Why is the horse considered trickier to calculate than the cannon, even though the cannon has the extra screen rule?
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
Because a horse's threats depend on far more moving parts. A cannon's capture depends on one condition you can check at a glance, is there exactly one screen between it and a target. A horse's threats depend on up to eight destination squares and four separate leg points, any of which can appear or disappear the instant an unrelated piece moves nearby, which makes tracking a horse's real attacking range far harder to hold in your head.
The cannon's simplicity
Once you know a cannon's screen and target, its threat is fixed and easy to verify; either the condition holds or it does not. Reassessing a cannon after a random move elsewhere on the board is usually a quick check of one or two lines.
The horse's complexity
A single piece moving anywhere near a horse can silently open or close one of its eight potential moves by clearing or blocking a leg point, without that piece ever coming close to the horse's actual destinations. Keeping an accurate mental picture of what a horse threatens means re-checking all four of its legs after almost any nearby change, not just the obvious ones.
Related questions
Does this mean horses are stronger than cannons?
Not necessarily, it means they are harder to calculate accurately, which is a different question from raw strength. See piece values for how the two typically compare.
Does experience fix this problem?
Largely, yes. Strong players develop an instinct for a horse's real range that beginners have to calculate square by square.
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