How can I calculate the probability of A winning against B, C and D in one simultaneous race?
I have generated probabilities of one athlete winning against another athlete in a race within python for loops. Now I want the probability of athlete A winning against all other athletes (as group) in one race they do together at once - not successively / consecutively.
However, I am not sure if I am allowed to simply multiply those probabilities.
I will do this for 70 athletes in groups of 8. This is just a simplified example to get the math right.
Probabilities
- A wins against B in 85.2% of 1000 runs.
- A wins against C in 51.3% of 1000 runs.
- A wins against D in 21.6% of 1000 runs.
Calculation of A winning against B,C and D in one simultaneous race.
When calculation the events 1) * 2) * 3) = 0.852 * 0.513 * 0.216 = 0.0944
This value of 9.44 % seams too low and only covers consecutive races. Therefore I thought of calculating 6*0,0944 to get 56.64 % for all possible combinations of A beating B,C and D.
- Combination of 1-2-3
- Combination of 1-3-2
- Combination of 2-3-1
- Combination of 2-1-3
- Combination of 3-2-1
- Combination of 3-1-2
When doing this for only 3 athletes in another test example I got a probability above 100 and now I am not sure if the above example works or if I am missing something.
Thank you for any guidance.