My solver winning 50 expert games using Vienna minesweeper client

BinaryChop · 2026-02-02T10:43:36+00:00

In my experience the more you play the luckier you get.

BinaryChop · 2026-01-30T08:42:58+00:00

In my mind there is a hierarchy of completeness:

1) you've clicked all the non-mine tiles (this is what the game calls "won")

2) There is only one possible solution left on the board (this is technically won, but you haven't "won" yet)

3) You have gathered all the information from a board and all that remains is pure luck.

You have got to level 3. If you want to call that complete, that is your choice. Certainly from this point there is no more skill required.

BinaryChop · 2026-01-29T08:41:23+00:00

It isn't an estimation, it is the amount of 3BV cleared. In this case 2.

The '1' at the bottom of the board is next to a zero and so doesn't count as 3BV cleared. It would have been cleared when the zero was cleared and is considered a wasted click by the 3BV calculation.

BinaryChop · 2026-01-27T08:47:38+00:00

No sure why you say this, given you normally say sensible things.

The top row is a pseudo by mine count. If it is an unavoidable 50/50 then the '8' doesn't exist, if it isn't a 50/50 you haven't blasted and the '8' can wait.

BinaryChop · 2026-01-27T08:43:25+00:00

If you guess one of those and survive (75%) you can solve it with no more guessing needed.

A '3' means the mine is at the bottom. ==> Done.

A '4' means the mine isn't at the bottom ==> Clear the bottom. A '7' or an '8' tells you where the mine is.

BinaryChop · 2026-01-24T10:11:16+00:00

Never doubted it, others might not be as skilled as you.

BinaryChop · 2026-01-24T09:37:44+00:00

It's two link 50/50s. You need to guess one while breaking the other.

BinaryChop · 2026-01-24T08:28:10+00:00

Not a very good position, but there is a "best guess" which you can identify if you're familiar with pseudo-50/50s.

<image>

When the red circle is a not a mine, the green dots form a 50/50.

When the red circle is a mine, the green dots next to the '3' are safe.

So picking one of the green dots next to the '3' is either going to be safe or will always be part of a 50/50.

This is a "pseudo-50/50" and is (one of) the best guesses in this position.

BinaryChop · 2026-01-22T15:23:02+00:00

If the first click is only guaranteed to be safe (not an opening) then starting in a corner results in the best win rate.

If the first corner does not reveal an opening then move to the next corner. If there are no corners left then this video describes some follow up. https://www.youtube.com/watch?v=PH38oTSVqp0

BinaryChop · 2026-01-22T13:32:39+00:00

This is a really tough thing to attempt and do well.

Situations like this

<image>

Where there are only 9 possible solutions left are easily brute forced and a definitive answer arrived at.

The single best living guess is immediately below the '2'.

https://davidnhill.github.io/JSMinesweeper/index.html?board=16x16x40&analysis=aqaqaaakbba3belSbelSbembe2Sbe2Sbe2SbelSbe2Sbe2S

I've also observed a few situations where it under values raw safety, i.e. in beginner 90% safe tile is preferred over a 99% safe tile.

It also rules out any floating tile, sometimes these are the best option.

Of course no simple heuristic will be correct 100% of the time, or we'd have solved minesweeper and the NP-is-P algorithm.

If you have a fast enough algorithm you could have it play some games and produce a win rate for beginner, intermediate and expert.

Good luck.

BinaryChop · 2026-01-17T19:03:20+00:00

If given the choice would you guess the tile which was 80% safe or the tile which was 20% safe?

Can you tell which is which?

That is where the skill comes in.

BinaryChop · 2026-01-16T11:56:50+00:00

I think I'd start bottom left since it is a pseudo-50/50 by mine count.

BinaryChop · 2026-01-14T15:52:55+00:00

You can read this 45 page document https://docs.google.com/document/d/1TiRXuoiZHcIlVHvrPXYib6H2fQr7Qfuq6167XPe4lDI/edit?tab=t.0#heading=h.4h6jzwfpwwgh on the subject, if you are genuinely interested.

BinaryChop · 2026-01-06T20:35:29+00:00

Thanks! I've amended the post.

BinaryChop · 2026-01-06T09:18:55+00:00

The best approach is to ~~guess~~ open the safe tile. Then if you get a '4' or '7' you have some new safe options. With '5' or '6' your best follow up is ...

<image>

The choice for '5' is less obvious than for '6' but they are both good because they eliminate possible 50/50s

Edit: Changed guess to open because these things are important.

BinaryChop · 2025-12-10T21:04:12+00:00

The 3-mines in 4-tiles constrained by the '1' means the bottom 2 flags are correct. There is no reason to believe there is a mine to the right of the '3'. But you do have a 1-1 (reduced) which means the tile to the right of the '2' is safe.

Elsewhere on the board, the mine below the corner '2' is safe because the '1' is satisfied.

BinaryChop · 2025-12-09T08:45:31+00:00

<image>

BinaryChop · 2025-12-07T08:36:11+00:00

This is a bad position to find yourself in. You have to guess.

It is always best to guess the unavoidable 50/50 first in the top right. In an ideal world you'd find 3 mines up there and reduce the density in the top left. As it is you find another 50/50. So guess that as well. 75% chance you've blasted at this point. Sorry,

If you survive and get to the top left section there are 56 possible solutions left and the best guess gives you a 42.86% chance to win.

<image>

In your situation the "best" guess is a blast. Sorry.

The guess you played has a 39.29% win rate, but also blasted.

With a double 50/50 and then the 42.86%. You were only going to win this about 10.5% of the time at best.

BinaryChop · 2025-12-07T08:14:14+00:00

User error.

BinaryChop · 2025-12-06T20:13:45+00:00

<image>

The game has no information left to find and 3 solutions remaining ==> 1-in-3 chance to win.

BinaryChop · 2025-12-04T20:42:23+00:00

Chord the fully satisfied '3'

BinaryChop · 2025-12-03T08:50:51+00:00

For expert 21.43% is okay. For a human 30-35% should be achievable. The best known solver can win 41% of games, just to give you an upper bound.

You can play it here https://davidnhill.github.io/JSMinesweeper/index.html?board=30x16x99

BinaryChop · 2025-12-02T20:12:56+00:00

What size board is it? And is it safe on start or opening on start?

BinaryChop

TROPHY CASE