A Race 5 competitors who all have an equal chance to win...?

Question

If there is a race with 5 competitors, all equally skilled, is there any way to accurately predict the outcome? Or give yourself an advantage?

Also assume that you are able allowed to watch race as many times as you want. You dont have to predict the first winner, I think thats impossible.

Answer 1

No. If there is no way to distinguish who will win, then there is no way to guess with any advantage. The probabilities of each winning are:

Racer 1 - 20%
Racer 2 - 20%
Racer 3 - 20%
Racer 4 - 20%
Racer 5 - 20%

There is no way to have an advantage, and unless the outcome of one race depends on the outcome of previous races (which you have not stipulated) then watching previous races will not help (since they will all have an equal chance of winning those races too).

Answer 2

Without additional supplemental data to this problem the win ratio of competitors is 1:1:1:1:1 or 1/5 or 20% each.

Answer 3

If the outcomes of the races are statistically independent of each other, the answer is no. Otherwise, you might be able to gain some advantage if you can detect some sort of dependency of the outcome of one race on the previous ones. For example, if the winner of the previous race is more tired and therefore runs slower than usual.

Answer 4

Since all five competitors have an equal chance to win, the probability of any certain competitor winning is 20%.

That means no matter who you guess as the winner, your chances of guessing correctly are always exactly 20%.