Clobber — Every Move Is a Capture
Play Clobber against a perfect opponent. Every move removes a stone, so the game lasts at most one move fewer than the stones on the board.
Click one of your stones, then an adjacent enemy stone to capture it. Every move is a capture. If you cannot move, you lose. The computer plays perfectly.
The whole game lasts at most (stones − 1) moves
There is no move that is not a capture, so every move takes exactly one stone off the board. Start with k stones and there can be at most k−1 moves, because the last stone standing has nothing left to take. The bound is real and it is sometimes tight:
| Board | Stones | Perfect play | Longest possible game |
|---|---|---|---|
| 1 × 6 | 6 | second player wins | 4 of 5 |
| 1 × 8 | 8 | first player wins | 6 of 7 |
| 1 × 10 | 10 | first player wins | 7 of 9 |
| 1 × 12 | 12 | first player wins | 9 of 11 |
| 2 × 4 | 8 | first player wins | 7 of 7 — tight |
| 2 × 5 | 10 | first player wins | 9 of 9 — tight |
| 2 × 6 | 12 | second player wins | 10 of 11 |
| 3 × 3 | 9 | first player wins | 7 of 8 |
| 3 × 4 | 12 | second player wins | 10 of 11 |
And the winner is not a parity rule — which took twenty boards to learn
Solving every single-row board exactly, from n = 1 to 20, where W means the player to move wins:
Stop at n=10, as any reasonable person would, and it looks like a lovely period-6 pattern: three losses, three wins, three losses, three wins. It fits the first ten boards exactly. It is also wrong.
From n = 11 onwards (the dashed boxes) it settles into plain alternation — even boards win, odd boards lose — and the tidy blocks at the start are a coincidence of small numbers. So the honest statement is the one with a boundary in it: the first ten boards are irregular, and from eleven on the answer is simply the parity of n. There is no neat rule that covers both, and the test now asserts that period-6 fails so the page cannot be tidied back into being wrong.
Two-row boards, for m = 1 to 6, come out W W L W W L. That looks like period 3 — and this page is not going to make the same mistake twice, so: checked that far, and no further.
How to use
- Click one of your stones, then an adjacent enemy stone to capture it.
- There are no other moves — if you cannot capture, you lose.
- Pick a board size; the label says who wins it with perfect play.
- Try the other colour on a board you keep losing.
Frequently asked questions
What are the rules of Clobber?
Stones start filling the board in alternating colours. On your turn you move one of your stones onto an orthogonally adjacent enemy stone and remove it. That is the only legal move. If you cannot make one, you lose.
How long can a game of Clobber last?
At most one move fewer than the number of stones, because every move removes exactly one stone and the last one standing has nothing to capture. A ten stone board allows at most nine moves, and some sizes really do run that far while others fall short.
Who wins Clobber on a single row?
It depends on the length, and not by any simple rule. Solving every row from one to twenty gives L W W W L L L W W W L W L W L W L W L W, where W means the player to move wins.
Is there a pattern to which Clobber boards are wins?
The first ten single-row boards fit a period-six pattern exactly — and it is wrong. From eleven onwards the sequence settles into plain alternation, even boards winning and odd boards losing, so the tidy blocks at the start are a coincidence of small numbers.
Can a game of Clobber be drawn?
No. Stones only ever come off the board, so the game must end, and it ends when somebody cannot move. Whoever that is has lost.
Is Clobber solved?
On small boards, yes, and exactly — this page solves each one outright rather than searching to a depth. Large boards are open, which is why the sizes here stop at twelve stones.
Why is Clobber interesting to mathematicians?
Because a position splits into independent regions as stones disappear, which is exactly the setting combinatorial game theory was built for. The values of small Clobber positions are a standard worked example in the subject.
Does this send anything anywhere?
No. The solver runs entirely in your browser and nothing is stored or uploaded.
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