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.

Black to move. Black has two tiles left, and from where Black sits each could be a soldier, horse, chariot or cannon. The a10 tile moves as a chariot on its first move, whatever it is, so a10-a1 lands on the back rank. If it turns out to be a chariot it is mate; anything else and it is lost. That is one chance in four, 25%, against 2% for the next best move. Black played it and turned over a soldier.

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 seenWhere it really was
ChariotTaken face down by Red on its move 17
CannonTaken face down by Red on its move 20
SoldierThe tile on a10
HorseThe tile on i10
Four pieces for two tiles, so each tile was a chariot one time in four from where Black sat. The chariot had left the board 11 moves earlier.
The same move with a chariot dealt to a10: mate. This is the deal Black was playing for, and it was not possible in this game.
Black to move. a10-a1, taking Red's face-down piece, and a10-b10 turn over the same tile, a soldier or a chariot at even odds from where Black sat. If it is the chariot, a10-a1 wins 95 to 98% of the time whatever it captured, and a10-b10 48%. On average that is 49.2% against 24.1%. Black found it, and turned over a soldier: Red had taken Black's chariot face down on its second move.

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.

Black to move. The i10 tile can run down the file as a chariot and take Red's i4 tile on this turn and each of the next five. Black plays elsewhere, the capture stays, and its score rises from 85% to 97%. Black takes on move 15; the tile is an elephant.

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.

Red to move. c1-a3 stops the mate but leaves the a5 cannon hanging, and Black took it at once. The tile was an advisor. Only a chariot on a3 would have guarded a5.
c1 turns out to beLeft face downBlack's best replyRed's winning chance
Chariot2a10-b1043%
Advisor2d5xa534%
Elephant2d5xa538%
Horse2d5xa533%
Cannon1d5xa536%
Soldier1d5xa532%
After c1-a3, by what the tile turns out to be. Black takes the cannon unless the tile is a chariot, and is better in every case. c1-a3 is the best move in the position and still loses most of the time: 36% on average, against 13% for the next best.

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.

StepPositions left
Scanned2,939
Passed the xiangqi miner's rules15
Mates in one dropped, as the miner does5
Positions with a single legal move dropped4
The same 2,939 positions through the rules our xiangqi puzzles pass.

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.

Red to move. e3-f3 and the engine's line after it. The interest is mostly jieqi's: Red's revealed elephant and advisors stand outside the zones they could never leave in xiangqi.
Red to move. i10-f10 and the engine's line, in which Black loses the chariot two moves later. No face-down piece is left on the board. Red played i10-i9 instead.
Red to move. h10-h9 and the engine's line. It is ordinary xiangqi: a tile turns over only on the line's last move.
Black to move. e7-f7 and mate in six, with no face-down piece left on the board. The bot played e3-c3 instead.

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.

WINNING CHANCE BY WHAT THE TILE TURNS OUT TO BELottery ticket: a10-a1, Black to moveSoldier0%Horse0%Chariot100%Cannon0%average 25%Which tile: c1-a3, Red to moveChariot43%Advisor34%Elephant38%Horse33%Cannon36%Soldier32%average 36%
The mover's winning chance after the answer, once for each piece the tile could be, from the two examples above. The dashed line is the average the review grades by.

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.

Red to move. The h1 tile moves as a horse and takes Black's chariot on g3, and it does that whatever the tile is. Red's winning chance is 93 to 95% for each of the three pieces it could be, against 78% for the next best move. The bot, Pikafish at level 2, missed it two turns running. The tile was a chariot. It is the only capture of the 22 that beat the next best move by 15 points.

Limits

LimitWhat it could change
One engine, AB-JChess, set every answerA second engine could disagree
Only its top five to eight moves were scoredAn unscored move could narrow a gap
50 games from one day, guests against a botOther games could turn up other positions
The bot was to move in half the positionsHalf 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.

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