Fair Dice Comparison: d20 vs. 3d6

Two players each roll dice independently and repeatedly. Player A rolls a single fair 20-sided die (faces 1 through 20). Player B rolls three fair 6-sided dice and takes their sum. Each round, both players roll simultaneously. If their results are equal, they roll again. The game ends the first time the results differ, and whichever player has the higher number wins. What is the probability that Player A wins?