Odds

Nov 2014
7
0
Canada
I'm having trouble with a question, and need some help:
A race track betting board has the following odds against:
Horse A 9:2
B 6:1
C 11:3
D 19:2
E 10:1
F 13:2
A bet called a "triactor" is when you name the exact order of the first 3 horses in the race. What is the probability of winning the triactor?

I have been told that odds at the race track doesn't translate from straight probabilities, but factors in the number of betters etc.

I'm treating it more as a question on probabilities.

I assumed that the question is assuming that I'll pick the horses with the top 3 probabilities to win: so C, A, and B, in that order. What I'm also assuming is that the odds/probabilities listed are for finishing first. So, I thought I'd take 3/14 and multiply by (2/11)/(1-(3/14)) since we want to know the probability that A finishes first given C is out and then do the same for B. Is this reasoning flawed?
 

mathman

Forum Staff
May 2007
6,932
774
The probability of winning the triactor depends on which horses you pick!
 
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Nov 2014
7
0
Canada
Yes, but if I pick C, A, and B in that order (as mentioned) bc they have the highest probabilities, did I do the rest of it correctly?