###The maximum number of mines on a solvable board is:###
616
The most optimal mine-placing strategy is to work with 3x3 areas. The reason being is that there must be a number indicating adjacent mines, including diagonals. From my understanding of the rules, a mine must have a corresponding number (cannot have multiple mines in a row without a number accounting for it).
The optimal setup for this would then be:
[x][x][x]
[x][8][x]
[x][x][x]
where 'x' is a mine. Copying this pattern across an Excel spreadsheet, (overlapping the pattern once on the last two rows and columns due to the dimensions of the board), we get this:
Note that this is not the only solution, but similar logic would follow.