MisNim+: A Variant of Misère Nim

MisNim+ is an accessible and strategic variation of the classic Nim game, designed for children, families, and educational settings. It combines traditional Nim gameplay with a unique scalable heap-splitting mechanic. While often played with sticks, the rules apply to any countable units such as bottle caps, coins, or paper drawings, adding strategic depth while keeping the rules easy to learn.

Standard Setup

The game begins with 4 heaps arranged in a pyramid:

Row 1: | Row 2: ||| Row 3: ||||| Row 4: |||||||

This represents heap sizes of: 1, 3, 5, and 7 units.

Rules of Play

On each turn, a player may perform one of the following actions:

• Partial Removal: Remove any number of units from a single heap.
• Whole Heap Removal: Remove an entire heap completely.
• Split Move (Special Rule): Remove any number of units from the interior of a heap, dividing it into two distinct heaps. The availability of this move scales according to the chosen gameplay mode.
  Example: Removing 1 unit from the center of a 5-stack results in stacks of {2, 2}.

Winning Condition (Misère Rule):
The player forced to take the last remaining unit loses the game.

Gameplay Modes & Variations

I. Foundation Level

• Easy Mode (Classic Misère Nim): No split moves allowed. This mode follows traditional rules and serves as the baseline for learning the core game before introducing the MisNim+ mechanics.

II. Standard MisNim+ (The Core Experience)

• Standard Mode: Uses the 1-3-5-7 setup. Each player is granted exactly one Split Move per game.
• Challenge Mode: Uses the 1-3-5-7 setup. Each player is granted two Split Moves per game.

III. Extended Field Variations

• Standard Mode+: Uses the 1-3-5-7-9 setup (5 rows). Each player is granted one Split Move.
• Challenge Mode+: Uses the 1-3-5-7-9 setup (5 rows). Each player is granted two Split Moves.

IV. The Ultimate Complexity

• Infinite Mode: This mode can be applied to either the 1-3-5-7 or the 1-3-5-7-9 setup. There is no limit on Split Moves; players may choose to split a heap on every turn if they wish. This transforms the match into a pure "take-and-break" game where every move drastically alters the mathematical nim-sum.

Official Identity Statement

“MisNim+ is an educational combinatorial game created by Jandee R. Bonifacio. Inspired by Misère Nim, it is enhanced by scalable heap-splitting mechanics designed for accessible strategic play.”

© 2026 Jandee R. Bonifacio. All rights reserved. MisNim+ is an original variant of Misère Nim.