How could this be extended to a negative bomb space like in Bombe (https://store.steampowered.com/app/2262930/Bombe/)?
Minesweeper thermodynamics
11–20 of 65 posts
Re: Minesweeper thermodynamics
#12The 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…
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.
Re: Minesweeper thermodynamics
#13The 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…
Yes! Units are up to you (with some constraints)! Physicists do this in practice a lot: https://en.wikipedia.org/wiki/Natural_units
Physicists also sometimes deal with inverse temperature aka "coldness".
Re: Minesweeper thermodynamics
#14What would the winrate of a bot doing these calculations be compared to one that doesn't?
Re: Minesweeper thermodynamics
#15I 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…
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".
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.
Re: Minesweeper thermodynamics
#16The 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…
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.
Re: Minesweeper thermodynamics
#17What would the winrate of a bot doing these calculations be compared to one that doesn't?
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.
Re: Minesweeper thermodynamics
#18Only 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
This is actually a quite interesting game, I played it for like 2 hours when I saw it first time.
Re: Minesweeper thermodynamics
#19The 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…
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.
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.
Re: Minesweeper thermodynamics
#20The 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