In the game Tetra Master, two players play a card with a number n between 0 and 15, inclusive. Then, both players roll a 16-sided die numbered from 0 to 15.
Both players than add up their dice rolls like so:
16 * n + dice(0, 15) = A
Then, both players roll another die from 0 to the number they previously rolled A inclusive (with an equally likely chance for every number) and subtract them:
A - dice(0, A) = B
The player with the higher B wins.
Given two different n, what is the probability that one n beats another? For instance, what is the probability that Player 1 with n=5 will beat Player 2 with n=2? Is there a formula that can be used to figure out the probability given two n without running simulations?