https://github.com/beling/impartial-games
Rust software for solving impartial games.
https://github.com/beling/impartial-games
cgt chomp chomp-game combinatorial-game combinatorial-game-theory cram game-tree game-tree-search grundy impartial-games mex solver solvers sprague transposition-table
Last synced: 7 months ago
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Rust software for solving impartial games.
- Host: GitHub
- URL: https://github.com/beling/impartial-games
- Owner: beling
- Created: 2023-05-30T16:31:27.000Z (about 2 years ago)
- Default Branch: main
- Last Pushed: 2024-09-12T21:20:19.000Z (9 months ago)
- Last Synced: 2024-09-13T11:02:12.684Z (9 months ago)
- Topics: cgt, chomp, chomp-game, combinatorial-game, combinatorial-game-theory, cram, game-tree, game-tree-search, grundy, impartial-games, mex, solver, solvers, sprague, transposition-table
- Language: Rust
- Homepage:
- Size: 192 KB
- Stars: 3
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
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README
Rust libraries and programs for solving [impartial games](https://en.wikipedia.org/wiki/Impartial_game) and calculating their [nimbers](https://en.wikipedia.org/wiki/Nimber), developed by [Piotr Beling](http://pbeling.w8.pl/).
Currently, only the [normal play convention](https://en.wikipedia.org/wiki/Normal_play_convention) is supported, but support for [misère games](https://en.wikipedia.org/wiki/Mis%C3%A8re#Mis%C3%A8re_game) is planned.
Included libraries:
- `igs` ([crate](https://crates.io/crates/igs), [doc](https://docs.rs/igs)) - solves [impartial games](https://en.wikipedia.org/wiki/Impartial_game) under the [normal play convention](https://en.wikipedia.org/wiki/Normal_play_convention);
- `ogs` ([crate](https://crates.io/crates/ogs), [doc](https://docs.rs/ogs)) - solves [octal games](https://en.wikipedia.org/wiki/Octal_game).
Included programs:
- `igsolve` ([crate](https://crates.io/crates/igsolve), [doc](https://docs.rs/igsolve)) - a console-based application for calculating nimbers with `igs`;
- `ogsolve` ([crate](https://crates.io/crates/ogsolve), [doc](https://docs.rs/ogsolve)) - a console-based application for calculating nimbers with `ogs`.
# Installation
Programs can be compiled and installed from sources. To do this, a Rust compiler is needed.
The easiest way to obtain the compiler along with other necessary tools (like `cargo`) is
to use [rustup](https://www.rust-lang.org/tools/install).
Once Rust is installed, to compile and install a program with native optimizations, just execute:
```RUSTFLAGS="-C target-cpu=native" cargo install ```
for example
```RUSTFLAGS="-C target-cpu=native" cargo install igsolve```
# The results obtained so far
Here I provide the nimbers calculated using my software.
## Cram (under the normal play convention)
| | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
|------:|:-:|:-:|:-:|:-:|:-----:|:-----:|:-----:|:-----:|
| **4** | 0 | 2 | 0 | 3 | 0 | 1 | 0 | **1** |
| **5** | - | 0 | 2 | 1 | 1 | 1 | **2** | 0 |
| **6** | - | - | 0 | 5 | 0 | **1** | 0 | ? |
| **7** | - | - | - | 1 | **3** | **1** | ? | ? |
The table shows the nimbers of initial [cram]() positions for different board sizes computed so far.
Note that the symmetry strategy implies that even-by-even boards are losing and therefore of nimber 0 (the second player can win by responding with moves symmetrical to the center of the board).
To the best of my knowledge, the bold values (for the largest boards: $9 \times 7$, $8 \times 7$, $9 \times 6$, $10 \times 5$, $11 \times 4$) were calculated by me and published here for the first time.
The nimbers of the smaller boards were earlier computed by [Glop](http://sprouts.tuxfamily.org/wiki/doku.php?id=records), which is the solver developed by Lemoine and Viennot.
Nimbers of most boards no larger than $5 \times 7$ were first given by Martin Schneider in his master's thesis entitled *Das spiel juvavum* in 2009.
Uiterwijk reported that the $11 \times 5$ board is losing (and thus of nimber 0) in his paper [*Solving Cram Using Combinatorial Game Theory* (Advances in Computer Games: 16th International Conference, ACG 2019, Macao, China, August 11–13, 2019)](https://dl.acm.org/doi/10.1007/978-3-030-65883-0_8).
I have verified the correctness of all the nimbers in the table with my solver.
# Publications and citations
When using my software for research purposes, please cite the following paper which details the key algorithms used:
* Piotr Beling, Marek Rogalski, *On pruning search trees of impartial games*, Artificial Intelligence, Volume 283, 2020, 103262, ISSN 0004-3702,
https://doi.org/10.1016/j.artint.2020.103262