I don't think the dev would leave the top left without a mine until one is moved there, as that would always be a safe square to click first.
So if the probability of finding a mine at any given spot is given by p, then the probability of finding a mine in the top left during gameplay for cases where one does not click it first (in which case it is 0?) is 1 for the case where you clicked on a mine first with probability p, and then p for the remainder.
So the total probability p' is p * 1 + (1 - p) * p, or 2p - p^2.
Wikipedia says
> Beginner is usually on an 8x8 or 9x9 board containing 10 mines, Intermediate is usually on a 16x16 board with 40 mines and expert is usually on a 30x16 board with 99 mines; however, there is usually an option to customise board size and mine count.
8x8 10 mines p = 0.16 p' = 0.29 ratio = 1.84
9x9 10 mines p = 0.12 p' = 0.23 ratio = 1.88
16x16 40 mines p = 0.16 p' = 0.29 ratio = 1.84
30x16 99 mines p = 0.21 p' = 0.37 ratio = 1.79
I was curious to see the concrete effects for no reason other than to procrastinate.
My daughters have for years enjoyed dropping their plastic straws into their Jarritos bottle where it sits out of reach until the bubbles magically bring it back up.
My algorithms class taught to think of it not as "describing performance" in an absolute sense, but as "describing how performance changes as the size of the input data increases".
It is not necessarily true that an O(1) algorithm will outperform an O(n^2) alternative on a particular set of data. But it is true that an O(1) algorithm will outperform an O(n^2) alternative as the size of the input data increases.
This sometimes doesn't work out in practice because the scaling involved runs into a limitation your big-O model didn't account for. Typical examples are: The size of the machine registers, physical RAM, addressable storage, or transmission speeds.
If your O(1) algorithm takes an hour for any input, and the competition is O(n) it may seem like there must be cases where you're better, and then you realise n is the size in bytes of some data in RAM, and your competitors can do 4GB per second. You won't be competitive until we're talking about 15TB of data and then you remember you only have 64GB of RAM.
Big-O complexities are not useless, but they're a poor summary alone, about as useful as knowing the mean price of items at supermarkets. I guess this supermarket is cheaper? Or it offers more small items? Or it has no high-end items? Or something?
> (...) but as "describing how performance changes as the size of the input data increases".
Yes, that's the definition of asymptotic computational complexity. That's the whole point of these comparisons. It's pointless to compare algorithms when input size is in the single digit scale.
You could have an O(N^2) algorithm outperform an O(N) on the scale of 10,000 (or whatever scale you want to imagine). The big-O notation compares only asymptotic behaviour, and sometimes the lower power factors are overwhelming.
I work in a hospital system. The OR is only doing emergency cases today; ambulatory clinics are closed; everything is being done on paper; response communication is via email and peer-to-peer text.
This is a great point, and perhaps we do need a new popular license or set of variants that exclude certain industries. "MIT-Peaceful" perhaps.
I know very many people who would refuse to work for certain companies and in certain industries — and have rejected certain projects — but would happily contribute to something MIT licensed that would end up in those systems anyway!
Have you read Alien Information Theory: Psychedelic Drug Technologies and the Cosmic Game by Andrew R. Gallimore [0], and do you have any thoughts on his cosmology vis a vis cellular automata? And perhaps also the same question related to Stephen Wolfram's physics project?
That's your own prejudice coming out. The word boy may have a negative connotation in some usages, but in this case it's referring to literal boys.
The term was used for family and community farms, not for large ranches / plantations.
The fathers and sons would tend to a small head of cattle used to feed their family and the community. They did not and could not afford to own slaves.
Plus the term was used well after Britain outlawed slavery.
I think the point being made is that it seems plausible that a term used in Britain to refer to literal boys was repurposed later in a different context to be a demeaning way to refer to an adult man working with cattle in the US.
So if the probability of finding a mine at any given spot is given by p, then the probability of finding a mine in the top left during gameplay for cases where one does not click it first (in which case it is 0?) is 1 for the case where you clicked on a mine first with probability p, and then p for the remainder.
So the total probability p' is p * 1 + (1 - p) * p, or 2p - p^2.
Wikipedia says
> Beginner is usually on an 8x8 or 9x9 board containing 10 mines, Intermediate is usually on a 16x16 board with 40 mines and expert is usually on a 30x16 board with 99 mines; however, there is usually an option to customise board size and mine count.
I was curious to see the concrete effects for no reason other than to procrastinate.