Tournament won by two consecutive victories

With three evenly matched players, the previous winner plays the previous spectator. A pair of successive distinct winners $ij$ moves to $jj$ or $jk$ with equal probabilities, where $k$ is the remaining player. The transient states form two directed 3-cycles and each step has absorption probability one half. Starting with a game between two specified players, their overall winning probabilities are each $5/14$, while the original spectator wins with probability $2/7$.