Checkers

Hard Algorithms: Minimax, Alpha-Beta Pruning, Move Ordering

Checkers

Hard Algorithms: Minimax, Alpha-Beta Pruning, Move Ordering

Overview

Checkers (also known as Draughts) is a strategic game with roughly 5 × 10^20 possible positions—far too many to evaluate exhaustively. Here we use alpha-beta pruning, which reduces computation without sacrificing optimality.

Rules

  • Players move diagonal pieces forward
  • Capture opponent pieces by jumping over them
  • Reach the opposite end to become a “king” (moves in any diagonal direction)
  • First player to eliminate all opponent pieces wins

Alpha-Beta Pruning

Alpha-beta pruning eliminates branches of the game tree that cannot affect the final decision:

alphaBeta(position, depth, alpha, beta, isMaximizing):
  if depth == 0 or position is terminal:
    return evaluate(position)
  
  if isMaximizing:
    maxValue = -∞
    for each move in position:
      value = alphaBeta(nextPosition, depth-1, alpha, beta, false)
      maxValue = max(maxValue, value)
      alpha = max(alpha, value)
      if alpha >= beta:
        break  // Beta cutoff
    return maxValue
  else:
    minValue = +∞
    for each move in position:
      value = alphaBeta(nextPosition, depth-1, alpha, beta, true)
      minValue = min(minValue, value)
      beta = min(beta, value)
      if alpha >= beta:
        break  // Alpha cutoff
    return minValue

Optimizations

  • Move Ordering: Evaluate promising moves first to maximize cutoffs
  • Transposition Tables: Cache previously evaluated positions
  • Opening Books: Pre-computed optimal moves from the starting position
  • Endgame Tablebases: Perfect play when few pieces remain

Complexity

  • Search Depth: 10-12 plies (half-moves) with alpha-beta pruning
  • Speedup: Alpha-beta typically searches 100-1000x fewer positions than minimax
  • Branching Factor: ~8 legal moves per position

Interactive Demo

Challenge the AI in a game of checkers:

Checkers Game

Click a piece to select it, then click a destination to move. Red pieces are yours, black are the AI's.

Implementation Notes

A complete checkers engine requires:

  • Move validation and jumping logic
  • King promotion
  • Forced capture rules
  • Endgame evaluation heuristics

Code on GitHub

View the full checkers implementation with move ordering strategies and alpha-beta optimization.

Next Steps

Continue to Connect-4 to explore transposition tables and killer move heuristics for even more efficient search.