Minimax on the whiteboard's tic-tac-toe game trees

It's O's move. Who will win? Expand the tree like you did on the whiteboard, score the endings yourself, and back the values up — X takes the max, O takes the min.

Tap a board to expand its children — you get one child per empty cell, and the box heading lists those cells · tap a finished board to score it · tap a scored parent to back up its value. Each boxed group is one player's set of replies to the board above it. Chips: X ▲ max · O ▼ min · a board whose game is already over is ringed on its three-in-a-row, says who won, and stops there — it has no children.

Set up a position (X = O or O+1):

Scoring: X wins = +1, O wins = −1, draw = 0. On X's turn the value is the max of the children (X wants the score high); on O's turn it's the min (O wants it low). That single rule, applied bottom-up, is the whole algorithm.

Try: score O's four replies — one of them hands X the game.