How to Play 4D Chess 

i wonder how many checks happened that weren't even thought of

This should be an international competition and the winner gets the title, "Grandmaster of the 4th Dimension"

To be fair, I could see that 3d chessboard being something that people could legit buy.

1D Chess: A Contemplation of War. 2D Chess: An Attempt at War. 3D Chess: An Understanding of War. 4D Chess: A Mastery of War. 5D Chess: Becoming the War.

Welcome to 4d chess, where you have to convince the other player about the legality of your move every turn.

You think he lost, but actually he was just playing 5d chess.

+ You wanna play chess? - Ok bring the board. + What board? - What do you mean? +We ain't no noobs now come to the 12 dimentionel chess room.

1 dimensional beings watching this be like: Impossible, all i see is a dot.

4D chess is fun, but 1D chess is for the real pros

5th dimensional beings watching this be like “bruh, those guys are so bad”

The No Game No Life opening at the end is done in such great taste. Some could say, it is a 4D chess move. But seriously, imagine “ “ playing this.

You can represent 4D chess in 2D too, though. In this case, instead of having just a line of boards representing the third dimension, you'd have a grid of boards, with one axis of the grid representing dimension 3 and the other representing dimension 4. And you can repeat the process to achieve any number of dimensions you want, the number of boards used just keeps getting more absurd. If you think of the grid of boards described above as a single 4D board, and make a line of such boards, you can achieve dimension 5. Turn that line into a grid, and you have dimension 6. Now you have a 6D board and by making a line of that you get dimension 7. You get the idea by now.

I think my brain melted

This 4D chess concept is actually really interesting, with some refining the game could be much more balanced and fun.

"I am 4 parallel moves ahead of you".

For anyone like me who has a brain that took hours to process this: 4D chess simply allows a piece to move up and down too, not just to the sides (no diagonal moves allowed, though). So a knight could go up or down two platforms then shift to the left, right, front, or back square on that platform it lands on.

there is a game called 5D chess you can move to the past and make a new timeline or create a timeline like 4D chess but instead your brain gonna snap out of existance

That anime sequence!! Haaa!! Allen It was so good. This was the weirdest and (don’t tell the other ‘tubers) most entertaining collaboration I’ve ever done. We played chess in more than 2 dimensions for what, 8 hours? I LOVED IT. Maybe because I won...

I would love to see what grand masters of 4D chess would be like.

"Thanks Diana, for kicking my but in a direction I can't even comprehend." - Allen Pan 11:32

This is an amazing representation of a 4th dimension. Chess is perfect because movement in the game is discrete and not continuous. This makes it super easy to visualize and understand. The problem with looking a tesseract and thinking about moving around with a 4th dimension is that you can't conceive of a continuous motion from one 4d coord to another.

Imagine trying to actually get a checkmate instead of just ending at a concede

"It's perpendicular" No, it's orthogonal.

That anime bit was 100% a No Game No Life reference

Physics Teacher: "Ok class, you have a choice for your final assignment, either take a written test, or beat me in 4D chess."

The No Game No Life intro earned my like

Did this show up in everyone's recommendation after 2 years?

Chess: not updating* This guy: fine, ill don't myself.

Im only slightly dissolved that you didnt call it a "chesseract"

You guys should play this out on a popular street and see how many looks you get

I can’t even play normal chess. WTF

When showing the moves in 3d I immediately understood them because it's basically how 5D chess with Multiverse Time Travel handles the moves of it's pieces.

Teseract to 3D shadow to 2D screen, but to be transfered to the screen it has to be reduced to 1D by representing it with binary code.

You're watching... Someone playing 4-Dimensional chess In a 3-Dimensional world From a 2-Dimensional screen wItH yOuR 1-dImEnSiOnAl bRaIn

alan: lets make an anime op but chess in 1 week also alan: fuck it steal some scenes from monogatari

Not only does this sound fun and nerdy, but it looks super super cool and futury

Getting checkmate in 4d chess might not even be possible assuming both players are trying to avoid being mated. If you compare it to a random walk, an experiment where you choose a direction at random and move a set distance in that direction, you start to see why. In a 1-dimensional random walk, you tend to return to your start point because you only ever have 2 possible moves. This is also true in a 2-dimensional walk (assuming you can't move diagonally) where you have 4 possible moves. However, once you reach higher dimensions, the number of possible moves expands exponentially so you quickly reach a point where you are less likely to undo your original moves (returning to the starting point) than you are to move further away. PBS Infinite Series has a video on random walks if you want to learn more. This principle of exponentially expanding moves also applies to chess. In order to get checkmate, you need to attack the king's square and all spaces the king could move to. This means that in a hypothetical 1D chess game you need to attack the king and the squares on either side for a total of 3 squares. This continues as we go up in dimensions with the maximum number of squares you need to attack being equal to 3^n where n is the dimension. In classic 2D chess, you need at most 9 spaces (3^2). In 3D chess, you'd need to simultaneously attack up to 27 spaces (3^3), and in 4D chess, you'd need to attack a whopping 81 spaces (3^4) simultaneously, all while your opponent can actively change which spaces you have to attack. Just for fun let's calculate the number of possible board states, there are 4^4 (256) spaces and 96 (48 per side) pieces in the ruleset you used in the video. Using the piece distributions and board from the video, we can calculate that there are over 2.68x10^112 possible arrangements of pieces. And that's only the ones where you have all the pieces still in play. Just writing out the equation to calculate the number of possible states would take hours if not days. The length of that equation would be about 94^10 times as long as the equation I linked below. You would need a supercomputer to analyze every one of these arrangements in order to find out if any were checkmates and even if you found one, you probably wouldn't be able to set it up in an actual game while your opponent was trying to stop you. Here's the math for the possible arrangements of pieces if anyone is interested: www.wolframalpha.com/input/?i=(256+nCr+17)*(239+nCr+17)*(222+nCr+4)*(218+nCr+4)*(214+nCr+4)*(210+nCr+4)*(206+nCr+4)*(202+nCr+4)*(200+nCr+2)*(198+nCr+2)*197*196 I might try writing a python script later to generate the equation to calculate the total arrangements with pieces being captured if anyone is interested.

What if I want to play 4d kahoot

Can't wait for a 5D chess tutorial

Nice! This helped me in understanding the concept of 4D

Now I can lose in 4 Dimensions!!! _Sobs_

It's more fun if you make one of the dimensions actually be Time, so you can move pieces into past or future turns of the game. I wrote a rule-set for that, never built it physically though. scribd dot com/document/151074661/Time-Chess

"here's the moves for the other pieces" King: F O R T R E S S

I don't "like" many videos, but this is worth one.

Where can I get the print files or buy a set? that is crazy sweet!

I would love to see Magnus Carlsen play a game of 4D chess.

That was incredible holy shit. great breakdown of how to do this and how it works. Love it

*changing* *dimensions?* *MADE* *IN* *HEAVEN!*

4D Chess sounds neat and all, but 5D Backgammon is the truest game of kings.

I’m calling it There’s gonna be a sport anime based on this

In 4D chess you can knock over a piece that knocked over one of your pieces or even check-mated you before it has done so, but after the fact, like in a pile-mechanic scenario. You can prevent moves your opponents made before by acting now, but onto a past state of the board, so it becomes a game of retconning the opponent in 8x8x8 grid.

Love the No Game No Life reference song near the end! Great reference!

I have a slightly easier solution. Only have one 3D Chess Board. We replace the black and white spots for the Board Zones. You have Blue, Green, Yellow, and Red in a 2x2 square. The White Zones are Brighter versions of the Color, and Vice Versa. Each piece stands in a corner of their Zone to signify which Dimension it's in. Profit

it's a chesseract edit:they stole my joke

This man is a genius. He played the NGNL op during the sponsorship to appease my anime brain enough to watch the sponsorship.

Yo this is actually really cool! I want to play this!

Very well now invent 5D chess.

You could wire it with leds that light up the available movements to be sort of a tutor

I appreciate the ngnl op in the background at the end

I was worried you weren't going to make it to "chesseract". You got there. Splendid.

New project: Program a four dimensional chess board and make an AI play each side.

this reminds me of the board game from the anime "Kekkai Sensen" that becomes more complex the longer you play

i was gonna rag on you abt how that was 3d chess until you pulled out the beast, makes me excited to learn how to play XD, either way definitely earned a sub on this one

BETH HARMON WHERE YA AT! ITS 2021, WELCOME TO THE FUTURE! #Queen'sGambit

It actually seems like a good representation of 4D for humans. Each section of the board is a 3D portion of the universe that cant directly see what's in the next section, but can see a shadow of it (a single square) that they can move to. Once you travel in a 4D direction you can move around in the new 3D like normal.

Interviewer:So what's your spacial awareness? Diana: yes

I subscribed! You guys are great! And somewhat funny... I wanted to learn how to play 3-dimensional chess but watching you guys play 4-dimensional chess was more entertaining. 😂 Thanks, I needed this.

is that tinkercad?! I love this channel

There is an episode where Data loses a game of 3D chess to Deanna Troi because she makes an "intuitive move" that isn't researched and wasn't expected. And I was so mad about it that I apparently kept that anger 20 years to vent it here in this forum. Ahhhhhhhhh!!! Side note: I would watch Sufficient Girl

A Chesseract if you will

Allen: Is trying his best to explain it. Me: *Internal Screaming*

I learned that you can represent 4D chess in a much better way with a flat 2D board. You just have a 16x16 board thats partioned into the 4x4 boards. It sounds counter intuitive but because of the limited movement of the chess pieces their movement in the 2D representation is somewhat similiar to straight lines again.

Speaking as a lover of both chess and math, I have to say there's a bit of an inconsistency here. From 2D to 3D, you extrapolated that 8^2=4^3, and that chess could therefore be played on a 4x4x4 space, with 32 pieces total, 16 on each side, 8 on each individual 4x4 plane. However, these rules went out the window for the 4D variant. The 4D variant was just 4^4, which represents much more squares than classic chess. Furthermore, the piece counts were completely off, with some 2D planes having 8 pieces, and some having 4. This is not only a poor way to extrapolate chess to 4D, it also requires more chess sets. In order for a multidimensional chess variant to be valid, it needs to maintain the same y for z=log base x of y, where z is the dimension of the chess, y is the number of squares, and x is the number of squares on any given side. Furthermore, only positive non-zero interger solutions can exist for this, as playing chess on fractional squares is even more nonsensical. 2D chess can be expressed as 2=Log base 8 of 64, and 3d chess can be expressed as 3=Log base 4 of 64. There is no way to represent chess for 4=log base x of 64 with intergers. The next valid chess variant would be 6D chess, where 6=Log base 2 of 64. An alternative approach would involve Shogi, Japanese chess. Japanese chess is played on a 9 by 9 board, with 20 pieces a side. Shogi can be represented as 2D, wherein 2=Log base 9 of 81. 3=Log base x of 81 has no interger solution, BUT 4=Log base 3 of 81 is valid! And it's actually fairly easy to picture, because unlike in the video we're not being asked to 4D picture 256 squares. We're still picturing the same number. 3^2 is 9, working us with 3 by 3 planes. 3^3 means we're picturing a 27 square cube. Imagine a rubik's cube, and you're good to go. 3^4 means we have 3 27 square cubes, each perpendicular to each other. Set up, we have the traditional shogi set up just cut up slightly. Kings start on the middle plane of their cubes, with bishop below for player 1 and above for player 2, vice versa for rooks. Rules wise for Shogi, stuff gets interesting. Any piece can promote into a Gold General, with the exception of the Gold, King, Bishop, and Rook, when it hits the opponent's starting cube. Any piece can be placed on any square as a move after its been captured from an opponent. The knight, which is allowed to move 2 squares forward in the direction of the enemy king followed by one square perpendicular to the king, implies that on the x and z (across planes) axis, it can go one square +or-, whereas on the y or w(across cubes), it must cumulatively move 2 closer to the enemy king. This comes out to moving the knight's legal move options from 2 to a lot more. It can move either forward by 2 squares or 2 cubes, and then either left or right or up or down. That's... oh that's 8 moves. Still a much more powerful piece now. Pawns and lances have similar rules. Pawns cannot move on the x axis. As such, in shogi, they would move one space along the wyz axis, approaching the enemy king's starting plane. At least, we'd think so, but then we'd have two pawns in a file, as moving a pawn up a plane would have it join another pawn on the same file, and two pawns in a file is not allowed. So, we can conclude that the pawn also cannot move across the Z dimension, and that dropped pawns cannot be in the same columnplane as another pawn, but the same rowcube is fine. However, since pawns start at the 3rd row of each cube, pawns at the start can only proceed cubes "forward". Once captured, pawns have a wider range of movement. Silvers move diagonally, that is to say moving with a change of two axes by 1, or they move orthagonally forward. Now, this gets tricky to translate.Essentially, now instead of changing both x and y in one direction, you change 2 of the following: w, x, y or z, OR, you increase y or z but keep the other values the same. Essentially you can move it to orthagonal equivalents on different planes and cubes, diagonal equivalents on the same plane, or otherwise total equivalents that have proceeded closer to the king in either plane, or column. Golds move one square orthagonally, or any square forward diagonally. That means 1 change to any of wxyz in any direction, or two changes in directions that approach the value of the enemy kind across yzw. Now, this wider range does give the silver more reach than the gold, but the gold still has the luxury of covering more squares + than the silver does, as well as being able to retreat without giving up significant axes. Kings of course change either one or two of wxyz. Rooks move by increasing one value of WXYZ as much as they want, so long as they're not moving over any other piece. For instance, a rook on cube 1 plane 2 square 22 (the starting square), could capture the enemy rook on turn one, but not if there was a piece on cube 2 plane 2 2 2. A bishop is actually a ridiculously powerful piece, able to change two of any 4 wxyz values as much as they want, so long as both are changed by the same amount and no other value is changed. A bishop in the center of plane 2 cube 2 has 24 moves available, whereas a rook only had 8. Of course, blocking rules still apply. Because each plane is 3 by 3, promoted Rooks or Bishops become nearly identical, with only distinctions when they're considering moving across multiple planes/cubes/planecubes in one move. Overall, the game becomes absurdly volatile, with bishops and rooks vulnerable to each other from the first moves, and knights able to give checks on turn 1.

"Soooo do you wanna make a Video about 4d chess with me?" "Yeah that sounds cool" "Do you mind if I just throw in a random chess anime intro wich will make us look like a couple?" "What?"

"Can you move please that a little to the time, and a little to the multiverse?"

For some reason i had a yt recommendation on this video today, i can see potential for a new generationof chest. Instead of moving like the 4d in video, we can have like a 3d layer tower on 2 sides as a strong hold, and a middle board act like a battle field board which is just normal flat zone, which act like a traditional chest. 2 sides will start at their own strong hold on top floor, pawns can beplaced either in their 2nd floor stronghold(which suitable for defending since attqck side cannot move up floor without entering the lane first) or outside the first lane of the field. All chest pieces will be stopped once they cross another lane (like a queen can move freely, but if she enter another lane, she will be stopped atthe first lane) to give room and balancing, andif there are more than 4 chest pieces from one side of the battle field, the other side can not enter the stronghold lane, except for the queen or the knights.

Remember kids: if there's an infinitely big 3D wall in your way, just walk around it!

So if they can play a 2-D game in 4-D... Is it possible to play 4-D chess in 8-D?

i really love getting my ears blown out by a random anime intro in the middle of a video, thanks mr pan

* When they get to 4D chess * Now try to think 3 moves ahead...

Me: hey bro wanna play a board game? Bro: yeah sure what game... is.. it... Me: 😏

The directions in 4D are Up/Down, Forward/Backward, Left/Right, and Ana/Kata

Who ever did the animation needs to make a show like this

Hey, this is really amazing. It would be tough being the smartest person around. Tough to find people who can teach you something.

If only the grandmasters and international masters play this kind of monstrosity.

I liked the No Game No Life opening.

Someone coughing every second in the 4th dimension for these professionals.

Nice choice using the No Game No Life theme at the end there

Wait.. So they’re playing in 4-D on a 3-D plane, which we are perceiving on a 2-D plane... 🤯

"Kicking my butt in a direction I can't even comprehend" LOL ! Great vid! Good comedy!

Love the shirt !!!

Dad: are ya winnin' son? Son: I don't know dad

New level of chess: 4D ches !! Asian : *Heavy breathing*

"Did we just anime" *a weeb foming at the mouth, Perhaps...

I just love it!

incredible no game no life reference with this game playing in the background

Our condolences about getting murdered by Dianna! ☠️⚰️... a moment of silence... but ahh LOVE the anime intro sequence, so perfect! Now we're trying to brainstorm some excuse to make one too lol 😋

"Chess Tesseract" Ch... Chesseract edit: oh he says it in the video

I hate you for making this, but I applaud you for making something that requires you to feel like you’re on another plain of existence

I kinda wish i had that chess set the pieces look pretty slick