[tydok]

The mines are uniformly distributed, yes, but the numbers are not. In a relatively sparse minefield, how likely is to find a 4? Of course depending on the "shape" of a cluster, chances can be 50%. The mines influence the distribution of numbers, not the other way around.

Try to apply the tactic I mentioned to solve the minefield in the article.

[Retr0spectrum]

Your logic is faulty, but it's hard to explain why. I think this might be variation of the Monty Hall Problem:

https://en.wikipedia.org/wiki/Monty_Hall_problem

Or more likely, just the Gambler's fallacy:

https://en.wikipedia.org/wiki/Gambler's_fallacy

[tydok]

It's not based on math, it's empirical. In practice seems to work.

I applied it on the minefield in the article and I solved it.

To put it another way, on two adjacent tiles where there's one mine, if you had the choice to reveal a 2 or a 6, which one would you choose?

[ufo]

Someone should build a little computer simulation to test this over a million minefields.

[seanp2k2]

Better, have it actually learn from mistakes and see what logic it comes up with.

[tydok]

Good idea, I could do it.

[WmyEE0UsWAwC2i]

I think the parent's argument could rewriten as:

The numbers induce a probability distribution in the adjacent tiles. But you also should take into account that the remaining mines are uniformily distributed.

In other words, consider the prior.

I couldn't write math neither in favor nor against this claim.

1. Maybe for uniformly distributed mines the numbers have all the information you need.

or

2. Maybe using the fact the the mines are uniformily distributed, in addition to the numbers, has impact on the probabilities distributions EDIT:

you play a 10x10 game with 20 mines.

your initial move in a non-border tile reveals a `1`.

you now know that around that `1` there is a 1/8=0.125 chance of hitting a mine.

ITOH there is a 19/91 = 0.20879 chance to find a mine in a tile not adjacent to the `1`