Red’s first turn alone makes 2,554 positions
Red has 44 moves from the starting position in both games. In xiangqi, black’s replies to them make 1,920 positions. In Duck Xiangqi, red’s turn is not over until the duck lands on one of the empty points, about 58 of them, so red’s first turn alone makes 2,554.
The gap compounds with every turn. After one turn each, Duck Xiangqi already has more positions than xiangqi has after two turns each.
| Positions after | Xiangqi | Duck Xiangqi |
|---|---|---|
| Red’s first turn | 44 | 2,554 |
| One turn each | 1,920 | 6,166,242 |
| Two turns each | 3,290,240 | Not counted |
Half of those positions are the same position
The duck matters when it lands where black’s next move goes: a point a black piece moves to, slides through, or jumps over. Anywhere else, black has exactly the replies it would have with no duck on the board.
The busiest point is e8, in front of black’s palace: a duck there takes 8 replies away whatever red played first. The 28 grey points change nothing. Put the duck on any of them and black faces the same choices, then moves the duck somewhere new, so the game that follows is the same game. Two small things differ: black cannot leave the duck where it is, and repetitions count the duck’s square.
So a search can look at one of them and skip the rest. Count every duck placement that leaves black the same replies once, and at the first move red’s 2,554 turns come down to 1,310.
A duck away from your opponent’s pieces wastes half your turn
The same board is a rule of thumb for players. Put the duck on a grey point and your opponent’s choices are exactly what they would be without it, so you have played a xiangqi move and passed on the rest of your turn. The duck earns its place in the paths of your opponent’s pieces: on the files their chariots and cannons use, and in front of their horses and elephants. At the start, the points that take the most away are on your opponent’s cannon row, where one duck cuts across both cannons at once.
The duck’s share of the tree grows as pieces come off
To see past the opening, we had Fairy-Stockfish play 64 games of each against itself and counted the choices at every move. Xiangqi’s choices shrink as pieces come off the board. In Duck Xiangqi each capture also frees a point for the duck, so a turn stays nearly as wide as it was in the opening, and 200 half-moves in it has about 100 times the choices of a xiangqi move.
The same search sees 25 turns ahead in xiangqi and 14 in Duck Xiangqi
That width costs search depth. Given the same number of positions to look at, Fairy-Stockfish sees a little over half as far ahead in Duck Xiangqi. We counted depth in turns in both games, and a Duck Xiangqi turn includes the duck. A search that counted each set of equivalent duck placements once would win some of that depth back. We have not measured how much.
| Positions searched | Xiangqi depth | Duck Xiangqi depth |
|---|---|---|
| 100,000 | 12 | 8 |
| 1,000,000 | 16 | 10 |
| 10,000,000 | 25 | 14 |
One small rule makes xiangqi a new game
The board, the pieces and the way they move are all xiangqi’s, so a xiangqi player can sit down and play Duck Xiangqi straight away. The duck still changes almost everything under them. Opening theory stops after the first move, because every line in it assumes there is no duck. And the game is harder for the kind of engine that plays it now. Classical search, the alpha-beta search Fairy-Stockfish runs, pays for every extra choice at every turn it looks ahead, which is why the depth gap grows with the budget.
We don’t know yet what strong Duck Xiangqi looks like. Some placements are pure technique, like the duck on e8 that takes away eight replies. Others might be aimed at the player rather than the position: a duck on a quiet point that invites one move, or a duck that blocks the line your opponent is watching while the real threat is somewhere else. An engine that sees 14 turns ahead finds the first kind. The second kind will show up only in games between strong players.
How we counted
The site’s own rules engine, the code that checks every move played here, counted the first move’s positions, and Fairy-Stockfish counted the deeper ones. Fairy-Stockfish also played the 64 games per variant, at 100,000 positions a move, with its neural network off. Xiangqi counts are strictly legal, so a move that leaves your own general capturable does not count. Duck Xiangqi has no check rule (you win by capturing the general), so every piece move counts.