The Chances of Unlikely Layouts in Minesweeper

I’ve saved this one up for a while. For those of you who remember when Minesweeper was distributed — for free?? — with every copy of Microsoft Windows. What are the odds that unlikely layouts, like 8s, or neighboring 7s, are possible in that game? Alternatively, is it possible to get a game that can be completed in one move? Find out here (16 minutes):

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