Claude
94b51347c3
Nine pieces each on twenty-four points: place them, then move them, and every line of three takes an enemy piece off the board. Two pieces left, or no legal move, and the game is over. See docs/RULES-morris.md. The board is numbered ring * 8 + index, so its geometry falls out arithmetically rather than being typed in as a table of twenty-four rows: neighbours around a square are the index either side, the ladders between squares run through the odd indices alone, and a mill is three consecutive points centred on an odd one. A table would say the same thing and could be wrong in one row. A turn is one move object — the piece placed or stepped, and the enemy piece taken when that closes a mill. Generating the removal as part of the move rather than as a turn of its own means there is no moment where a player is halfway through a turn, so a device that drops off the network between closing a mill and choosing what to take cannot leave the table stuck, and the search counts one ply for what is one decision. Three rules about mills are easy to get backwards and all three are tested: the piece that arrives is what closes a mill, so stepping out takes nothing and stepping back in pays again; a slide along the line being completed is not a mill, because the third piece it needs is the one that just moved; and a piece in a mill is spared unless every enemy piece is in one, without which a player could never be reduced and the game would not end. The AI is negamax with alpha-beta and iterative deepening over the same rules engine, with a node budget so the placing phase does not stall a phone. It has no quiescence tail and does not need one: there are no exchanges in Morris. Its evaluation knows that being down to three is dangerous even with flying on — without that term the search reads three pieces going anywhere as freedom and starts steering towards losing pieces to get there, which is a real game it would throw away. Co-Authored-By: Claude Opus 5 <[email protected]> Claude-Session: https://claude.ai/code/session_019Pr6B8xDDtJJcb6WJMw7Ud
131 lines
5.6 KiB
Markdown
131 lines
5.6 KiB
Markdown
# Nine Men's Morris
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Two players, nine pieces each, on twenty-four points. Make a line of three and
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you take one of theirs. Take them down to two and the game is yours.
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## The board
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```
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a7 ────────── d7 ────────── g7
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│ │ │
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│ b6 ─────── d6 ─────── f6 │
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│ │ │ │ │
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│ │ c5 ─── d5 ─── e5 │ │
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│ │ │ │ │ │
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a4 ─ b4 ─ c4 e4 ─ f4 ─ g4
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│ │ │ │ │ │
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│ │ c3 ─── d3 ─── e3 │ │
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│ │ │ │ │
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│ b2 ─────── d2 ─────── f2 │
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│ │ │
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a1 ────────── d1 ────────── g1
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```
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Twenty-four points on three squares. A piece moves along a drawn line to the
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next point on it: around a square, or between squares along one of the four
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ladders that run out through the middle of each edge. **The corners have no
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ladder**, which is why the middle of an edge is worth more than the corner
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beside it — four ways off the middle square's mid-edge points, two off a corner.
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There is no point at the centre of the board, and the diagonals some boards are
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printed with are not part of this game.
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Points are named as the game is normally recorded: files **a**–**g** left to
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right, ranks **7**–**1** top to bottom. Only the intersections listed above
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exist; `d4` is the hole in the middle.
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## A game
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**Placing.** Starting with White, each player puts one piece at a time on any
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empty point until all eighteen are down.
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**Moving.** After that, a turn is one piece stepping along a line to an adjacent
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empty point.
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**Flying.** A player reduced to three pieces may move a piece to *any* empty
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point instead of stepping. This is on by default and can be turned off.
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## Mills
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Three of your pieces on one of the sixteen marked lines is a **mill**, and
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closing one takes an enemy piece off the board. Four mills to a square, twelve
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in all, plus the four that run out along the ladders.
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Three things about mills are easy to get wrong, and all three are implemented as
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written here:
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- **A mill is closed by the piece that arrives.** Moving a piece *out* of a mill
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takes nothing. Moving it back in closes the mill again and takes another
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piece — the same mill, opened and closed repeatedly, is a perfectly good
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way to win, and it is the strongest thing in the game.
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- **Sliding along the line does not count.** If the point you left is part of
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the line you have just completed, it is not a mill: the third piece it needs
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is the one that made the move.
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- **A piece standing in a mill cannot be taken** — unless every enemy piece is
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standing in one, in which case any of them may be taken. Without that
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exception a player whose pieces were all in mills could never be reduced, and
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the game would not end.
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Closing a mill is not optional, and neither is taking for it: a move that
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completes a line always carries the piece it removes. The only exception is the
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case where there is nothing left to take, when the mill simply goes unpaid.
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## Winning
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- **Reduced to two.** A player with two pieces left cannot make a line and has
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lost. This only applies once their hand is empty — a player mid-placement with
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two on the board has seven more coming.
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- **Nowhere to go.** A player with no legal move has lost. Since there is always
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an empty point to place on, this can only happen once pieces are being moved.
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## Draws
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Two players who can each hold a position have no reason ever to stop, so:
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- **Threefold repetition.** The same board with the same player to move, three
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times over, is a draw.
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- **No mill for a hundred plies.** Fifty moves each with nothing taken is a
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draw. Both figures are options, and the second can be turned off.
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## Options
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| --- | --- |
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| **Opponent** | Casual, Club or Strong — how deep the computer searches |
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| **Pieces each** | 3, 6 or 9 |
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| **Flying on three** | on by default |
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| **Threefold repetition** | on by default |
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| **Draw with no mill for** | never, 50, 100 or 200 plies |
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Fewer than nine pieces is a shorter game on the same board. It is *not* Three or
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Six Men's Morris, which are played on smaller boards of their own; calling it
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that would be claiming more than the code does.
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## Playing it here
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Tap an empty point to place a piece. Once everything is on the board, tap one of
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your own pieces and then tap where it goes; tapping a different piece of yours
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picks that one up instead. When a move closes a mill, the pieces you may take
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are ringed in red — tap one. If only one piece may be taken there is nothing to
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choose and the move goes straight through.
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The board is not turned round for Black. It is symmetrical and both players are
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looking at the same lines.
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## What the computer does
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A negamax search with alpha-beta pruning and iterative deepening, over the same
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rules engine the game itself runs on, with a node budget so a phone does not
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stall on the placing phase.
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It has no quiescence search and does not need one: in chess a fixed-depth search
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goes wrong by stopping halfway through an exchange, and in Morris there are no
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exchanges — a piece is taken for a mill and nothing is taken back.
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Its evaluation counts pieces first, then mills, lines that are one piece short
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of a mill, how much room each side has to move, and how many of the mid-edge
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junctions each side holds. It also knows that **being down to three is
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dangerous even with flying on** — without that, the search notices that three
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pieces can go anywhere, reads it as freedom, and starts steering towards losing
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pieces to get there.
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