## NIM Game

**1. About the standard nim game**

Tradicionally, the NIM game is a board game for two players with quite simple rules. Starting with any number of counters distributed in any number of piles, two players take turns to remove any number of counters from a single pile. The winner is the player who takes the last counter.

Matematically, NIM is a subject of study in Combinatorial Game Theory, for which there is a ‘winning strategy’ and all the moves can be analysed. See for example:

- NIM-like Games
- Combinatorial Game Theory
- The eletronic Journal of Combinatorics: Combinatorial Games
- Integers: Electronic Journal of Combinatorial Number Theory
- Journal of Combinatorial Theory

**2. Our NIM Game for Android**

The game was developed by the group Geometrix. Besides the standard features, we added the following:

- Three variations to the standard rules: Misére, NIM 21 and Fibonacci;
- Each game can have more than 2 players (e.g. against computer players and/or other humans) in the local multiplayer mode or in the online multiplayer mode;
- A ‘power-up’ is available which allows a player to break the adversary winning strategy (just once), based on a harmonic oscillator equation (i.e. a second order ordinary differential equation). Graphically, the power-up is implemented as a gauge with damping, oscillating in the screen for ten seconds, where the frequency and amplitude are function of the difficulty level, the number of counters in the board, etc. The player may add or remove counters with it.
- Achievements unlocked by completing game related goals.

#### 3.** Our aim in developing this game**

Besides the fun and mathematical interest of the NIM game by itself, we intend to use this game as a tool to research how an anonymous player deal with a combinatorial problem. In particular, we are interested in the research issues behind the understanding of building and classifying user’s learning profiles by using techniques from deep learning, linear optimization, algebra and graph theory. For such reason, we collect basic statistics about players performance and their way of playing. If you are a player, we acknowledge your valuable collaboration to this project.

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