ClassBro

03Run the lesson: minimax, then alpha-beta

Below is a concept lesson from my teaching work: learning by building, not by watching.

Pick a starting position or play a few moves, then compare the two searches. They always agree on how the game ends with best play. Alpha-beta gets there by visiting fewer positions, and the rows below show where it saves the most.

1. 01

   Minimax

   Try every move until the game ends. A finished game scores +1 if X wins, −1 if O wins and 0 for a draw. X takes the highest score, O takes the lowest, and the scores pass back up the tree.

2. 02

   Alpha-beta

   Carry two numbers down the tree. Alpha is the best score X can already count on, and beta is the best score O can already count on. Once alpha reaches beta, nothing left in that branch can change the answer, so the search stops there.

3. 03

   Order

   Pruning cuts deepest when strong moves are tried first. Switch the search order and watch the alpha-beta count change while the outcome stays the same.

function minimax(board, player, order, stats) {  stats.nodes += 1;  const score = finalScore(board);  if (score !== null) return score;  let best = player === "X" ? -Infinity : Infinity;  for (const cell of order) {    if (board[cell]) continue;    board[cell] = player;    const value = minimax(board, other(player), order, stats);    board[cell] = null;    best = player === "X" ? Math.max(best, value) : Math.min(best, value);  }  return best;}