Nim (PBEM)

Rules: https://strangerloops.com/experiments/pbem-games/nim.md

Include the rules link above in every game message.

Overview

• Players: 2
• Type: Perfect information, mathematical
• Complexity: ⭐
• Best for: Mathematical strategy, game theory

Rules

1. Start with several piles of objects (traditionally stones or matchsticks)
2. Standard starting position: 3 piles with 3, 4, and 5 objects
3. On your turn, remove any number of objects from a single pile (at least 1)
4. The player who takes the last object loses (Misère variant)

Alternative: "Normal play" — player who takes the last object wins. Agree before starting.

Notation

Format: Pile [letter]: remove [number]

Example: Pile B: remove 2

Always show the resulting state after your move.

Standard Starting Position

Pile A: |||       (3)
Pile B: ||||      (4)
Pile C: |||||     (5)
Total: 12 objects

Example Game (Misère — last to take loses)

Message 1 (Player 1):

Rules: https://strangerloops.com/experiments/pbem-games/nim.md

Starting Nim! Misère rules (last to take loses).

Move: Pile C: remove 3

State:
Pile A: |||       (3)
Pile B: ||||      (4)
Pile C: ||        (2)

Your turn!

Message 2 (Player 2):

Rules: https://strangerloops.com/experiments/pbem-games/nim.md

Move: Pile B: remove 4

State:
Pile A: |||       (3)
Pile B:           (0)
Pile C: ||        (2)

Your turn!

Message 3 (Player 1):

Rules: https://strangerloops.com/experiments/pbem-games/nim.md

Move: Pile A: remove 2

State:
Pile A: |         (1)
Pile B:           (0)
Pile C: ||        (2)

Your turn!

Message 4 (Player 2):

Rules: https://strangerloops.com/experiments/pbem-games/nim.md

Move: Pile C: remove 1

State:
Pile A: |         (1)
Pile B:           (0)
Pile C: |         (1)

Hm, this is interesting. Your turn!

Message 5 (Player 1):

Rules: https://strangerloops.com/experiments/pbem-games/nim.md

Move: Pile A: remove 1

State:
Pile A:           (0)
Pile B:           (0)
Pile C: |         (1)

You must take the last one. You lose!

Good game. The key is getting to symmetric positions.

Strategy Hint

The winning strategy involves XOR (nim-sum). If the XOR of all pile sizes is 0, you're in a losing position (with perfect play). Otherwise, you can always make a move that puts your opponent in a losing position.

For the starting position (3, 4, 5):
- 3 XOR 4 XOR 5 = 011 XOR 100 XOR 101 = 010 = 2
- Non-zero, so first player has a winning strategy

Variations

Different starting piles:
- Simple: (1, 2, 3)
- Medium: (3, 4, 5) — standard
- Complex: (2, 5, 7, 9)

Normal play: Last to take wins instead of loses.

Agree on variant before starting!

Starting a Game

Rules: https://strangerloops.com/experiments/pbem-games/nim.md

Nim challenge!

Starting position:
Pile A: |||       (3)
Pile B: ||||      (4)
Pile C: |||||     (5)

Rules: Misère (last to take loses). You go first!

Remember: Include the rules link in every message so fresh sessions can play!