Fair price of a put struck at 4 on a dice product

A contract settles at the product of two fair dice rolls. What is the fair value of a put on it with strike $4$, paying $\max(4-\text{product},0)$?

$1/4$. The put pays only when the product is $1$ (one way, paying $3$), $2$ (two ways, paying $2$) or $3$ (two ways, paying $1$). Its expected payoff is $(3+4+2)/36=\tfrac14$.