throughout
3) Ps hits 0 precisely when S = 0
Which should be doable.
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