A mathematical model can be established: A and B make a series of fair gambling, so in each game, the probability of A winning is 0.5 and the probability of losing is 0.5. The result of each game is independent of each other, depending on the meaning of the question, and there is no draw.
Party A and Party B originally had A and B chips respectively, so
The probability of a losing light is B/(A+B), and the probability of b losing light is A/(A+B).
The topic of proof can be understood by the owner himself.