How we looked
We took the 50 most recent finished jieqi games on the site with 20 plies or more, 2,939 positions in all. All 50 were played on 8 October by guests against a bot: 34 against AB-JChess, 13 against Pikafish at level 2 and 3 against full-strength Pikafish.
AB-JChess scored the candidate moves in every position. A move that turns a piece over was scored once for each piece it could be, and the scores were averaged, weighted by how many of each piece the side to move had not yet seen. The site's jieqi game review grades a reveal the same way, from only what the player could know.
A position counted when the best move beat the second best by at least 15 points of winning chance, both at our standard depth and at four times that, with every move searched to at least one full ply.
What turned up
58 positions passed, from 24 of the 50 games. 43 of them are ordinary tactics with a quiet move as the answer, and 15 of those never touch a face-down piece in the first five plies of the line. They are xiangqi puzzles that happen to come from jieqi games.
The other 15 turn on a hidden piece, and they come in two kinds. Of the 58, 25 had a person to move, and the person found the answer 19 times.
The lottery ticket
The side to move is lost on every quiet move, and one tile could save it. We found five, all from lost positions, and the right answer usually loses.
One chance in four was right for what Black could see, and the ticket was blank all the same. A piece taken face down leaves the board without being shown to its owner, so Black's count of unseen pieces still included two that were already gone.
| Black piece not yet seen | Where it really was |
|---|---|
| Chariot | Taken face down by Red on its move 17 |
| Cannon | Taken face down by Red on its move 20 |
| Soldier | The tile on a10 |
| Horse | The tile on i10 |
A stored move
A capture that wins whatever the tile turns out to be can wait: in the game below it stayed available for six turns. It works because a face-down tile moves as the piece whose starting square it stands on, so its first move, capture included, does not depend on the deal.
In 46 of the 2,939 positions a face-down tile could make a capture that won whatever the tile turned out to be. They came from 22 such captures, and the same capture was often there turn after turn; one stayed on the board for eight of its owner's turns. Nine were played. Holding one was usually free: in all but two of the 46 positions another move came within 15 points of it, and those two are one capture on consecutive turns, shown further down.
Which tile
The question is which face-down piece to move, and the right one works whatever it turns out to be. We found ten.
In the example below Black threatens d5xd1 check, with mate on the next move. Four of Red's 38 moves stop it. c1-a3 is the best of them, and it works by getting out of the way: the a1 tile moves as a chariot, so with c1 empty it can take back on d1. The tile on c1 can be any of six pieces, and c1-a3 stops the mate for every one.
| c1 turns out to be | Left face down | Black's best reply | Red's winning chance |
|---|---|---|---|
| Chariot | 2 | a10-b10 | 43% |
| Advisor | 2 | d5xa5 | 34% |
| Elephant | 2 | d5xa5 | 38% |
| Horse | 2 | d5xa5 | 33% |
| Cannon | 1 | d5xa5 | 36% |
| Soldier | 1 | d5xa5 | 32% |
Held to the xiangqi puzzle rules
Our xiangqi puzzles come from a miner with stricter rules. The opponent has just blundered, giving up 25 or more points of winning chance. The game was not already decided before that. After the right move the solver is winning, and after the second best move it is not.
| Step | Positions left |
|---|---|
| Scanned | 2,939 |
| Passed the xiangqi miner's rules | 15 |
| Mates in one dropped, as the miner does | 5 |
| Positions with a single legal move dropped | 4 |
A person was to move in three of the four and missed all three; the bot was to move in the fourth. None turns on a hidden piece. Every lottery ticket and every which-tile position failed, because the side to move was not winning or the opponent had not blundered.
Why we stopped
The chart shows the problem. A lottery ticket is all or nothing: right because one deal in four wins outright, and usually lost. A which-tile answer scores about the same for every piece, because it meets the threat on the board and the tile hardly matters. A fair puzzle needs a single line that works, and a decision about a hidden piece rarely has one.
We tried two ways round it. The first was to grade as if the face-down pieces were known, using the real deal. That gave 16 positions through the xiangqi rules: the same 15, plus one reveal that wins only because the tile was a cannon (100% for a cannon, 59 to 73% for anything else). A puzzle whose answer depends on what the solver cannot see is not one we would publish.
The second was to look for reveals that win whatever comes up: the best move turns a tile over, every piece it could be scores 81% or more, and the next best move 60% or less. There were none in the 2,939 positions.
The nearest thing to a fair jieqi puzzle we found is a stored capture, where the capture is certain and only the piece after it is luck.
Limits
| Limit | What it could change |
|---|---|
| One engine, AB-JChess, set every answer | A second engine could disagree |
| Only its top five to eight moves were scored | An unscored move could narrow a gap |
| 50 games from one day, guests against a bot | Other games could turn up other positions |
| The bot was to move in half the positions | Half of what we found no person faced |
What the 50 games say
Jieqi does not produce puzzles the way xiangqi does. Four positions in 50 games passed our xiangqi rules, none of them about a hidden piece, and the hidden-piece answers were bets or moves the tile hardly touched.
Skill shows in timing more than in guessing. A tile on its starting square moves as its home piece, so a capture it threatens is a move in reserve: play something else while it is safe, and take it before it can be blocked. When a tile must turn over, pick the one that holds whatever it is, and remember that your count of what it could be includes pieces your opponent took face down.
We would look again for puzzles about that timing, with an answer that holds for every deal, in thousands of games where a person was to move, checked by a second engine. Until then, the hidden pieces in jieqi are something to play, not something to solve.