75 — Game: a simple opponent

A game opponent needs a rule, not just luck. In Nim, players take 1 to 3 stones from a pile; the one forced to take the last stone loses. The computer can play a strategy that keeps a winning position — and a fair mode that just rolls the dice.

#Steps

1. Start a pile and explain the rule:

   pile = 12
   show f"The pile has {pile} stones. Take 1, 2, or 3."
   

   copyrun it →

2. A move removes stones: pile = pile - taken. The game ends when the pile reaches 0 — the player who took the last stone loses:

   while pile > 0:
       ask take, "How many (1-3)? "
       taken = int(take)
       if taken < 1 or taken > 3:
           show "Take 1, 2, or 3."
           continue
       pile = pile - taken
   

   copyrun it →

   continue skips the computer's turn and asks again for a valid number.

3. The computer's strategy: after your move, the pile is n. If the computer leaves a pile of n % 4 stones... no — taking n % 4 stones (when it is not 0) leaves a multiple of 4, a losing position for you. When n % 4 is 0, any move gives you a winning position, so the computer takes a random 1-3 in that fair mode:

   move = pile % 4
   if move == 0:
       move = random_number(1, 3)
   pile = pile - move
   

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4. The full game. Save nim.nme:

   # nim.nme — take 1-3 stones; the last stone loses.
   # Run: nme r nim
   
   use random latest
   
   pile = 12
   show f"The pile has {pile} stones. Take 1, 2, or 3."
   
   while pile > 0:
       ask take, "Your turn — how many (1-3)? "
       taken = int(take)
       if taken < 1 or taken > 3:
           show "Take 1, 2, or 3."
           continue
       pile = pile - taken
       if pile == 0:
           show "You took the last stone. You lose!"
           break
       move = pile % 4
       if move == 0:
           move = random_number(1, 3)
       pile = pile - move
       show f"Computer takes {move}. Pile is now {pile}."
       if pile == 0:
           show "The computer took the last stone. You win!"
   

   copyrun it →

5. Run it with the player taking 2, then 2, then 1:

   printf '2\n2\n1\n' | nme r nim
   

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   The pile has 12 stones. Take 1, 2, or 3.
   Your turn — how many (1-3)? Computer takes 2. Pile is now 8.
   Your turn — how many (1-3)? Computer takes 2. Pile is now 4.
   Your turn — how many (1-3)? Computer takes 3. Pile is now 0.
   The computer took the last stone. You win!
   

   copy

   pile % 4 leaves a multiple of 4 after the computer's move, which is exactly why the strategy works.

#Try it yourself

Change the starting pile to 15 and play again: the strategy still wins unless the random fair mode helps you. Add a best counter of how many games you win.

#What you learned

• % (modulo) tells you the remainder — the key to the Nim strategy.
• continue skips to the next loop turn for an invalid move.
• A strategy is just a rule computed from the game state.
• A random fallback keeps the opponent honest when the strategy can't win.