The question is: You have 2 fairly weighted dice. You and an opponent pick any integer one after the other. If your number is closer to the sum of the faces on the rolled dice, you win. Do you want to go first and what number do you choose? What's the probability of winning?
I want to pick 7 and be the first one to go because the expectation of the sum of two dice is 7. But what's the probability of winning the game ? the answer is 7/12, I don't understand how to arrive at this number. Thank you.