Clobber every move is worth almost nothing

Black (Left) and White (Right) take turns. A move picks up one of your stones and puts it on an orthogonally adjacent stone of the other colour, which is removed. Whoever cannot move loses. Every Clobber position is all-small: its value is an infinitesimal such as ↑, *2 or {⇑* | ↓*}, so the side panel also shows the atomic weight, which counts the position in units of ↑. With hints on, the moves that keep the win are drawn as arrows; pick up a stone to see every capture marked ✓ or ✗.

value of the position

independent groups

How the values are computed

Stones that do not touch are separate games, so a board is the sum of its connected groups and a group of one colour is worth 0. Each group is valued once from its options, keyed by its shape up to the eight symmetries of the square, and reduced to canonical form (dominated options deleted, reversible ones bypassed), so equal games get the same id. The atomic weight follows Definition 3.8 of the paper below, comparing with a far star *m that no position of the game can equal.

Checked against the literature

The repository recomputes M. H. Albert, J. P. Grossman, R. J. Nowakowski and D. Wolfe, An introduction to Clobber, INTEGERS 5(2) (2005): the values and atomic weights of Figure 1, the lemmas, the conjectures on 1×n and 2×n strips (further than the paper took them), the award-winning problem of Figure 2, and the zero position of Figure 3. Every board up to 3×4 is also checked against a plain win/lose search.