Dice duel where ties win and one outcome forces a reroll

Two players, Dave and Buster, each roll a fair six-sided die at the same time. If the dice match, Buster wins. If Buster's die is strictly higher, Dave wins. If Dave's die is strictly higher, the round is void and both roll again, repeating until one of the first two outcomes happens. What is Buster's probability of winning?

$\tfrac27$. Each round is a tie with probability $\tfrac16$ and each of the two strict orderings has probability $\tfrac{5}{12}$. Ignoring the void rounds, Buster wins with probability $\tfrac{1/6}{1/6+5/12}=\tfrac27$.