When I play the game Minesweeper, I make the puzzle more difficult by increasing the amount of mines and still keep the board. Once I set the maximum number of mines for a 9x9 board, which is $67$, I realise that the chance to win is almost zero(!). And when I play a game with a $24$x$30$ board with $150$ mines, I sometimes have to guess in order to win the game.
And after all, my question is:
Given a m by n Minesweeper board, what is the maximum number of mines can exist so that any puzzle with those mines is solveable without guessing?
Note: This question has some similarity to mine.