Nim Environment Documentation

Overview

Nim is a classic two-player mathematical strategy game involving several piles of objects. Players take turns removing at least one object from a single pile, and the player who takes the last object wins the game. This environment supports standard Nim gameplay, customizable pile configurations, and turn tracking.

Learn more about the game on Wikipedia.

Action Space

• Format: Actions are strings representing the player's move:

  • Removing Objects: Players choose a pile and the number of objects to remove using the format [pile_index quantity].

• Examples:

  • Remove 3 objects from pile 2: [2 3]
  • Remove 1 object from pile 0: [0 1]

• Notes: Players must remove at least one object from a single pile. Invalid moves, such as removing more objects than available, are rejected.

Observation Space

Reset Observations On reset, each player receives an overview of the initial pile state and gameplay instructions:

You are Player 0 in a 2-player Nim game.
Initial piles:
  pile 0: 3
  pile 1: 4
  pile 2: 5

Rules:
- On your turn, choose a pile and remove at least 1 object from it.
- The player who removes the last object wins the game.

Your action? (e.g., '[1 3]' to remove 3 objects from pile 1)

Step Observations After each move, players receive updates on the game state and actions taken:

[Player 1] Removes 2 objects from pile 1. [1 2]
[GAME] Player 1 removes 2 objects from pile 1.

Updated piles:
  pile 0: 3
  pile 1: 2
  pile 2: 5

It's now Player 0's turn.

Gameplay

• Players: 2 players (fixed)
• Initial Setup: Each game starts with a customizable list of piles (default: [3, 4, 5])
• Turns: Players take turns removing objects from any single pile
• Objective: Be the player to take the last object

Key Rules

1. Removing Objects:

   • On your turn, select any pile with at least one object remaining
   • Remove at least one object from that pile

2. Invalid Actions:

   • You cannot remove objects from an empty pile
   • You cannot remove more objects than the pile contains

3. Winning Conditions:

   • The player who removes the last object wins the game

4. Game Termination:

   • The game ends immediately when all piles are empty

Parameters

• piles (List[int], default: [3, 4, 5]):

  • Description: Sets the initial number of objects in each pile
  • Impact: Changing the pile sizes affects game strategy and length

• max_turns (int, default: 50):

  • Description: Maximum number of turns allowed
  • Impact: Prevents games from running indefinitely

Example Output

Player 0's turn.
Current piles:
  pile 0: 3
  pile 1: 4
  pile 2: 5

Action: [0 1]  # Removes 1 object from pile 0

Updated Piles:
  pile 0: 2
  pile 1: 4
  pile 2: 5

Player 1's turn.

Variants

Contact

For questions or issues related to this environment, please contact guertlerlo@cfar.a-star.edu.sg