A custom three-sided die with faces 1, 2, and 3 has probabilities $P(1) = 0.5$, $P(2) = 0.3$, and $P(3) = 0.2$. Two players play a game where the die is rolled repeatedly. The game ends immediately and Player A wins if the cumulative sum of all rolls is congruent to $0 \pmod 3$. Player B wins if the cumulative sum is congruent to $1 \pmod 3$. If the game continues until one player wins, what is the probability that Player A wins?