Question (Diablo 2)

Suppose purely hypothetically that there are abstract players A and B (player A does not know about the existence of player B). Player B creates a password game and flips a symmetrical coin. In case of heads-up, player B tells player A the name of the game / password and the experiment ends there. In the case of tails, player B creates another game with a different name / password, after which he informs player A (without throwing coins).

Now imagine yourself in the shoes of Player A. You have been given the name of the game with a password where Player B is waiting for you. What is the probability that the coin fell tails?