The Dice Duel
Two players each roll a fair six-sided die. The player with the lower number pays the other player the difference between the two numbers, in dollars (nothing changes hands on a tie). What is the expected amount of money that changes hands, that is, E|X − Y| where X and Y are the two rolls? Give a reduced fraction (a decimal rounded to two places is also accepted).
Related problems
Source: Standard expected-value exercise in wide circulation; no traceable original source. Statement written for AxiomIQ.