How to Improve Your Peg Solitaire Performance

Peg Solitaire is a single-player board game that requires strategy and problem-solving skills to win. The game involves moving pegs (pins) around a board, jumping over neighboring pegs, and removing them to clear the board. While the rules may seem simple, improving your performance can be challenging. In this article, we'll explore ways to enhance your Peg Solitaire gameplay using symmetries.

To start with, let's understand the basic mechanics of the game. The game is won when there's only one peg left in the center of the board, and it's lost when you cannot make any more moves or the last peg is not in the center. Each turn allows you to pick a peg, jump over a neighboring one (either horizontally or vertically), and remove the jumped-over peg.

To represent the game state, we use a 2D array, which encodes the board as a matrix with specific values for each cell. The board representation is crucial in implementing the algorithm. Before diving into the solution, let's create a class to represent a single move. This class will include information about the peg to be moved and its destination.

The method `getPegToRemove()` returns the position of the peg to remove. In this case, the peg at y=2|x=4 gets removed. The first value indicates the row (y) and the second one the column (x). For example, Move(Pair(2,3), Pair(2,5)) means that we want to move the peg at y=2|x=3 to y=2|x=5.

To check if the player has won, we need to determine when the last peg is in the center of the board. The printed board looks like this:

- | X X X | | X X X | | X X X X X X X | -

1 => ' ' | X X X o X X X |

0 => 'o' | X X X X X X X |

1 => 'X' | X X X | | X X X |

The board is encoded as a matrix (2D array) with specific values for each cell. We'll implement the algorithm in Kotlin, but you can use any other language.

Using symmetries to improve performance might seem counterintuitive at first. However, by exploiting the game's symmetry properties, we can reduce the number of possible moves and increase our chances of winning.

To get started with the implementation, we need to write some game logic first. This includes defining the rules of the game, such as not being allowed to jump over multiple pegs or empty cells at once. With a solid understanding of the game mechanics, we can begin implementing the algorithm using backtracking.

Backtracking is a common approach for solving Peg Solitaire, and it involves exploring all possible moves until we find a solution that leads to winning the game. By using symmetries to prune the search tree, we can significantly reduce the number of nodes to explore, making the algorithm more efficient.

In this post, we'll delve deeper into the implementation details of solving Peg Solitaire with backtracking and symmetries. Stay tuned for a step-by-step guide on how to improve your performance in this challenging game.

Peg solitaire pegs left