I disagree that it fails logically. The argument, written modus ponens, is:

"If believing in God has positive expected utility, then you should do so".

Okay, now I think I'm starting to see the miscommunication: PW does not simply say what you've quoted there. It's typically associated with an argument about how the possibility of infinite utility from believing (and perhaps infinite disutility from not believing) outweights the small probability of it being true, and the utility of other courses of action, on account of its infinite size.

You're taking "Pascal's Wager" to refer only to certain premises the argument uses, not the full argument itself.