I agree. Imagine that time is used (instead of current balance), and A pays out if the current second is divisible by three, and B pays out if it is one more th

I agree. Imagine that time is used (instead of current balance), and A pays out if the current second is divisible by three, and B pays out if it is one more than a multiple of three. A and B are both losing games if played every second, but it's not hard to combine them to win. And few people would call this a paradox.