Haven't looked at other responses yet because I want to try and do this on my own first.
EV = x * $3 + (1-x)[(4/46) * $7 - (42/46) * $2]
we set EV = 0 and solve for x:
1.2174 = 3x + 1.2174x
x = 28.87% of the time he needs to fold
Final conclusion: This really doesn't seem like that much, especially if he's the type of player who's going to peel flop wide.
Is this right? I had to look back at caddie's showdown thread to double check my equation but I think its correct.