Hope the algorithm smiles upon your reupload. I have notifications on so I didn't miss it either way. I love this series and it has gotten me addicted to minesweeper again. I'm not very good yet, I can barely even clear an expert level, but I'm learning, and this series is great fun!
i recently started playing minesweeper because of the opening theory videos that got recommended to me, and look forward to seeing how this series goes as well. (i'm still very newbie)
5:00 Intuitively before seeing the probabilities I would've gone with the very bottom click, next to the 2. After seeing the probabilities I agree with the corner move but actually the one at the bottom is not that much worse actually.
I went back to playing this game yesterday since it seems like the site no longer complains about adblock. I like the depth and the puzzle density of 9x9/20, maybe I should start tracking my mastery on 9x9/20 since the site won't do it for me
Would you ever be interested in showing how to calculate exact probabilities for complex configurations? It seems unintuitive how it comes up with the numbers it does.
Mathematically, a very "simple" thing you can do is consider all ways to arrange the X remaining bombs in the Y remaining cells, throw out all configurations that do not match the numbers and count how many do have a mine in a certain spot, divide that by the total number of remaining boards and you're done. I say "simple" in quotation marks because the number of boards you have to donsider is astronomical and not computable for any supercomputer in the world. One quick improvement you can do is to realize that mines that do not border any opened cell cannot invalidate a configuration. Therefore, what you would actually do is something like this: 1. Consider all configurations along the border of the opened cells (these are usually way less) 2. For every border configuration do the following: a) Count the mines in the bordering cells -> say this is B b) Calculate the number of mines in the remaining cells -> If there are X mines remaining, this is just X-B c) Calculate how many ways there are to arrange X-B mines in the remaining Y cells This is (Y nCr X-B) aka (Y choose X-B) and has a pretty easy formula -> This then is the amount of configurations in which the border configuration is present. Mathematically, you would call this the "multiplicity" of the border configuration. 3. For each border cell, look at which border configurations have that cell as a mine. Add up their multiplicities and divide by the sum of all multiplicities (I'll leave out the non-border cells here) To use this to form an intuition, here's the key observation tho: The likelihood of a cell being a mine goes down when the sum of the multiplicities of the border configurations with it as a mine goes down. This can be due to two things: * There are just few border configurations where a cell is a mine * The configurations have a low multiplicity The first one here should be somewhat intuitive: If you assume a cell somewhere and it forces a lot of things, it's should feel less likely. The second one has a mathematical reasoning to figure out when a multiplicity is low: When considering (Y nCr X-B), we know X and Y beforehand. Only B varies with border configuration. In general, (N nCr K) is smallest when K is closest to 0, or K is closest to N. The worst case (i.e., the case where it is biggest) is when K is exactly N/2. Usually, in Minesweeper the number of mines is way less than half the number of cells, i.e., X < Y/2. Hence, we prefer X-B to be as close to 0 as possible. For that to be the case, B should be large, i.e., we should have many bombs in the bordering region. So to recap this: If a border configuration has a lot of mines it is unlikely. Or even shorter: 3:05 So what you're looking for in particular is cells that: * Are a mine in few border configurations, and * The configurations in which they do appear ALL have a lot of mines in the border region Sometimes this is very clear: If a cell fullfills both properties it is very safe. In the last few episodes there were a few 1% tiles which have exactly these properties. The hard part comes when all cells only fullfill one of these properties (i.e., either appear in a lot of high-mine-density border configurations or very few low-mine-density border configurations). For there you just have to build an intuition by playing (or do the math) and I'd usually advise to either look for progress or just do the newbie approach and click the next corner.
Efficiency has recently been added to the trophies categories, and for good reason: it is a very skill based category, however I am not nearly well versed enough in it to do a video about it. Maybe one day I can collab with an efficiency pro player and bring you a video about it but I can't tell for the moment being
The 50/50s still having good and bad squares has been a helpful concept, ty
Mine Buoy when he reaches 0.3% or higher:
50/50: "Why hello there."
I, too, put in a rewatch for you. This really is a great Minesweeper series and it deserves the support it's getting.
Hope the algorithm smiles upon your reupload. I have notifications on so I didn't miss it either way.
I love this series and it has gotten me addicted to minesweeper again. I'm not very good yet, I can barely even clear an expert level, but I'm learning, and this series is great fun!
Wow, I loved the approach of more depth in approaching 50/50, I need to try thinking more about probabilities and their outcomes.
this series is really awesome! I love the format and editing and commentary, keep it up sir
i recently started playing minesweeper because of the opening theory videos that got recommended to me, and look forward to seeing how this series goes as well. (i'm still very newbie)
I love this series man keep it up. Bella l'allusione alla pasta lol
Your videos have a meditative quality to them, I don't even play minesweeper but the explanations are great!
i dont know why but I love this series, keep playing mine buoy
In case there's a bug somewhere, glitched mastery count and display at 5:09 through 5:50
Thank you, it's just an editing error, sorry about that :)
5:00
Intuitively before seeing the probabilities I would've gone with the very bottom click, next to the 2.
After seeing the probabilities I agree with the corner move but actually the one at the bottom is not that much worse actually.
I went back to playing this game yesterday since it seems like the site no longer complains about adblock. I like the depth and the puzzle density of 9x9/20, maybe I should start tracking my mastery on 9x9/20 since the site won't do it for me
You mean 20 mines on a 9x9 board, right?
@@trevoreyre2775 Yes. After the first click there will be 25% mine density.
I'll watch it again
oh my god another perfect example of minesweeping *-*
You should make a video on how you look at guessing situations and find the best situation
Despite your previous videos in this channel, 50/50s seem not so easy to break 😢
Would you ever be interested in showing how to calculate exact probabilities for complex configurations? It seems unintuitive how it comes up with the numbers it does.
I am. It seems like a very high effort video and I would want to have more time to dedicate to it
Mathematically, a very "simple" thing you can do is consider all ways to arrange the X remaining bombs in the Y remaining cells, throw out all configurations that do not match the numbers and count how many do have a mine in a certain spot, divide that by the total number of remaining boards and you're done.
I say "simple" in quotation marks because the number of boards you have to donsider is astronomical and not computable for any supercomputer in the world.
One quick improvement you can do is to realize that mines that do not border any opened cell cannot invalidate a configuration. Therefore, what you would actually do is something like this:
1. Consider all configurations along the border of the opened cells (these are usually way less)
2. For every border configuration do the following:
a) Count the mines in the bordering cells -> say this is B
b) Calculate the number of mines in the remaining cells -> If there are X mines remaining, this is just X-B
c) Calculate how many ways there are to arrange X-B mines in the remaining Y cells
This is (Y nCr X-B) aka (Y choose X-B) and has a pretty easy formula
-> This then is the amount of configurations in which the border configuration is present. Mathematically, you would call this the "multiplicity" of the border configuration.
3. For each border cell, look at which border configurations have that cell as a mine. Add up their multiplicities and divide by the sum of all multiplicities (I'll leave out the non-border cells here)
To use this to form an intuition, here's the key observation tho:
The likelihood of a cell being a mine goes down when the sum of the multiplicities of the border configurations with it as a mine goes down. This can be due to two things:
* There are just few border configurations where a cell is a mine
* The configurations have a low multiplicity
The first one here should be somewhat intuitive: If you assume a cell somewhere and it forces a lot of things, it's should feel less likely.
The second one has a mathematical reasoning to figure out when a multiplicity is low: When considering (Y nCr X-B), we know X and Y beforehand. Only B varies with border configuration. In general, (N nCr K) is smallest when K is closest to 0, or K is closest to N. The worst case (i.e., the case where it is biggest) is when K is exactly N/2. Usually, in Minesweeper the number of mines is way less than half the number of cells, i.e., X < Y/2. Hence, we prefer X-B to be as close to 0 as possible. For that to be the case, B should be large, i.e., we should have many bombs in the bordering region. So to recap this: If a border configuration has a lot of mines it is unlikely. Or even shorter: 3:05
So what you're looking for in particular is cells that:
* Are a mine in few border configurations, and
* The configurations in which they do appear ALL have a lot of mines in the border region
Sometimes this is very clear: If a cell fullfills both properties it is very safe. In the last few episodes there were a few 1% tiles which have exactly these properties.
The hard part comes when all cells only fullfill one of these properties (i.e., either appear in a lot of high-mine-density border configurations or very few low-mine-density border configurations). For there you just have to build an intuition by playing (or do the math) and I'd usually advise to either look for progress or just do the newbie approach and click the next corner.
@@patrickwienhoft7987love the high-effort comment :D
5:34 that paid off... you wouldve been blown
Would you be interested in video about efficiency? I thought there'd be some nice strategy to discuss too to achieve the maximum
Efficiency has recently been added to the trophies categories, and for good reason: it is a very skill based category, however I am not nearly well versed enough in it to do a video about it. Maybe one day I can collab with an efficiency pro player and bring you a video about it but I can't tell for the moment being
what type of mouse input are you using? if this is a mouse these movements are unreal lmao
I think the cursor is added in post-processing
watch episode zero for a background, it is edited to look more smooth
im probably really dumb but i cant find the hints, the way you worded it imply its a built in feature of minesweeper online and also maybe paid ? idk
They're at the bottom right of the board. It looks like a square with a magic wand in it
3:20 🤌
Is this the previous video?
Did you resubmitted it?
Yeah...a copyright issue, sorry about that :(
sad :(
Could have been worse I guess :P
Keep up the god work!
nooooo
Dont worry I still remember the nice comment you had left :)