Computes all positions of a small boardgame.

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# fafl/boardgame-enumeration

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# Boardgame Enumerator

## Introduction

This program creates a database of optimal moves for a specific boardgame. With this database you can run an AI that plays the boardgame perfectly. The boardgame-webserver project does this.

According to this Wikipedia article the boardgame can now be considered strongly solved.

## Boardgame

The game is similar to chess. It is played by two players, one white and one black, on a board of 4 * 6 squares, where each player faces the short side. Each player owns four pieces: The rock, the paper, the scissors and spock. Before the game starts, each player arranges these pieces in any order on the four squares of the row closest to him (his "base row").

The game is started by the white player. Players take turns alternately until the game is over. To make a move, the player chooses one of his pieces and moves it onto one of the eight squares next to it. A piece can only move to a square that is empty or where an opponent's piece is standing that can be taken. Taken pieces are removed from the game. Each piece can take opponent's pieces according to this table:

Taking Piece Taken piece
Rock Scissors
Paper Rock, Spock
Scissors Paper
Spock Rock, Scissors

The game is won when a piece reaches the opponent's base row or when all opponent's pieces are taken.

## Approach

For each position the database contains the number of moves it takes to win or lose it, assuming that both players play perfectly. Stalemate positions are not stored. A position consists of the squares where the eight pieces are standing. It is assumed to be the white player's turn. To cut storage need in half, only one of two positions is stored, where the positions are mirror-symmetric to the longer axis.

The program runs in iterations. The first iteration finds all positions that can be won in a single move. This is achieved by generating all positions where the white player has won and then undoing all moves that may have lead to it. Duplicates are eliminated.

The second iteration finds all positions that are lost in two moves. To do this, for each position of iteration 1 the board is turned and all possible moves of the white player leading to it are undone, resulting in candidates for iteration 2. A candidate is valid only if any move by the white player results in the black player being able to win in one move. In other words the white player has to lose no matter which move he chooses.

The third iteration finds all positions that can be won in three moves. For each position found by iteration 2 the board is turned and all of white's moves that may have lead to this position are undone. Duplicates are eliminated.

This pattern is repeated until an iteration does not find any results. For the boardgame described above this happens in iteration 66.

When all iterations are done, a compacted database in binary format is created that contains the positions and its number of turns in sorted order. This makes lookups in O(log(n)) time possible.

This approach is transferable to other boardgames where two players take turns alternately. In chess it is known as retrograde analysis.

## Why C

I wrote this program in Python first using generators, but the performance was abysmal. With C i was able to write the program using macros, which unfold to a large amount of simple code. This is perfect for GCC to optimize.

## Executable Steps

On my Macbook Air it takes around 20 days of runtime to create the database. The earlier iterations take longer than the latter. The result is a binary file of 6.89 GB. Intermediate storage of around 50 GB is needed.

To create the database, execute the file `run_all.sh`

## Trivia

The retrograde analysis finds positions that can be won in 1, 3, or 5 moves, which a human could also easily find, but it also finds longer sequences. The longest sequence consists of a staggering 65 moves. Watch this video to view the sequence.

## Consistency check

You can check your files after each iteration. They should have the following number of lines:

Filename Lines
moves.iteration04.txt 230639947
moves.iteration05.txt 143046924
moves.iteration06.txt 89414104
moves.iteration07.txt 106380854
moves.iteration08.txt 55198111
moves.iteration09.txt 68116035
moves.iteration10.txt 38613983
moves.iteration11.txt 64890877
moves.iteration12.txt 33665125
moves.iteration13.txt 54835648
moves.iteration14.txt 28466469
moves.iteration15.txt 45658027
moves.iteration16.txt 24747712
moves.iteration17.txt 36869842
moves.iteration18.txt 20404246
moves.iteration19.txt 27574927
moves.iteration20.txt 14870130
moves.iteration21.txt 18137894
moves.iteration22.txt 9639076
moves.iteration23.txt 10888931
moves.iteration24.txt 5748707
moves.iteration25.txt 6244507
moves.iteration26.txt 3307494
moves.iteration27.txt 3460633
moves.iteration28.txt 1856069
moves.iteration29.txt 1857722
moves.iteration30.txt 996373
moves.iteration31.txt 973126
moves.iteration32.txt 534691
moves.iteration33.txt 531445
moves.iteration34.txt 284135
moves.iteration35.txt 285375
moves.iteration36.txt 154092
moves.iteration37.txt 144030
moves.iteration38.txt 82880
moves.iteration39.txt 75105
moves.iteration40.txt 46100
moves.iteration41.txt 39733
moves.iteration42.txt 26455
moves.iteration43.txt 20251
moves.iteration44.txt 13134
moves.iteration45.txt 10078
moves.iteration46.txt 6536
moves.iteration47.txt 4553
moves.iteration48.txt 2771
moves.iteration49.txt 1659
moves.iteration50.txt 1141
moves.iteration51.txt 726
moves.iteration52.txt 527
moves.iteration53.txt 477
moves.iteration54.txt 401
moves.iteration55.txt 217
moves.iteration56.txt 160
moves.iteration57.txt 103
moves.iteration58.txt 71
moves.iteration59.txt 43
moves.iteration60.txt 23
moves.iteration61.txt 13
moves.iteration62.txt 8
moves.iteration63.txt 6
moves.iteration64.txt 5
moves.iteration65.txt 1

Computes all positions of a small boardgame.

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