Alpha-beta minimax algorithm:

inputs:
  state, current state being explored
  alpha, the best score for max along the path to state
  beta, the best score for min along the path to state

return: minimax value of state

def maxv (state, alpha, beta):
 if cutoff(state): 
    return evalFun(state)
 for s in successors(state):
    val = minv(s, alpha, beta)
    alpha = max(alpha,val)
    if alpha >= beta: return beta
 return alpha

def minv (state, alpha, beta):
 if cutoff(state): 
    return evalFun(state)
 for s in successors(state):
    val = maxv(s, alpha, beta)
    beta = min(beta,val)
    if beta <=  alpha: return alpha
 return beta

def playGame(start):
   result = maxv(start,-infinity,+infinity) 
   while not gameOver(result):
      # The system makes the move it just discovered;
      # Gets his opponent's move;
      # Then calls maxv again.
      #
      # In the actual implementation, maxv and minv need to return
      # both the minimax value and the state to move to. See the
      # adversarial search code on the resources page for the full
      # implementation.