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-pirates.md

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+# Pirates and Bulgars
+
+Two pirates hold a stronghold at the head of a cross-shaped board. Twenty-four
+Bulgars come at it from the other three arms. Only one side can take pieces, and
+it is not the big one.
+
+## Note the caveats about the reconstruction
+
+**"Dalmatian Pirates and the Volga Bulgars" is Sid Sackson's theming, in *The
+Book of Classic Board Games*, of the game usually called Asalto** — itself a
+nineteenth-century descendant of Fox and Geese. That much is attested.
+
+The book could not be obtained, so **what is implemented here is Asalto**, and
+where Asalto's own sources disagree a choice had to be made. What follows says
+which is which, in the same spirit as the Ta Yü document: the game is playable
+and coherent, and it is not a transcription of a rulebook nobody here has read.
+
+**Attested** — the shape of the board and its thirty-three points; the
+stronghold being one nine-point arm; two hunters against twenty-four; the
+hunters taking by jumping and the crowd being unable to take at all; the crowd
+winning by filling the stronghold or by penning the hunters in; the hunters
+winning by cutting the crowd below the number needed to fill it.
+
+**Chosen here** —
+
+- **Which side is which.** Sackson's theme names two peoples; nothing available
+  said which of them is the pair and which the crowd. The pirates are the two,
+  on the reasoning that a raiding party is small and a stronghold is what you
+  raid.
+- **The diagonals.** Boards of this family are printed with diagonals in a
+  pattern rather than everywhere. The pattern used is the usual one: a diagonal
+  exists where the row and column of a point add to an even number, which gives
+  the centre eight lines and its neighbours four.
+- **Compulsory capture instead of huffing.** Traditionally a hunter who fails to
+  take when it could is *huffed* — removed by the other player. That is the same
+  rule with an extra step and a way to forget to use it, so a pirate that can
+  take simply must. It is an option, and turning it off restores the choice
+  without restoring the punishment.
+- **Bulgars may not retreat.** Standard for the soldiers in Asalto, and stated
+  here as an option because it is the single rule that most changes how the game
+  feels.
+- **The draw rule.** No source gives one. Sixty plies with nothing taken and no
+  ground gained is called a draw, because two sides that can each hold a
+  position otherwise have no reason ever to stop.
+
+## The board
+
+```
+        c7  d7  e7          ← the stronghold, nine points
+        c6  d6  e6
+        c5  d5  e5
+a4  b4  c4  d4  e4  f4  g4
+a3  b3  c3  d3  e3  f3  g3    (the middle band is seven wide)
+a2  b2  c2  d2  e2  f2  g2
+        c1  d1  e1
+```
+
+Thirty-three points: a seven-by-seven grid with the four corners cut away. The
+top arm — nine points — is the stronghold, which leaves exactly twenty-four
+points outside it. That is not a coincidence: the board and the pieces are cut
+to each other, and the game opens with every point occupied except the seven the
+pirates are not standing on.
+
+Lines run orthogonally between all neighbouring points, and diagonally where the
+row and column add to an even number. **The lines the screen draws come from the
+same table the moves come from**, so what you can see and what you may play
+cannot disagree.
+
+## The two sides
+
+**The Bulgars** — twenty-four. Move one step along a line, towards the
+stronghold or across it, **never back down the board**. They cannot take
+anything at all.
+
+**The pirates** — two. Move one step along a line in any direction, and take by
+jumping an adjacent Bulgar to the empty point directly beyond. A jump may be
+followed by another with the same pirate, and then it must be: a chain is one
+turn, and it cannot be abandoned halfway.
+
+The Bulgars move first. The pirates are already where they want to be.
+
+## Winning
+
+**The Bulgars win** by occupying all nine points of the stronghold, or by
+leaving the pirates with no legal move.
+
+**The pirates win** by cutting the Bulgars below nine, at which point there are
+not enough of them left to fill the stronghold however long the game runs.
+
+## What the computer does
+
+Negamax with alpha-beta pruning and iterative deepening, over the same rules
+engine the game runs on.
+
+The interesting part of a hunt game is that the two sides want opposite shapes
+out of the same board, and one evaluation has to speak for both. The terms are
+written from the Bulgars' point of view and negated for the pirates, so the two
+cannot drift apart and start valuing the same position differently.
+
+What it counts: how many Bulgars are left and how far up the board they have
+come; how much of the stronghold they hold; how much room the pirates have to
+work in; and — the term that does the most work — **how many Bulgars are
+standing where a pirate could jump them**. A Bulgar with an empty point behind
+it on a line is a Bulgar about to be taken, and not being jumpable is most of
+staying alive in this game.