probability - Dice rolling problem

Alice and Bob are playing a game. Alice has an $a$-sided die. Bob has a $b$-sided die. (The faces of an $n$-sided die have numbers $1$ through $n$ written on them.)

The game is simple: Each player rolls their die, and the player who rolls a strictly larger number wins. (It is possible that neither player wins.)
What is the expected value of the number Alice rolled.

For example if $a = 4$ and $b = 2$ then the result is $3.2$.