What happens when a chased piece also threatens the piece chasing it?
These answers restate the rules implemented by our open-source engine, which follows the WXF laws for movement, checkmate and both repetition rulings: a side that forces a repetition by perpetual check or perpetual chase loses rather than drawing. The chase half has not been validated against the official casebook. Where an answer refers to a specific position, that position lives on the linked reference page, where the build verifies it before publishing.
Direct answer
It becomes a mutual situation rather than a one-sided chase, and the adjudication has to look at the specifics rather than apply a simple rule. If both pieces are genuinely threatening each other in a way that keeps recurring, neither side may be solely responsible for the repetition, which typically points toward a draw rather than a loss for either player.
Why mutual threats change the analysis
The whole justification for requiring a chaser to vary is that they alone are choosing to force the repetition. If the piece being chased could just as easily capture the chaser, both players have a genuine choice available, and the repetition is not something either side is unilaterally imposing on the other.
Why this is one of the harder cases to rule on
Working out whether both threats are equally real, and not just one side dressing up an empty gesture as a counter-threat, is exactly the kind of judgment call the 110-diagram casebook exists to settle with worked examples rather than a short abstract rule.
Related questions
Does this apply to mutual checking the same way?
Yes, the same underlying idea as both players checking each other, mutual forcing generally points toward a draw.
Who decides whether both threats are genuinely equal?
The arbiter in formal play. This site's engine applies fixed tests instead, and has not been validated against the casebook: when the two pieces are of the same kind, such as chariot facing chariot, neither side is counted as chasing; otherwise each side's threats are judged on their own, and if both sides are chasing, the repetition is a draw.