How do you know if material is insufficient to win in xiangqi?
These answers restate the rules implemented by our open-source engine, which follows the WXF laws and is regression-tested against the official 110-diagram repetition casebook. Where an answer refers to a specific position, that position lives on the linked reference page, where the build verifies it against the engine before publishing.
Direct answer
Compare what remains against the standard list. A lone horse and a lone cannon cannot force mate against a bare general. A single chariot can. So can horse and cannon, two horses, either minor piece with a soldier, and cannon with an advisor as its screen. Against an intact defence of two advisors and two elephants, the bar is considerably higher still.
Why a lone cannon is the special case
It needs a screen to capture or check anything at all, and a bare general in an empty palace supplies none, so a lone cannon cannot even give check. Add a single advisor and the picture changes completely, since cannon and advisor beats a bare general comfortably.
Checking before you simplify
Before trading down toward what looks like winning material, run the comparison: what will actually be left, and is it on the winning side of the list. Trading into a lone cannon against a bare general throws away a win with no resistance required from the opponent.
Related questions
Does insufficient material ever change with more soldiers on the board?
Yes, a soldier is often enough to tip an otherwise insufficient combination into a winning one.
Is a chariot against a full defence ever insufficient too?
Yes, effectively; two advisors and two elephants intact typically hold a lone chariot to a draw.