How does a defender with a full advisor-and-elephant setup actually hold a draw against a lone horse or a lone cannon?
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
By simply not moving anything unnecessarily. A lone cannon cannot force mate even against a bare general. A horse and its general do mate a bare general, but every defender added takes that away: a single advisor already saves almost one position in ten, and with a complete advisor-and-elephant defence the defenders have more than enough pieces to cover every point the lone attacker could threaten, and they are under no pressure to create a weakness by moving.
Why the attacker cannot make progress alone
A horse can be blocked at its leg by the defender's own pieces, and a cannon needs a screen it does not have inside an empty palace. Against a full set of advisors and elephants, the lone attacking piece simply cannot threaten enough points at once to force a defender to abandon a key square, so no combination of threats ever actually lands.
The one thing the defender must avoid
The only real danger is self-inflicted: moving a defender to an exposed square for no reason, or trading away a defensive piece that did not need to go. As long as the defence stays intact and simply mirrors the attacker's approach, the position is a completely safe, standard draw.
Related questions
Does this change if the attacker also has a soldier?
It can. A soldier gives the horse or cannon a second attacker, and the cannon a possible screen, so many more positions become winnable, though an intact defence still holds some of them. Against a bare general, horse and soldier wins every position and cannon and soldier 86.8% of them.
Is this the same reasoning as the insufficient-material rule?
Only for the cannon. A lone cannon is insufficient material even against a bare general. A lone horse is not: horse and general mate a bare general in every position, so what holds the draw here is the defence itself, not a shortage of mating material.
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