41–50 of 65 posts
Earlier quoted context omitted.
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.
Is this better compared to an actual expert human?
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…
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.
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.
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.
Earlier quoted context omitted.
This is to an extent a party trick to befuddle lay people. Physicists know perfectly well that temperature is not a well-defined concept out of equilibrium. And when in a population inversion experiment when "temperature" is determined to be negative (or "beyond infinite" if you will) it arises because for a short while you have a non-Boltzmannian distribution.
I don't think they were talking about negative temperature, they just mean that sometimes the convenient quantity to work with is β = 1/T.
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 po…
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.
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 po…
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.…
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 mi…
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.