There are five different mine arrangements which are consistent with the given minesweeper board. See here: Spoiler alert!

Each of five arrangements is equally likely.* So if we want to maximize our chances of winning, we should first try the square which is least likely to contain a mine. The upper left unknown has only a 1/5 chance of containing a mine, so we might pick that. If it turns out to be a 3 or a 5, then we can figure out the rest of the mines from there. If it turns out to be a 4, then we'll have to guess one more square. Let's just guess the square below it. In total, we have a 3/5 chance of surviving.

*The reason for this is that we are assuming that all arrangements are equally likely at the beginning of the game. As we click more squares, we prune the possibilities, but never do we make any of the remaining possibilities more likely than others.

We know there is no way to improve on this survival rate, because if we picked any other square first, we would already have at least a 2/5 chance of dying.

However, there is one alternative strategy which matches the 3/5 survival rate. If we pick the lower

## 2 comments:

Hi miller

Thx for the puzzles and musings. For the 2nd option I think you mean lower

rightunknown.Right you are. Thanks!

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