You and your friend both play a game: you both pick a number (doesnât necessarily need to be an integer), and then roll two weighted sided dice with the values on the sides. The person who gets closest to the sum wins. The dice are non-uniform: there is a chance of rolling a sum of , and a chance of rolling each of the other sums . Assuming both you and your friend play optimally, if you go first, what is your strategy? Report your probability of winning as a percentage.