I am reading the book Introduction to Probability by Dimitri Bertsekas and John Tsitsiklis Athena Scientific 2nd edition 2008 and I stumbled upon a probabilistic model problem and I can't seem to understand the answer to it. It goes as follows:
You enter a special kind of chess tournament, in which you play one game with each of three opponents, but you get to choose the order in which you play your opponents, knowing the probability of a win against each. You win the tournament if you win two games in a row, and you want to maximize the probability of winning. Show that it is optimal to play the weakest opponent second, and that the order of playing the other two opponents does not matter.
I don't get it. Why is it optimal to play the weakest opponent second? Why should I wait to use my best chances to a win? And after I do that, why is it that the order of the other two guys is not relevant?