I have the following question, just as in the title. Two players, let us name them A and B, play a game. 2 dice are rolled. Players A, B take turns to guess the sum. The one closer to the sum wins. Note, the person only wins but does not get the sum as a reward.
I would like to ask whether the following strategy is best, for this particular game as well as games like this one in general.
We go first and pick a number N such that the expected value of the absolute value of the difference between our number N and all the other ones is minimised. That is, we minimise $\sum_{k=2}^{12}p(k)|N-k|$ and thus deduce N.
The underlying probability distribution for two fair six-sided dice is as follow: show
If you're looking for the best strategy in this scenario (e.g, one time or endless independent rolls & the person only wins but does not get the sum as a reward), you would want to bet that your opponent's dice roll sum is 7 each and everytime.