Total Winning Saddlecloth Numbers

[mozzie789]

There is a race meeting with a number of races.

Each race has horses entered and each horse has a (saddlecloth) number, 1….x, with x being the number of horses entered in each race.

Each horse has a known probability of winning a race (reflected in its price).
I’d like to set a market where the winner is determined by adding the saddlecloth numbers of the winners of each race for the whole race meeting.

So, if there were 7 races in a meeting and saddlecloth no.3 won each race, then 21 would be the Total Winning Saddlecloth Number.

To simplify the overall market offered, there would be 3 brackets of numbers to choose the total from - for example, in a meeting with 7 races the brackets might be (7-26), (26-45) & (45+). Dead heat winners would have saddlecloth numbers averaged.

How would I determine the probability of each bracket occurring? Also, how would I determine the totals to include in the brackets (for a relatively equal chance of each bracket winning)?

 

[Office_Shredder]

Are there few enough horses that you could have a computer loop over all combinations of winners? If so you can explicitly compute the probability of every combination winning, and then add those up for each saddlecloth sum to see the chance of every sum ending up a winner.

If not, then this is probably going to be really hard or impossible