I don't think we can categorize it under a single fallacy. Furthermore...why would we want to? We'd have to explain our reasoning anyway.
What we do instead is simply look for the premises of the argument and attack them.
Pascal's Wager makes the following problematic premises:
- There either exists a god C or there don't exist any god.
- We either believe in a god C or we don't.
- If there exists a god C and we believe in this god then we benefit
- If there exists a god C and we don't believe in this god
then we suffer infinitely.
A similar argument to the original Wager can be used to say that it is
prudent is to believe in the devil (ofcourse not in conjunction with a
Christian God) or that black magic works or really any unlikely belief
that might have some potential benefit. When it justifies many cases does it not weaken the argument in case of God?
It does. Your argument basically denies (1). We could also just change the conception of a single god for (3) or (4) with a similar idea.
Pascal's Wager presupposes ignorance - god can't be proven or disproven through reason . Pascal's Wager excludes proof due to reason. Therefore we've no reason to think that (1) is true, and we can assume any number of possibilities. Hence we can't make a sensible choice anymore. And so on.
If someone posits that premise (1) just says that, "There exists a god or there doesn't.", then the firstly leaves us the possibility of adding a premise for other gods and secondly doesn't directly lead to (3) or (4).
Now if someone objects that the other conceptions are just impossible then that person tries to include reason. This breaks with the assumption of ignorance. So then we can just argue with other arguments against the conception that the person holds. So this at least makes Pascal's Wager unsucessful, because we need the condition of ignorance. The soundness is dependent on whether we consider only one god C possible, but that is outside the argument.
edit: edited for a significant flaw, as I intended for slightly different premises but then wrote other premises. Added explanation when the latter option - the one I used beforehand - of premises is used.