There is a target number between [1, 100]. Player A and Player B guess a number. Who ever has a closer distance to the target, that player win.
Eg. A guesses 70, B guesses 80, but the target is 72. So A wins.
What would be the optimal strategy for player A and B? If you are player A, do you want to go first or second?
Attempt:
Assume uniform distribution, The expected value of [1,100] = 50.5
Thus, player A should pick 50. After that, player B should pick 51.
If player B picks 51, then player A have a chance of winning = 50% (because numbers from 1 ~ 50 will be closer to player A). And player B have also have a chance of wining = 50%.