Python: The Nim game

Today we are going to look at a small algorithm exercise in python, through the game called the nim game. The rule This is a two-player game. We have n matches to start with (for example 10). In turn, each player will take 1, 2 or 3 matches. The player who takes the last match loses. The algorithm This is a fairly deterministic game, in the sense that when you know the trick, you can't lose (unless you started from a losing position). Here is a table of the right number of matches to take (x representing a losing position): We can therefore observe an infinite periodic loop, with a period of 4. The player has lost (if the other plays well), when we have a modulo 4 = 1 (in other words the remainder of the division is equal to 1). The winning strategy is therefore to send the other player to a losing position. 1-player version We will formalize this in the algorithm, using the modulo function, to write the computer's AI. n = int(input("Enter the initial number of matches: ")) print("Number of matches : ", n) while n>0: j=-1 print("P1 turn") while j3 or j>n: j=int(input("How much do you take ? (1-3) ")) n=n-j if n==0: print("You lost !") else: print("P2 turn (cpu)") print("Remaining ", n) if n%4==3: p=2 elif n%4==2: p=1 elif n%4==0: p=3 else: p=1 print("I take some", p) n=n-p print("Remaining ", n) if n==0: print("I lost !") Two-players version Here is a version if you want experiment with a friend, keeping in mind this strategy : def nim_game(): print("Welcome to the Nim Game!") print("Rules: Players take turns removing 1 to 3 objects from the pile.") print("The player forced to take the last object loses.") # Initialize the pile pile = int(input("Enter the initial number of objects in the pile: ")) while pile 0: print(f"\nThere are {pile} objects in the pile.") print(f"{current_player}'s turn.") # Get the number of objects to remove try: remove = int(input("How many objects will you take (1-3)? ")) if remove 3: print("Invalid move. You can only take 1, 2, or 3 objects.") continue if remove > pile: print("Invalid move. You cannot take more objects than are in the pile.") continue except ValueError: print("Invalid input. Please enter a number between 1 and 3.") continue # Update the pile pile -= remove # Check if the game is over if pile == 0: print(f"\n{current_player} is forced to take the last object and loses!") break # Switch players current_player = player2 if current_player == player1 else player1 print("Game over. Thanks for playing!") # Run the game if name == "main": nim_game() Here is a little logic exercise, that you can use to practice algorithms in Python. Also, you know the secret and will not be fooled by this game anymore, have fun!

Mar 17, 2025 - 15:12

Today we are going to look at a small algorithm exercise in python, through the game called the nim game.

The rule

This is a two-player game. We have n matches to start with (for example 10).
In turn, each player will take 1, 2 or 3 matches. The player who takes the last match loses.

The algorithm

This is a fairly deterministic game, in the sense that when you know the trick, you can't lose (unless you started from a losing position).

Here is a table of the right number of matches to take (x representing a losing position):

We can therefore observe an infinite periodic loop, with a period of 4.

The player has lost (if the other plays well), when we have a modulo 4 = 1 (in other words the remainder of the division is equal to 1).

The winning strategy is therefore to send the other player to a losing position.

1-player version

We will formalize this in the algorithm, using the modulo function, to write the computer's AI.

n = int(input("Enter the initial number of matches: "))
print("Number of matches : ", n)
while n>0:
    j=-1
    print("P1 turn")
    while j<1 or j>3 or j>n:
        j=int(input("How much do you take ? (1-3) "))
    n=n-j
    if n==0:
        print("You lost !")
    else:
        print("P2 turn (cpu)")
        print("Remaining ", n)
        if n%4==3:
            p=2
        elif n%4==2:
            p=1
        elif n%4==0:
            p=3
        else:
            p=1
        print("I take some", p)
        n=n-p
        print("Remaining ", n)
        if n==0:
            print("I lost !")

Two-players version

Here is a version if you want experiment with a friend, keeping in mind this strategy :

def nim_game():
    print("Welcome to the Nim Game!")
    print("Rules: Players take turns removing 1 to 3 objects from the pile.")
    print("The player forced to take the last object loses.")

    # Initialize the pile
    pile = int(input("Enter the initial number of objects in the pile: "))
    while pile <= 0:
        print("The pile must contain at least 1 object.")
        pile = int(input("Enter the initial number of objects in the pile: "))

    # Player names
    player1 = input("Enter Player 1's name: ")
    player2 = input("Enter Player 2's name: ")

    # Start the game
    current_player = player1

    while pile > 0:
        print(f"\nThere are {pile} objects in the pile.")
        print(f"{current_player}'s turn.")

        # Get the number of objects to remove
        try:
            remove = int(input("How many objects will you take (1-3)? "))
            if remove < 1 or remove > 3:
                print("Invalid move. You can only take 1, 2, or 3 objects.")
                continue
            if remove > pile:
                print("Invalid move. You cannot take more objects than are in the pile.")
                continue
        except ValueError:
            print("Invalid input. Please enter a number between 1 and 3.")
            continue

        # Update the pile
        pile -= remove

        # Check if the game is over
        if pile == 0:
            print(f"\n{current_player} is forced to take the last object and loses!")
            break

        # Switch players
        current_player = player2 if current_player == player1 else player1

    print("Game over. Thanks for playing!")

# Run the game
if __name__ == "__main__":
    nim_game()

Here is a little logic exercise, that you can use to practice algorithms in Python.

Also, you know the secret and will not be fooled by this game anymore, have fun!