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Minesweeper thermodynamics

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Re: Minesweeper thermodynamics

#51

Post by modeless »

OscarCunningham wrote: post #44
AtlasBarfed wrote: post #42

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.

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.

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.

Re: Minesweeper thermodynamics

#52

Post by kqr »

srean wrote: post #22
kens wrote: post #5

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…

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.

> 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.

Re: Minesweeper thermodynamics

#53

Post by kqr »

pizza wrote: post #20
kens wrote: post #5

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…

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

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

Re: Minesweeper thermodynamics

#54

Post by npteljes »

Eddy_Viscosity2 wrote: post #40
gregfjohnson wrote: post #4

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 firs…

> 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.

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.

Re: Minesweeper thermodynamics

#55

Post by srean »

kqr wrote: post #52
srean wrote: post #22

Earlier quoted context omitted.

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.

> 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.

Yes. Similar idea. Sometimes they would also use minutes. Whether this was as a result of contact with the Greeks I do not know. Indian trigonometry however has a different flavour from the trigonometry of Hipparchus.

What Indian mathematicians typically used was a circle with radius 3438 units. Where units would be one of the standard units of length.

Why 3438 you may wonder.

They also wanted to divide the circle into 360 x 60 minutes. For the standard circle they wanted each of those minute arcs to be of 1 unit length. The radius that would accomplish this is (360 x 60)/ 2pi ~= 3438 units.

An angle of 1 minute would then be described as arc length 1 unit on that standardized circle of radius 3438 units.

Indian version of sine and cosine were not expressed as ratios but the corresponding (half) chord for a hypotenuse of 3438 units.

Re: Minesweeper thermodynamics

#56

Post by kqr »

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.

Re: Minesweeper thermodynamics

#57

Post by kqr »

srean wrote: post #55
kqr wrote: post #52

Earlier quoted context omitted.

> 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.

Yes. Similar idea. Sometimes they would also use minutes. Whether this was as a result of contact with the Greeks I do not know. Indian trigonometry however has a different flavour from the trigonometry of Hipparchus. What Indian mathematicians typically used was a circle with radius 3438 units. Where units would be one of the standard units of length. Why 3438 you may wonder. They also wanted to divide the circle in…

Very neat. Alternative-length radians seem quite common. Radians are by definition one radius, but NATO mils are 0.00098 radii (and apparently the Finnish piiru are 0.00105 radii). What you describe are effectively a unit that is 0.0018 radii. Makes sense.

Re: Minesweeper thermodynamics

#58

Post by cyclotron3k »

throwaway82408 wrote: post #25
gregfjohnson wrote: post #4

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 firs…

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

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

Re: Minesweeper thermodynamics

#59

Post by freedomben »

npteljes wrote: post #54
Eddy_Viscosity2 wrote: post #40

Earlier quoted context omitted.

> 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.

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…

Agree completely. The luck aspect kinda wrecked minesweeper for me. It's a super fun simple game, but after spending a lot of effort logic-ing my way through it, only to have to take a 50/50 or worse guess toward the end and have it blow me up, is deeply unsatisfying. When it comes at the beginning (that first block can be a bomb after all) it's not too bad, but at the end isn't cool

Re: Minesweeper thermodynamics

#60

Post by srean »

kqr wrote: post #57
srean wrote: post #55

Earlier quoted context omitted.

Yes. Similar idea. Sometimes they would also use minutes. Whether this was as a result of contact with the Greeks I do not know. Indian trigonometry however has a different flavour from the trigonometry of Hipparchus. What Indian mathematicians typically used was a circle with radius 3438 units. Where units would be one of the standard units of length. Why 3438 you may wonder. They also wanted to divide the circle in…

Very neat. Alternative-length radians seem quite common. Radians are by definition one radius, but NATO mils are 0.00098 radii (and apparently the Finnish piiru are 0.00105 radii). What you describe are effectively a unit that is 0.0018 radii. Makes sense.

I see. Today I learned about piiru from you.

I do dislike the fact the libc sin takes argument in radians. For two reasons. One, the angles in the application are rarely in radians, so they need to be converted before the function call. Two, I would like the standard angles, such as the multiples of 15 degrees to have an accurate representation in 32 bits (or 64 bits).

Anyhow this is way off topic.

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