[fredup]

I think you need to do the algebra. You can't make a blanket statement like you want to.

You have taken things to an absurd extreme and gotten one result, I can "relax the assumptions" to the opposite extreme and get the opposite result:

Suppose the goalie only blocks 10% of shots when guessing correctly, and the kicker makes 80% to the strong side and 50% to the weak side. In this model it is obviously better to always kick to the strong side.