Does a cannon gain value by crossing the river, the way a soldier does?
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
Not in the way a soldier does. A soldier's value roughly doubles on crossing the river because it gains a whole new dimension of movement. A cannon already moves the same way everywhere on the board, so crossing the river changes what it can threaten, bringing it closer to the enemy palace, without changing how it threatens anything. Its underlying power is unaffected by which half of the board it stands on.
What actually changes when a cannon advances
An advanced cannon typically has more potential targets nearby, since the enemy's own pieces are closer and more numerous on that side of the board. That is a real practical gain, but it comes from proximity to targets, not from any change in the cannon's own movement rules.
The real risk of advancing too far
A cannon pushed deep into enemy territory can also run out of its own screens to use, since its own soldiers and other pieces are left behind. An advanced cannon with nothing nearby to jump can end up doing less than one still at home with a soldier or advisor sitting conveniently in front of it.
Related questions
So is there ever a reason to send a cannon across the river early?
Yes, if it has a clear target or screen waiting there, but not simply for the sake of advancing.
Does the cannon's screen rule change on the far side of the river?
No, the mechanism is identical everywhere on the board; the river has no special effect on cannons at all.