Stone Swap Showdown

Imagine a competitive game involving two participants, Player A and Player B. Player A starts with 8 stones, while Player B begins with 6 stones. The game unfolds as follows: Player A rolls a standard 6-sided die, and the result determines how many stones A takes from B. Subsequently, Player B rolls the same die, repeating the process in reverse. This marks the end of the round. The player with the most stones after the round concludes is declared the winner, ending the game. If both players possess an equal number of stones, the game results in a tie, prompting another round. What is the probability that Player B emerges victorious in 1, 2, ..., n rounds?