
12th April 2006, 09:16 PM
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Member
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Join Date: Jan 1970
Location: Sydney
Posts: 402
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Apparently there is something called the Harville Formula for these classes of calculations.
I haven't bothered delving into that as I'd already derived the formula from first principles as follows:
The Trifecta probability is
abc/(1-a)/(1-a-b)
where a, b, and c are the win probabilities for runners A, B, C.
For every permutation instance A, B and C in your field calculate that probability and add it to slots A, B and C of an array.
When complete that array will have the required probabilities.
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