Sharpe ratio in a marble game

Alice and Bob each hold one red and one blue marble and simultaneously reveal one marble, chosen uniformly at random and independently. If both reveal blue, Alice is paid $1; if both reveal red, Alice is paid $3; otherwise Bob is paid $2. (All payouts come from a third party, so exactly one player is paid each round.) For a player's payoff, let the "return-to-variance ratio" be $\mathbb{E}[\text{payoff}]/\operatorname{Var}(\text{payoff})$; call Alice's $A_r$ and Bob's $B_r$. Compute $B_r - A_r$.