Checkmate and assimilation

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QuaterniTS evaluates check and mate by controller, not just by the original colour of a piece. A piece retains its army colour when another controller gains it through assimilation. The rules below cover simultaneous mates, frozen kings, passes and draws. The examples are constructed positions designed to show a particular outcome; they are not official game records. The library also has a known unresolved checked-position boundary, for which it fails closed rather than inventing a game result.

0. Sources and conventions

• Official illustrated quick rules: turns, checkmate, frozen armies, draws and transfers.
• Official basic rules: game overview.
• Tutorial chapters 16–17: indirect checkmate and credit to the player completing the position.
• Tutorial chapters 18–20: frozen pieces and hypothetical defence of frozen kings.
• Tutorial chapter 21: two-player stalemate is a draw.
• Pawns and Starting position: movement and the 64-piece board.

Coordinates use files a–l, ranks 1–12, with White’s opening king at a1. Turns go White → Red → Black → Green, skipping frozen and eliminated controllers. An active controller may take a turn; frozen pieces stay on their squares but cannot move, attack or defend; an eliminated controller has lost its last king. Kings are never captured directly: mate removes them through adjudication.

1. Controllers, kings and army transfer

Every king controlled by the acting player must remain safe from all hostile controllers. This includes kings of other original colours in a validated custom position. A king is checked or mated according to its current controller, while its army colour remains unchanged.

When one controller still has another king after a mate batch, only the mated king’s retained-colour army transfers to the player who completed the position; other armies it controls remain under its command. If its last king is removed, every piece it still controls transfers, including previously assimilated, kingless armies. Each piece transfers at most once, and the survival decision uses the entire batch snapshot, including frozen kings still on the board.

Multiple-king example. White controls its own king a1 and a Red-army king a5, plus White rook b5; Black controls king l12 and rook h5. Only White and Black are active. White b5–b6 is illegal because it exposes the Red-army king on a5 to Black’s rook along rank 5. White a5–a4 is a legal move by the same controller, leaving both of its kings safe.

2. Indirect checkmate

The player whose action completes a mating position receives the mated army’s surviving pieces, even if a different player’s piece supplies the check. The tutorial’s indirect-mate examples establish this attribution.

In a constructed position, White has king e1, knight a3, queen b7; Red has king j12; Black has king l12, rook a5; Green has king a1, rook g8. No king starts in check: White’s knight blocks Black’s rook on file a. White moves the knight a3–c4, uncovering Black’s rook attack on Green’s king. Green cannot escape, block or capture the checker. Green’s king is removed and rook g8 transfers to White’s control, retaining its Green army colour. White made the action; Black’s rook delivered the check. Red and Black remain active, so there is no winner yet.

3. Frozen pieces and frozen kings

Frozen pieces occupy and block their squares but do not attack, defend or move. A non-king frozen piece can be captured; a frozen king cannot be captured directly. For mate evaluation only, a frozen king is assessed as though its own pieces could defend it. This avoids calling a frozen king mated when an otherwise legal hypothetical defence exists.

Fixture 3a: frozen pieces do not attack

With frozen Black king l12 and rook a5, active White king a1, Red king a12 and Green king l1, White may move a1–a2. The inert rook does not attack a2; Red moves next.

Fixture 3b: a frozen king can be mated

With frozen Green king a1 alone, active White king c3, Red king a12 and Black king l12, White c3–b2 mates Green. White’s king attacks a1, a2 and b1; the frozen king’s reciprocal attack does not make b2 unsafe. Green’s king is removed and Red moves next.

Fixture 3c: hypothetical defence prevents mate

White has king c2, knight c1 and rook b2; Red and Black have kings a12 and l12. Frozen Green has king a1 and rook a5. White b2–a2 checks Green’s king. Its escapes are covered, but under hypothetical active defence Green’s rook could capture the checker on a2 along the open file a. Green remains frozen and is not mated.

Fixture 3d: frozen pieces block and can be captured

White king a1 and rook d4 face frozen Black king l12 and ordinary pawn d6; Red king j12 and Green king l1 are active. The frozen pawn blocks White’s rook until White captures it with d4×d6 along an open d5. It did not attack or move, but its occupied square was a real obstacle. The frozen Black king remains on the board.

A frozen king still on the board counts when evaluating whether its controller retains a king, even though that controller is not active.

4. Mate batches and actor safety

After a committed action, evaluate all on-board kings in the same post-action snapshot. Award all kings mated in that snapshot to the player who made the action, in fixed White → Red → Black → Green order, then remove/transfer them together. Re-evaluate the resulting position for newly revealed mates and repeat until none remain. Removing one king must not retroactively revoke another mate from the same snapshot.

Fixture 4a: two simultaneous mates

White king e1, rook f1, knights c10, d10, i10, j10; Red king a12; Black king l12; Green king g6. White f1–f12 checks Red and Black along rank 12. The knights cover their escape squares, so both kings are mated in one snapshot. White receives both armies; Green remains active and moves next.

Fixture 4b: a cascade

White king e6, rook a1, knights b3, c5, d4, j4, k4; Red king b1; Black king l1; Green king g6. White c5–d3 removes Red’s last escape b2. Red is mated, so its king is removed. That removal opens the White rook’s rank-1 attack on Black; the knights cover Black’s remaining escapes. Black is mated in the next batch. Both awards go to White; Green moves next.

Fixture 4c: why a snapshot matters

This is an abstract attack example, not a playable board position. It isolates the order of operations: the tokens qR, qB and qG stand for Red’s, Black’s and Green’s king squares, while eR1/eR2, eB1/eB2 and eG1/eG2 stand for their escape squares. White also has a king qW. Each controller initially has one king and one non-king piece: White rook, Red rook, Black knight and Green bishop.

State	Attacks and resulting mates
Before White’s action	Red’s square qR is safe; Black’s square qB is attacked but escape eB1 is free; Green’s qG is safe. No king is mated.
After White’s action, same snapshot	White attacks qR, eR1, eR2, qB, eB1 and both Green escapes. Red’s king attacks eB2. Both Red and Black have their king square attacked and both escapes covered. Red and Black are mated together; Green’s king is not yet attacked.
If Red were removed first	Red’s attack on eB2 disappears. Black’s king is still checked but can escape to eB2; this incorrect sequential process misses Black’s mate.
After the proper Red-and-Black batch	Both kings are removed. Their rook and knight transfer to White, retaining Red and Black army colours. The open line lets White’s rook attack qG; both Green escapes are covered, so Green is mated in the next batch.
After the Green batch	Green’s king is removed and bishop transfers to White without changing its army colour. White is the only active controller and wins.

The simultaneous snapshot awards both Red and Black, even though Black ceases to be mated if Red is removed alone. Each king and piece is awarded or transferred once. This example illustrates the batch algorithm; actual mate detection also considers captures and blocks, not just king escapes.

Fixture 4d: post-batch safety

The acting controller’s own kings must still be safe after the complete hypothetical cascade. If a batch would remove one of its kings or leave one in hostile check, the candidate is an ordinary illegal move: no board, turn, history or award change. For example, in a constructed position with White king a1, rook d4, knights b2, f3, d3, h2; Red king e1; Black king l12, rook h1, knight b4; Green king a12, White d4–e4 would mate Red. Removing Red’s king e1, however, opens Black rook h1’s attack along rank 1 to White king a1. The move is rejected atomically, with no Red award or removal.

Internal pre-batch defences are not necessarily publicly committable moves. The unresolved checked position explains the distinct UnresolvedAdjudicationError guard; the software error is not a mate, pass or draw.

5. Passing and stalemate

With more than two active controllers, an on-turn controller that is not in check and has no legal move may pass(). The board stays unchanged, a pass event is recorded and the turn advances clockwise. Passing while checked is not allowed. With exactly two active controllers, no legal move while not in check is a stalemate draw, as specified in tutorial chapter 21. A checked king with no internal defence is instead mated. No repeated-position, move-count or insufficient-material draw is inferred.

Fixture 5a: pass with four active players

Start with active kings White a1 (on turn), Red a12, Black l12 and Green l1, plus Black rooks b5, c2. White is not checked, but all its escapes are covered (a2 by c2, b1 by b5, b2 by both). White may pass and Red moves next.

Fixture 5b: two-player stalemate

If Red and Green are eliminated from the same setup, leaving only White and Black active, White is still not checked and has no legal move. The result is a stalemate draw, not a pass.

A pass is a turn-advancing action and cannot hand the next checked controller an unresolved position: the library rejects such a pass atomically with UnresolvedAdjudicationError. It does not invent a mate batch for a pass, because no piece moved.

6. Draw proposals and responses

A draw offer must come from the controller on turn and requires unanimous agreement from all other active controllers. A rejection leaves play in progress; frozen and eliminated controllers do not vote. The proposal and responses are undoable administrative events. For example, from the four-army starting position White proposes; Red, Black and Green accept: the game ends in a draw. If Green rejects, White remains on turn. One undo() after Red accepts reverses only that response, leaving the proposal pending. See Draws and other actions for offer expiry and freeze sequencing.

Fixture 6: offer acceptance, rejection and undo

From the four-army starting position with White on turn, White proposes a draw. If Red, Black and Green all accept, the game ends in a draw. If Green rejects, the offer clears and White stays on turn. In a separate proposal, Red accepts and one undo() reverses only that response: the offer remains pending with Red’s vote restored to outstanding. None of these operations changes the board or advances the turn.

7. Last active controller

The last active controller wins even if frozen kings remain on the board.

Fixture 7: mate leaves one active player

White king a1, rook b10, knights c10, d10; Red king a12 active; Black king l12 and Green king l1 frozen. White b10–a10 mates Red: a11 is covered by the rook, b12 by c10, b11 by d10. Red’s king is removed and White wins as the sole active controller; frozen Black and Green kings stay on the board.

Fixture 7b: actions after the winner

With White king a1 active and Red a12, Black l12 and Green l1 frozen, White has already won as the only active controller. A subsequent resign("white") is rejected without changing the winner, board or history. A match cannot reach zero active controllers through valid sequential play: the game ends when only one remains. A validated in-progress snapshot with none is rejected rather than treated as a draw. See the example match for an administrative finish instead of a mate.