Minesweeper Solver

How to run

Run gui.py.

Game features

Main information

Game parameters are set in the constructor of the GUI class:

• height - the height of the field in pixels;
• width - width of the field in pixels;
• cell_size - size of the cell in pixels
• bomb_number - number of bombs;
• fps - number of frames per second;

Commands:

• Open a cell - LMB;
• Mark a cell - RMB;
• Return to menu - ESC.

Game modes

Two game formats are offered:

• Regular is a regular game;

• Solver - launches the solver. The Solver class takes a visible field as input.

The game is automatically saved after closing the interface in the data.pickle file.

Solver logic

The main idea is to calculate the probability of finding a bomb in each cell of the field, based on the already open cells. To start with, we calculate the probabilities for individual cells, which may result in several probabilities in the same cell as a consequence of the influence of several cells adjacent to each other. To calculate the probability of finding a mine in a cell adjacent to several open cells, we use the formula for calculating the probability of at least one event: the probability of the occurrence of the event A, consisting in the occurrence of at least one of the events A1, A2,..., An, independent in together, is equal to the difference between one and the product of the probabilities of the opposite events:

A = 1 - (1 - A1) * (1 - A2) * ... * (1 - An).

However, it should be remembered that the sum of probabilities in each group of cells must be equal to the number of mines in the group. Therefore, all values in each group must be multiplied so that their sum is finally is equal to the number of mines. This number is equal to the number of mines in the group divided by the current sum of cells in the group. A similar calculation for the second group is performed already taking into account corrections from the previous one. After that the probability in common cells will change again, so similar equalization for each group should be repeated several times, until system arrives at some stable values, which will be true probabilities of finding mines in cells. It remains only to choose one of the cells with minimum probability and make a move.