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Mathematical problem with placepot
The placepot is an accumulator in which you have to predict the horses that are placed in consecutive races.
More popular is the winpot in which you have to predict the winners, but placepot is easier.
The problem is this:
I have a set of probabilities for each leg (race) of the placepot.
Make it two legs for simplicity and the horses in the first leg have place probabilities {P1, P2, P3 ....}, those in the second leg have {Q1, Q2, Q3 ...}.
The rule is first and second horses place, so P1 + P2 + P3 + ... = 2, Q1 + Q2 + Q3 + ... = 2.
My playlines are N different playlines made up of two selections, one horse from each leg and the line probabilities are say P(i) x Q(j) for the first one, P(m) x Q(n) for the second one and so on, where i, j and m, n are the numbers of the runners in the first and second legs respectively for each of the lines.
The problem is how to compute the probability of at least one catch among the N lines ?
If it was winpot then it's simple of course. N different playlines can have only one winner line among them, so the sum of the P x Q products gives me the win probability.
But in placepot ?
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