Add Checkers, Backgammon, Mastermind, and Pirates and Bulgars

The four games that were listed but not written. Nothing in the
catalogue is marked "coming soon" any more.

Checkers is English draughts on the thirty-two dark squares, numbered
the way the game is written down. Captures are compulsory and a multiple
jump is one move object, so a player cannot stop halfway through one —
true by construction rather than by a rule that has to be enforced
somewhere. The move generator matches the published perft counts at one
to four ply (7, 49, 302, 1469), which fold in compulsory capture,
crowning and the men's forward-only rule all at once.

Backgammon's hard rule is not how a checker moves but that a player must
use as much of the roll as they can, and that cannot be checked one move
at a time: a move can be illegal precisely because playing it strands
the other die. So the generator works backwards from whole turns —
memoised depth-first over the remaining dice — and offers only the first
steps of the longest plays. Recomputing it after each checker is what
makes the rule true by construction. Every die comes from the table's
seed and a count of rolls made, which is in the state rather than beside
it so a game is reproducible from what crosses the wire. There is no
doubling cube; the rules document says so plainly.

Mastermind is played as a duel — both players are set a code and both
are breaking one — because the pencil-and-paper game gives the codemaker
nothing to do. It ends at the foot of a round, never mid-round, or going
first would be worth half a guess. It is the one game here with anything
to hide, so viewFor does real work: the host sends each device only its
own code, and a device that was never given a code refuses to score a
guess against it rather than quietly answering "nothing".

Pirates and Bulgars is Sackson's theming of Asalto, and the rules
document is explicit about which parts are attested and which had to be
chosen — the book could not be obtained. Two hunters who take by
jumping against twenty-four who cannot take at all, on a thirty-three
point cross whose drawn lines come from the same adjacency table the
moves come from, so the board and the rules cannot disagree.

130 unit tests across the four engines, all run locally as well as in
CI: game/ has no Android in it, which is what makes that possible.

Co-Authored-By: Claude Opus 5 <[email protected]>
Claude-Session: https://claude.ai/code/session_019Pr6B8xDDtJJcb6WJMw7Ud

docs/RULES-checkers.md

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+# Checkers
+
+English draughts, on the thirty-two dark squares of an eight-by-eight board.
+Twelve pieces a side, Black moves first.
+
+## The board
+
+Squares are numbered 1 to 32 the way the game has always been written down:
+square 1 at the top left, running along each row and down the board to 32. Black
+starts on 1–12, White on 21–32, and the two middle rows are empty. Only the dark
+squares are ever played on, so a move is two numbers — `11-15` for a quiet move,
+`11x18` for a jump.
+
+## Moving
+
+A man moves one square diagonally **forwards**. Black moves down the board,
+White up it.
+
+A man that reaches the far row is **crowned** and becomes a king, which moves
+one square diagonally in either direction.
+
+## Taking
+
+You take by jumping an enemy piece and landing on the empty square directly
+beyond it. Three rules follow, and all three are enforced by the engine rather
+than left to the players:
+
+- **A capture is compulsory.** If anything can be taken anywhere on the board,
+  a quiet move is not a legal move at all. The app simply will not offer one.
+- **A multiple jump is one turn.** Where a jump can be followed by another with
+  the same piece, it must be — and the whole chain is a single move. A shorter
+  prefix of a longer capture is never offered, so there is no way to stop
+  halfway.
+- **A man may not jump backwards.** Only kings take in both directions.
+
+You do *not* have to take the longest capture available: any complete jump will
+do. That is the English rule; international draughts requires the maximum.
+
+## Crowning mid-jump
+
+A man that jumps into the far row is crowned and **the turn ends there**, even
+with another jump available. This is the English rule and it is on by default.
+Turn *Crowning ends the turn* off and the man carries on jumping as a man,
+crowned only if it finishes on the back row — which is the international rule.
+
+## Winning
+
+A player who has no pieces, or who has pieces but no legal move, has lost. The
+two are the same condition as far as the engine is concerned: no moves is a
+loss, whatever the reason.
+
+## Draws
+
+- **Threefold repetition** — the same position with the same player to move,
+  three times over.
+- **Eighty plies without progress** — forty moves each with nothing taken and
+  nothing crowned. Both are options.
+
+## Flying kings
+
+Off by default. Turned on, a king slides any distance along a diagonal and takes
+an enemy piece from a distance, landing on any empty square beyond it — the
+international king.
+
+**One honest deviation:** a piece taken by a flying king is lifted immediately.
+International draughts leaves captured pieces standing until the turn ends, so
+they block the rest of the sequence, which occasionally forbids a chain this
+implementation allows. Fixing it properly means tracking captured-but-present
+pieces through the whole search, and it is written down here rather than
+pretended away.
+
+## What the computer does
+
+Negamax with alpha-beta pruning and iterative deepening, to seven ply at the
+strongest level — deeper than the chess player reaches, because compulsory
+capture keeps the branching factor low.
+
+There is no quiescence search and it does not need one: the usual failure of a
+fixed-depth search is stopping in the middle of an exchange, and compulsory
+capture handles that by itself, since a position where a piece has just been
+taken usually has the recapture as its only legal move.
+
+Its evaluation counts material first, with kings worth well over a man, and then
+two things beginners underrate: **men are worth more the closer they are to
+being crowned**, and **the back row is worth holding**, because an empty back
+row is a road to a crown for the other side. The two pull against each other,
+which is about right.
+
+## The move generator is checked against published numbers
+
+`CheckersRulesTest` counts the leaf nodes below the opening position — 7, 49,
+302 and 1469 at one to four ply — and those are the published figures for
+English draughts. A generator that matches them that far has very little room
+left to be wrong: the counts fold in compulsory capture, crowning and the
+men's forward-only rule all at once.