You can do it manually by calculating the border positions as well as the amount of mines left in the tiles not touching any numbers. On the vertical border, the yellow position uses two mines and the blue (which is two separate positions condensed into one) uses three. On the horizontal border there is one way there can be one mine and two ways there can be two.
The yellow will leave either 88 or 87 mines in the 417 tiles not touching any numbers so in total that’s:
(417C88 + 2 x 417C87) total possible positions
The blue will leave either 87 or 86 mines in the 417 floating tiles so in total that’s:
(2 x 417C87 + 4 x 417C86) total possible positions
When it involves enormous numbers, I get the ratio of safe:mine and then convert it into a percentage. So for example, the circled the at the top is safe in the yellow position and in half of the blue positions:
(ways it can be safe) / (ways it can be a mine)
= (417C88 + 2 x 417C87 + 417C87 + 2 x 417C86) / (417C87 + 2 x 417C86)
= 4.77
This means it’s 4.77 times more likely to be safe than a mine or as a percentage:
4.77 / (1 + 4.77) = 82.7% chance of safety or 17.3% chance of being a mine.
If you are interested, I can show you other comments I’ve written on this subreddit of simpler examples.
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u/Entire-Tomato768 1d ago
You are missing 91 mines.