Comment by dllthomas

I think that subtly misses the point. The problem is that you're implicitly using a distribution that... isn't a distribution. And with this particular not-a-distribution, whether you should switch or not does not depend on the value of A. But with any actual distribution (... I think?) it does, at which point... no paradox. It's true that it's not clear (at least to me, but perhaps more generally) what distribution we should assume, but as long as we avoid treating something that isn't a distribution as if it were one we avoid the worst of it.