In minesweeper, every square either holds a mine or shows a number. The number is how many of its neighbours hold mines, counting diagonal neighbours too. A revealed square never holds a mine. There is no limit on the total number of mines.
Look at a partially revealed board. A solution is any way of placing mines on the unrevealed squares that agrees with every revealed number. Assume all solutions are equally likely. For an unrevealed square S, P(S) is the fraction of solutions that have a mine on S.
Here is a 2x5 board. Two squares in the top row are revealed and show the digits a and b. The other eight squares, including S, are unrevealed (-):
col1 col2 col3 col4 col5
row 1 [ - a S b - ]
row 2 [ - - - - - ]You choose the digits a and b, and each can be any whole number from 0 to 8. The board must have at least one solution.
Task: Choose a and b so that P(S) is as large as possible while staying strictly less than 1.
Answer format: three values separated by commas, in this order: a, b, and the resulting P(S) as a fraction in lowest terms (for example a, b, p/q). The optimal pair is unique.