4 ms·

One thing I rarely see mentioned is that it's pretty common to have situations in Minesweeper where you need to guess, but the probability of each square being

One thing I rarely see mentioned is that it's pretty common to have situations in Minesweeper where you need to guess, but the probability of each square being a mine is not the same. While each individual square has the same probability of being a mine in isolation, the numbers leak information: eg. if you have a set of numbers that could be fulfilled by one or two mines, it's statistically more likely that the one-mine solution is correct. One example: https://math.stackexchange.com/questions/2511421/correct-probability-calculation-for-minesweeper https://math.stackexchange.com/questions/2511421/correct-pro...

woofie11 6y ago
I liked the metagame here of guessing the guess which would make the rest of the puzzle as solveable as possible. P.S. Document how to flag mines in the text (ctrl-click)
- bmn__ 6y ago
  The game follows standard 'sweeper conventions. The user is expected to already know them. LMB to reveal, RMB to mark, chord LRMB to complete from a reveal.
  - woofie11 6y ago
    Assuming you're not on e.g. Mac with one mouse button. Or mobile, with touch.
    - wutbrodo 6y ago
      It extends pretty naturally, as both of those have left- and right-click analogues. Long-press works fine on mobile.
      - woofie11 6y ago
        ... and if you get to the very end of the map, with everything clear, and find you need to flag the bombs, do you take the risk? That's the user experience.
    - yellowapple 6y ago
      Most Macs nowadays will let you do a two-finger click to emulate a right-click (as, indeed, will pretty much any touchpad with multi-finger support).
paxys 6y ago
Rarely mentioned, except in this very article. > If I was feeling especially mean, I could insist that the player choose the square with the best odds of being safe, rather than simply judging whether or not each square is theoretically knowable. But I think that would be taking things too far.
leni536 6y ago
One needs to be careful when calculating exact probabilities. http://nothings.org/games/minesweeper/ http://nothings.org/games/minesweeper/ previous discussion: https://news.ycombinator.com/item?id=13566730 https://news.ycombinator.com/item?id=13566730
OscarCunningham 6y ago
Drew Roos wrote this code to calculate the exact probabilities: https://github.com/mrgriscom/minesweepr/ https://github.com/mrgriscom/minesweepr/
- leni536 6y ago
  Notice that in the example the field 'H' has much higher probability to contain a mine than the fields 'I' and 'F'. This can be very unintuitive. The reason is when counting configurations one needs to consider the placement of all the mines, not only the ones that have a neighbour uncovered. When this is considered then there are (76 choose 6) configurations that have a mine on 'H' and (76 choose 5) configurations that have mines on 'I' and 'F'. (76 choose 6) is a much larger number than (76 choose 5). In general I found that in a normal game when a guess is needed then it's better to guess for configurations that have fewer number of mines on the perimeter of the uncovered area, as they have higher probability.

woofie11 6y ago

I liked the metagame here of guessing the guess which would make the rest of the puzzle as solveable as possible. P.S. Document how to flag mines in the text (ctrl-click)

bmn__ 6y ago
The game follows standard 'sweeper conventions. The user is expected to already know them. LMB to reveal, RMB to mark, chord LRMB to complete from a reveal.
- woofie11 6y ago
  Assuming you're not on e.g. Mac with one mouse button. Or mobile, with touch.
  - wutbrodo 6y ago
    It extends pretty naturally, as both of those have left- and right-click analogues. Long-press works fine on mobile.
    - woofie11 6y ago
      ... and if you get to the very end of the map, with everything clear, and find you need to flag the bombs, do you take the risk? That's the user experience.
  - yellowapple 6y ago
    Most Macs nowadays will let you do a two-finger click to emulate a right-click (as, indeed, will pretty much any touchpad with multi-finger support).

paxys 6y ago

Rarely mentioned, except in this very article. > If I was feeling especially mean, I could insist that the player choose the square with the best odds of being safe, rather than simply judging whether or not each square is theoretically knowable. But I think that would be taking things too far.

leni536 6y ago

One needs to be careful when calculating exact probabilities. http://nothings.org/games/minesweeper/ http://nothings.org/games/minesweeper/ previous discussion: https://news.ycombinator.com/item?id=13566730 https://news.ycombinator.com/item?id=13566730

OscarCunningham 6y ago

Drew Roos wrote this code to calculate the exact probabilities: https://github.com/mrgriscom/minesweepr/ https://github.com/mrgriscom/minesweepr/

leni536 6y ago
Notice that in the example the field 'H' has much higher probability to contain a mine than the fields 'I' and 'F'. This can be very unintuitive. The reason is when counting configurations one needs to consider the placement of all the mines, not only the ones that have a neighbour uncovered. When this is considered then there are (76 choose 6) configurations that have a mine on 'H' and (76 choose 5) configurations that have mines on 'I' and 'F'. (76 choose 6) is a much larger number than (76 choose 5). In general I found that in a normal game when a guess is needed then it's better to guess for configurations that have fewer number of mines on the perimeter of the uncovered area, as they have higher probability.