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.
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?
The lesson is that "should have been fired" was believed by the people who had power on paper; "should not have been fired" was believed by the people actually had power.
I think this critique would only be fair if we more completely understood how we ourselves work under the hood.
The "fancy math" is a bunch of non-linear functions that encode something derived from series of tokens. I believe we're still exploring what the derived vector spaces "mean" for LLMs, with research inspecting smaller and simplified models to try to make sense of it all.
It's clear that LLMs can "remix" in interesting ways. "ChatGPT, write me a Shakespearean-style sonnet about how LLMs work." (https://pastebin.com/FwzqWJ5W) It's not clear to me that our creativity and intelligence is not the same or a similar process.
Beyond that, I'm not convinced there are definitions of meaning, knowledge, creativity, intelligence, etc, that are both useful and don't refer solely to the output. If I need a solution and none exists yet and something creates it, I will call that creative irrespective of process.
It's been a hot minute since I've done work in this ecosystem, but I am not sure it is accurate to say that Storyboards do not support Auto Layout. I used to build iOS apps with Storyboards and Auto Layout a few years ago.
For all the men reading this, you should know that women discuss this as a tactic men take regarding housework, cooking, childcare, emotional labor, or any other traditional "women's work". Even when tolerated, they generally find it obnoxious and lose respect for men who do this.
That's oversimplified and overgeneralized, yes. But perhaps there's a little nugget in there that's useful for someone.
My 9 year old daughter told me last week that Uranus had rings, and I told her I really didn't think so, are you thinking of Saturn? And she said nope, they both do. What a weird bit of knowledge to get wrong, even at 9, so I looked it up. She was delighted to have taught me something.
I think there's a lot of value for classic server-side web applications rather than SPAs. That handles routing, state, etc. I'm personally a fan and hope that the server-based application renaissance happens as some predict.
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.