Minesweeper thermodynamics

https://oscarcunningham.com/792/minesweeper-thermodynamics/

by robinhouston • 11 months ago

206 62 11 months ago

grozmovoi• 11 months ago

now this is time well spent

modeless2• 11 months ago

Only tangentially related, but Dragonsweeper is an interesting extension of minesweeper where you have hit points and the "mines" have attack values. I got a better appreciation for the mechanics of minesweeper by playing it; it's surprisingly deep. https://danielben.itch.io/dragonsweeper

cuber_messenger• 11 months ago

This is actually a quite interesting game, I played it for like 2 hours when I saw it first time.

mamonoleechi• 11 months ago

Similar game: Mamono Sweeper https://duckduckgo.com/?q=mamono+sweeper (mamono is monster in japanese)

it's a RPG variant of Minesweeper, where you have life points, level up and fight against monster (mines) that gives you xp once killed (you loose HP if you fight a monster higher lvl than you).

it's a flash game, that had an android release at some point (it was removed from the store for some reasons)

gregfjohnson• 11 months ago

I hacked up a version of minesweeper that was “forgiving:” if there was no selection that was provably safe, it gave you a safe move. If you picked any square that was not provably a bomb, it would not be a bomb. Typically, as long as you don’t select a number of bombs equal to the number of squares , your first move is safe. I just extended that for the whole game. If you select N-1 bombs, you always win on the first move..

abetusk• 11 months ago

Ha! This is NP-Complete, no? In practice, it probably doesn't matter but my bet is that there are some configurations that will take exponential time to see if the player should be "forgiven".

alain_gilbert• 11 months ago

I made winsweeper, which will move the mine if there is no safe tile left for you to discover.

https://github.com/alaingilbert/winsweeper

mcmoor• 11 months ago

Yeah I've debugged another game that attempted this and this system resulted in the game lagging as hard sometimes.

OscarCunningham8• 11 months ago

Yeah, it's NP-complete to decide whether a cell in Minesweeper must be a mine: https://logic.pku.edu.cn/ann_attachments/np.pdf.

In practice I suspect a SAT solver would make quick work of the positions that actually appear in games.

anabab• 11 months ago

Prior art: https://news.ycombinator.com/item?id=21883875

throwaway82408• 11 months ago

I would also like to auto clear tiles that are unambiguous when I flag a mine. Perhaps by double tapping one of the adjacent tiles

cyclotron3k• 11 months ago

Can't you right-then-left-click the flagged mine? Iirc there's an awkward way of doing this

robinhouston• 11 months ago

Simon Tatham's _Mines_ deals with this in a different way: it generates the mine positions in such a way that they can never lead to an ambiguous state during a game. https://www.chiark.greenend.org.uk/~sgtatham/puzzles/doc/min...

yshklarov• 11 months ago

That's pretty neat. I wonder how it works. It's not obvious to me at all how to build something like this, as the program doesn't know the sequence in which the player will reveal the tiles.

I also once made my own variant of this (just like gregfjohnson's idea): A "lucky minesweeper" where luck can be toggled on/off at any point during the game: https://github.com/yshklarov/minesweeper

HPsquared• 11 months ago

The Windows 7 Minesweeper does something like this on the initial click, I think. You usually get a "good start".

lifthrasiir• 11 months ago

There is a Korean indie game made in RPG Maker MV that pushes this idea to the extreme, titled How can I be a brave in the isekai while I suck even at the minesweeper's novice level?! (rough translation, original: 지뢰찾기 초급을 겨우 깰까말까한 내가 이세계에서는 용사라고?). Too bad it's only available in Korean.

Eddy_Viscosity2• 11 months ago

a version of minesweeper that was “forgiving:”

I think this diminishes the game. Sometimes you just don't have enough information to know for sure. Experiencing this in a low stakes situation like a minesweeper game reminds us that life is like that sometimes and we just have to make a guess and accept the consequences.

npteljes2• 11 months ago

Yes, this really depends on what one's expectations are of a "game". Luck, as a component, is often contested. In case of the minesweeper, I'd argue there is either

A) No place for luck at all, either by making the game "forgiving", or generating a game that never has an ambiguous block, or

B) The game should make luck's presence more constant.

In case of Minesweeper, the most unfair event is when after a lot of pure skill-based play, the outcome ends up being luck based. As a game mechanic, this can work out to be challenging, or work as a surprise the first time, but it gets old pretty fast - because why bother putting in all that skill, just so be judged by luck in the end? And those who are thrilled by luck checks, will be turned away from the game because the exciting part comes last.

Because of this, I'd keep this logic game be about logic, or work luck into the game more deeply.

Solitaire is similar, with some of its starting positions being outright unwinnable. I'd just filter these out when creating a new game.

wkjagt• 11 months ago

I actually like the idea that it's always solvable. Like a sudoku puzzle. If a sudoku isn't solvable through logic, but requires guessing, it's considered an invalid puzzle.

IAmBroom• 11 months ago

Every version of Minesweeper I've ever played makes your first move safe. I realize this is not going as far as your version, but I've had this argument with ardent players who insist it isn't true (and somehow they've just been lucky, I guess).

kens• 11 months ago

The article discusses Boltzmann's formula exp(-E/kT). I was recently looking at the same formula in the context of semiconductors and I realized that Boltzmann's constant k is only needed because temperature uses bad units. If we measured temperature in energy instead of degrees, then Boltzmann's constant drops out. For instance, you could express room temperature as 25 meV (milli electron volts) or 2444 joules/mole and the constant disappears. Likewise, the constant in the ideal gas law disappears if you measure temperature as energy rather than degrees Kelvin. In other words, degrees Kelvin is a made-up unit that should be abandoned. (I'm not sure I believe this, but I don't see a flaw.)

donovanr• 11 months ago

Yes! Units are up to you (with some constraints)! Physicists do this in practice a lot: https://en.wikipedia.org/wiki/Natural_units

cperciva2• 11 months ago

Physicists also sometimes deal with inverse temperature aka "coldness".

wasabi991011• 11 months ago

This is true of any units. A lot of physicists say things like "set c=1", does that mean that meters/feet are bad units and we should instead be measuring our height in fractions of c? That sounds inconvenient to me.

Ma8ee• 11 months ago

I just calculated that I’m about 6.24 nanolightseconds. A nanolightsecond is just over a foot, so at least Americans should easily get use to the unit.

OscarCunningham8• 11 months ago

I don't think temperature would be measured as energy, but rather as energy per information; e.g. joules per bit. Boltzmann's constant defines the degree as one joule per a very large number of bits, to get numbers convenient at macroscopic scales.

kgwgk• 11 months ago

The argument of the exponential E/kT needs to be dimensionless. If E and T are not homogeneous you will still need a k to “cancel” the units.

pizza• 11 months ago

See: Temperature as Joules per Bit https://arxiv.org/abs/2401.12119

kqr4• 11 months ago

Landauer's cost is one of those things that frighten me because it makes clear how little I understand about how the world works.

srean3• 11 months ago

Another example that shows up in mid school is how we measure angle.

Like the Greeks and Babylonians we usually measure it in degrees. Later around 18th century radians started getting used, especially in power series expansions.

In India, historically, angle was measured in the units of length (for a standardized circle). That made functions like sin be a function from length to length.

kqr4• 11 months ago

angle was measured in the units of length

i.e. a variant of radians? A radian is the circular arc whose length is equal to the radius. If we standardise the unit circle then a radian is a length of 1.

RA2lover• 11 months ago

How could this be extended to a negative bomb space like in Bombe (https://store.steampowered.com/app/2262930/Bombe/)?

oerpli• 11 months ago

What would the winrate of a bot doing these calculations be compared to one that doesn't?

OscarCunningham8• 11 months ago

The bot at https://mrgris.com/projects/minesweepr/ does these calculations, and has a winrate of 37.8% on expert. I don't know what a more naive bot would achieve.

senfiaj• 11 months ago

Is this better compared to an actual expert human?

GistNoesis• 11 months ago

Minesweeper is a probabilistic game, that's why you should use probabilistic tools to solve it.

For example you can use a particle filter to approximate the distribution of mines. Every time you obtain new information you update the filter so that only distributions compatible with constraints remain.

Once you have an approximation to the distribution of mines you can calculate the probability of each spot being a mine. You can also calculate statistical indicator like the Information Gain of each action.

A good strategy is therefore to play low mine probability with highest information gain. But there is a trade-off, when the mine probability is non-zero. So you need to look-ahead.

Fortunately thanks to the mine distribution approximation you can also simulate any actions and their consequences, because you can use your approximation of the distribution to predict which number will be revealed upon a click.

So an even better strategy is to unroll the game tree for the best few candidate moves based on some heuristics, and calculate the cost gain probabilities after a few moves.

gus_massa• 11 months ago

Most of the times Minesweeper is deterministic, and you can just think and get an empty spot. From time to time, you are unlucky and has to guess.

A few years ago, I modified the version of minesweeper in the "Games" collection of Racket to get more mines per board and get more hard cases. (I added the trick to autoopen the squares that have enough flags around, so it solved all the easy cases and it was more fun. I never upstreamed the changes...)

I like Dragonsweeper (discussed in a sibling comment) because it has a more clear probability and information tradeoff.

AtlasBarfed2• 11 months ago

There are other squares to click on on the other side of that "probability wall" that might reveal more info at a lesser danger percentage.

OscarCunningham8• 11 months ago

Yes, (original author here) in fact all the cells outside this region have an even better safety probability of 80.1%. I think the best move might be to start fresh in a new corner.

modeless2• 11 months ago

Hmm, but how likely are clicks on random squares to reveal more safe clicks? Seems likely that even if you hit a safe square you might still not have any safe moves. The goal ought to be to create more safe moves for the next turn, to reduce your chance of dying over the whole game, not just in the current turn. I wonder what that analysis would look like.

todorov84• 11 months ago

Interestingly, the main problem with Minesweeper is that is a game of chance (so the approach discussed in the article is very appropriate).

For a minesweeper variant purely based on logic, I highly recommend the game Tametsi. It has 160 handcrafted levels, and some have very interesting geometrical arrangements. I have logged over 100 hours in this game.

kej• 11 months ago

Tametsi is amazing. I also like the drawing mode, and I think it should be added to the Steam overlay so that you could use it in every game.

The HexCells series is also worth a look for anyone interested in pure logic Minesweeper.

owenbrown• 11 months ago

The article makes a serious math error early on.

The author’s math considers how mines would be distributed if mines were distributed to the empty squares after reaching that board state.

This is wrong.

This is classic Monty Hall Problem. The author is doing the equivalent of saying “there are two doors left, so the odds are 50 / 50 that the prize is behind either door.

It invalidates all of the numbers after this point.

OscarCunningham8• 11 months ago

I don't agree (I'm the author).

The difference is that Monty knows which of the doors the car is behind and deliberately avoids it, thereby giving away information about where the car is.

Whereas in Minesweeper we've just blindly stumbled across a situation where we have to guess.

It would be like if every show Monty always revealed a random door. Sometimes he would reveal the car and the game would end immediately. In the cases when he didn't reveal the car it really would be 50/50 between the remaining two doors.

dako2117• 11 months ago

I agree, its definitely not Monty Hall, and IDK why they are so confident.

kqr4• 11 months ago

At first I thought the "equal probability assumption" wasn't too bad an approximation, but it has an average Brier score of 0.217. Much worse than I thought.

Minesweeper thermodynamics

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