Pebbles, Solved Whole

Backward scoring solves the game of Pebbles completely, on an index card.

The rules: five pebbles on the table; players alternate; a turn takes one or two pebbles; whoever takes the last pebble wins. Work upward from the smallest endgames, scoring each count for the player about to move. One pebble left: take it — win. Two left: take both — win. Three left: taking one leaves two, taking two leaves one — either way the opponent inherits a winning count. Three is a loss no skill repairs. Four left: take one, and the opponent faces the poisoned three — win. Five left: take two, same poison — win. The table is the whole game: five rows, every position settled, and the first player wins Pebbles by taking two and never letting the poison leave the opponent's side.