Generator

Clobber on 2×3 — and who wins

A Clobber board with its value stated before anybody moves. A move takes one stone onto an orthogonally adjacent enemy stone, which is removed. The board is worth zero, so whoever moves first loses — and the reader moves first. Every reply the machine makes was worked out in advance from the game recursion.

3 essays call play-clobber. The drawing above is what it returns with no arguments at all; every call below passes it something, because a placement that passes nothing draws whichever member of the family the generator happens to default to rather than the one its essay argues about.

The positions it draws

2 distinct positions, harvested by running this generator again at the options each essay passed it.

Position	Worth	Outcome	Drawn in
`1×6 xoxoxo`	`0`	P	One row of Clobber · When the bracket decides
`2×3 xoxoxo`	`0`	P	The class where nobody runs out first · A game where nobody can be ahead in moves · Three different claims are all called solved

It plays back

The winner is named before a move is made, and every reply was worked out in advance.

A game where nobody can be ahead in moves — Clobber on 2×3 — and who wins, worth 0, P, 15 positions solved before the page was served.
One row of Clobber — Clobber on 1×6 — and who wins, worth 0, P, 9 positions solved before the page was served.
Three different claims are all called solved — Clobber on 2×3 — and who wins, worth 0, P, 15 positions solved before the page was served.

Where it is called

Changing this generator changes every one of these figures.

Clobber: every value smaller than every number. Blue and red stones on a small board. A move takes one of your own stones onto an orthogonally adjacent enemy stone, which is removed. Because adjacency is symmetric, a player has a move exactly when the opponent does — so no position can ever be worth a whole move to anybody, and every value that comes out is an infinitesimal.

Particular games

A game where nobody can be ahead in moves

A blue stone beside a red one is a move for both players at once. So neither player can run out while the other still has something to do — and every value the game produces is smaller than every positive number, by the shape of the rule rather than by inspection.

Three things the word “solved” is used for. The three standard senses of a solved game, priced on positions this solver can settle completely. Ultra-weak names the winner; weak supplies a strategy from the opening; strong supplies one from every position. They differ by orders of magnitude, and a claim that a game is solved is nearly useless until it says which of the three it means.

What it costs

Three different claims are all called solved

Hex is solved in the sense that the first player provably wins, by an argument that names no move whatever. Nim is solved in the sense that a formula gives the right move from any position at any size. Between them sit strategies for one opening, and databases of a few billion positions. The word covers all four.

Particular games

One row of Clobber

Every string of blue, red and empty squares up to eight long — 9,840 rows — carries one of only 111 values, and every one of them is infinitesimal. A third of the rows are worth exactly zero. Six alternating stones are worth zero and eight are worth a form that takes four lines to print, so the values do not simplify as the row grows: they explode, while the row stays trivial to describe.

The whole library · The position index · The figures that play back