What this game is

Two players share a checkerboard. One places dominoes upright, the other lays them flat, and each domino covers two empty squares. There is no capturing and no moving: the board only fills up. The player who cannot place a domino on their turn loses, so there are no draws.

The game was invented by the Swedish mathematician Göran Andersson and reached a wide audience in 1974 through Martin Gardner's column in Scientific American, under the name Crosscram. It became one of the central examples in Winning Ways for Your Mathematical Plays (1982) by Berlekamp, Conway and Guy: a filling board falls apart into separate regions, and the theory they built adds those regions up like numbers.

Who wins on 8×8

The first player. Dennis Breuker, Jos Uiterwijk and Jaap van den Herik proved it by computer in 2000; Nathan Bullock settled 10×10 in 2002, and Uiterwijk 11×11 in 2016 — the first player wins on those too. None of these proofs is a recipe a person can remember: they are huge searches made fast by counting tricks.

That is why the first move alternates here: one game you start, the next the computer does. Starting is a real advantage — between two machines of equal strength the first player wins almost every game.

How the machine counts

The evaluation is plain arithmetic. How many places are left where you could still put an upright domino, and how many for a flat one. On top of that, the safe places: two empty squares that no opposing domino can ever reach, because their neighbours on the other axis are already covered. A safe place is a move in the bank — it cannot be taken away.

From that comes an exact rule. If the player to move has more safe places than the opponent could ever fill, the game is won, however long it still lasts. The rule kicks in early: after about a dozen moves the machine usually knows the outcome, and the status line tells you when it does.

Levels

• Normal — the computer looks one move ahead, with its scores jittered, and plays a quarter of its moves at random.
• Hard — two plies: its move and your best reply.
• Expert — deepens the search for one second, six to eight plies in the opening, and from the middle of the game counts to the end. Measured over 30 games from random openings, it beats Hard 18–12, and Hard beats Normal 28–2.

Changing the level starts a new game, so a game is always scored at the level it was played at.

How to play against it

Count room, not squares. Every upright domino you place also destroys up to two flat places for the computer. Prefer moves that do both: block its lines and leave pockets of single columns that only you can fill. Do not spend your safe places early — they will still be there at the end, when they decide the game.