Just saw this thread for the first time

OK I am going to think out loud on this one, ie on this page.

To use Mooee's last example, jockeys are called A,B,C, they ride in the two races on the $2.0, $2.50 and $10 chances each, in each race, adding to 100% in each race. (We have a friendly bookie)

OK.

There is 36 possible finishes.... I think, ie 6 possible ways in the first leg, six in the second. That's easy enough. So next we calculate the probability of each one coming up. Hang on, I'll go write an excel thing for that.

OK so what I did was write an excel thing working out the likelihood of each of the 36 combinations, and - most importantly - WHO WOULD WIN THE JOCKEY CHALLENGE given that that was the combination that came in.

I'll list here the 36 combinations, followed by their decimal chance of occurring, and who would win if that occurred.

a b c a b c 0.16 A
a b c a b c 0.16 A
a b c a b c 0.16 A
a b c a b c 0.16 A
a b c a b c 0.16 A
a b c a b c 0.16 A
a c b a c b 0.01 A
a c b a c b 0.01 A
a c b a c b 0.01 A
a c b a c b 0.01 A
a c b a c b 0.01 A
a c b a c b 0.01 A
b a c b a c 0.111111111 B
b a c b a c 0.111111111 B
b a c b a c 0.111111111 B
b a c b a c 0.111111111 B
b a c b a c 0.111111111 B
b a c b a c 0.111111111 B
b c a b c a 0.004444444 B
b c a b c a 0.004444444 B
b c a b c a 0.004444444 B
b c a b c a 0.004444444 B
b c a b c a 0.004444444 B
b c a b c a 0.004444444 B
c a b c a b 0.00308642 C
c a b c a b 0.00308642 C
c a b c a b 0.00308642 C
c a b c a b 0.00308642 C
c a b c a b 0.00308642 C
c a b c a b 0.00308642 C
c b a c b a 0.001975309 C
c b a c b a 0.001975309 C
c b a c b a 0.001975309 C
c b a c b a 0.001975309 C
c b a c b a 0.001975309 C
c b a c b a 0.001975309 C


total decimal chance of each jockey winning the challenge is:

A - 1.02
B - 0.69
C - 0.03
Total - 1.72

And, I suppose, therefore the chance of each winning the jockey challenge is:

A - 1.02/1.72 = 0.59 (59%) odds $1.68
B - same maths - $2.48
C - same maths - $56.63

Does this seem right? As I said, this is just 40 mins of me thinking as I went.

Duritz