There are exactly 8.4 Trillion Trillion games of 3D Tic-Tac-Toe
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- Опубліковано 29 тра 2024
- It turns out that adding a third dimension increases the number of games of Tic-Tac-Toe rather dramatically. To try it out for yourself, download CubeTacTix here:
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(Android link)
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It's good to finally see an octopus finally playing Tic Tac Toe!
Here I was hoping to see that only to have my hope crushed after pausing the video :(
The first TicTacTuber
12:25 an edge falls on 3 lines, you forgot the top face
No, the top face isn't counted for a separate line.
@@averyshaham1697 it is, for the corner
Glad I'm not the only one who noticed this. Corner 6, Center 4, Edge 3.
Edges still seem pretty bad, though. Geometrically 2/3 of the lines they can complete don't use corners, and you probably want to take a lot of corners.
I don't know much about octopodes playing Tic Tac Toe, but I think that it's neat that squid brains are toruses.
It's also nice to see somebody use the "proper" plural for octopus, being that the word is of Greek origin, not Latin 👍.
Children of ruin enjoyer?
@@RollcageTV well now that it's been loaned into english, anything goes - octopuses seems to be the most common plural
@@obonyxiam Hence the quotes I put around the word "proper" 😉.
@@RollcageTVimproper, er... "improper" here being octopi?
My matrix teacher always said humans weren't actually very well adapted to working in 3 dimensions (he was also a pilot), and I think this video more than demonstrates that. However, he failed to consider other creatures, such as octopi, and how well they could play a 3-dimensional game such as 3d tic-tac-toe.
You never considered with 8 limbs an octopus could cover almost an entire layer in a single turn, meaning that there are far fewer total games of tic-tac-toe :/
You say that as though the number of limbs is what determines the number of moves per turn. Human beings have 2 arms, why don't we get 2 moves per turn
centipede
@@zyaicob divide by 2
Octopi get 4 plays per turn
2:53 that has got to be the worst way to put a big number to scale that I have ever seen.
Isn't it though :-)
but you _have_ seen it
If that numbers was in millimeters, it would be 3 trillion times the distance from earth to the sun, or 42.6 MILLION LIGHT YEARS
@@SirNobleIZH wooow atoms do be small
There is a trivial strategy to always force a draw. Go second and always play the opposite side that your opponent did
That's Wrong! When your opponent creates a line, those cells become yellow (locked) so you can not reuse them to create a line
@@geladiatorkkkkBut since no line contains its own antipodes (edit: And the antipodes of all the cubes in a line forms another line), if you always play the opposite sides to your opponent, you must end up with the same number of lines as them at the end.
If you're always playing the antipodal point to your opponent, they can never block you from doing that (since the antipodal point to their move must be free, otherwise their move would have been blocked earlier in the game)
Gotta love strategy stealing
I think this strategy should also work for any dimension of tic tac toe without the center?
@@picalc314if the game doesn't end on first 3 in a row
I’ve actually recently been interested in 4D 4x4 tic tac toe and it’s a lot of fun to play because there’s more strategy involved. For example, getting two in a row isn’t immediately a threat to the other player because you need 4 in a row to win. The 4D also makes it harder for humans to visualize allowing strategy to set up complicated forks.
We used to call it Connect4D
Next video idea:-
This is a game I used to play in my childhood.
So it goes like this, There is a 5x5 grid of dots, where each dot is present a unit distance apart.
You first start by drawing one line randomly connecting any two dots to form a single unit length line,
After that the opponent draws another line and it continues.....
Once a square is created you mark the X or O in the square and you get an extra chance to draw a line,
If you create a second square using the extra line you get from winning, you get another chance to draw a line and so it continues.
Now, the person with the most squares in their name wins.
What is the ideal way to win and how many combinations can we get, also what is best possible route to get all the squares in our favour.
Part of my brain was expecting the Gamecube intro to play at the end there.
when i was like 10 i bought a 3D tic-tac-toe set which used gravity (like in connect 4) so you could only place a piece in the bottom row or somewhere there was already a piece below. much like the version you mentioned at 0:54, it is stupid. it took me like an hour to realise that the person who went first ALWAYS wins, and then another couple to brute force every line and to find how broken the middle square is.
my naive search found only like 1 line with play so poor that would allow the person who went second to win, and literally every other line had a forced victory after move 1.
moral of the story: dont buy it if you ever see it
You should look into quantum tic tac toe. It’s very fun
I somitimes play tic-tac-toe in a 4x4x4 cube where you need 4 in a row. This is quite balanced and doesn't get boring after 3 games like regular tic-tac-toe.
12:25 shouldn't an edge be 3? Not that it really matters to the point you're making, but it should also count the vertical line on the other face of the cube, right?
hes accounting for the symmetry
R.I.P milliards, billiards, and trilliards
I really like this because you can just play it with a friend if you have a rubik's cube and a whiteboard marker
7:12 Givng combinatorial game theory vibes
hackenbush moment
Tired of octopus content on UA-cam, but I didn’t think it would get to my favourite tictactuber, I’m disappointed
are you really not going to address player 2’s strategy of just copycatting and forcing a draw?
I love octopus('s?) playing tic-tac-toe
I love the music in these videos
I gotta go make stockfish for CubeTacTix now
I think that your position evaluation function may be a bit too inaccurate. The "/3" and "/7" that were entirely guesses are probably not optimal. (And they may even be better for evaluating board positions 2 moves ahead than ones that are 3 moves ahead).
Also, having 2 or 1 in a row probably has a *different value* for a *player that is about to make a move* than for a *player that has just finished* their move. If you're about to hand the option to block your 2-in-a-rows over to your opponent, then having one is basically having none and only having several gives you a real advantage. Whereas in that same situation, having just more 1-in-a-rows that aren't yet blocked would be better, since that gives you a choice of which ones you want to develop into 2-in-a-rows (ideally you'd have so many that you'd always be able to develop multiple 1-in-a-rows into 2-in-a-rows at once). Whereas for the player that's about to go, having a single 2-in-a-row that the player that just finished their move couldn't block is basically the same as having a 3-in-a-row; but having more 2-in-a-rows doesn't add that much.
In conclusion, the value of a 2-in-a-row and 1-in-a-row should depend on whether it's in the hand of the player that's about to go or the player that just went (as mentioned above). And also, the value of the *first* 2-in-a-row should be different from all *additional* ones (and maybe the same for 1-in-a-rows).
Also, for your "minimax with depth N" strategies, you don't really need to search the full configuration space. If a possible first move is rated worse than the best-rated first move by some large margin, then you can discard searching second moves that follow from that first move. That will allow you to get to higher N, which suppresses the influence that your position evaluation function has on determining which moves are good.
I definitely did think about some of these things. And I looked into using alpha-beta pruning to reduce the size od the search space/increase the depth of the tree. But then I thought, "What am I doing with my life?" and just went with what I had.
@@marcevanstein🐐
Ultimate tic tac toe the one with 9 boards is the one im most familiar with. Whatever spot you play your piece in a certain board, the opponent plays their piece in the respective board according to where you played on the smaller board
my game design professor made us make a version of tictac toe, we called it shapewars, basically, each player had 3 symbols, triangles (At least 2 in a line of 4 symbols of your color), squares (at least 2 in a square of 4 symbols of your colour) and circles (at least 2 in a pattern of symbols that form a diamond, since circles can't exist on a grid), it was on a 5X5 grid, i wanted to call it tic tac foe.
Cool assignment
imagine how good this would feel if you were the cube... or maybe even an cephalopod ...
Can't wait for next time, when we discuss the number of games of Tic Tac Toctopus!
Did anybody else get mesmerized by the sounds of the cube getting filled
My favorite variation of Tic-Tac-Toe is Tic-Tac. 2x2 grid, whenever I challenge someone, I win
I was really hoping for a Tom7 style chess tournament graph, and you certainly did not disappoint! I would love to see more silly strategies represented there, like maximizing symmetry.
this is as wild as an octopus playing tic tac toe
The ending music is horrifyingly eerie, truly encapsulating the fruitlessness of tic tac toe
I experimented with this myself a bit In Highschool. I found the method of blocking the center, but I also worked on something I recalled recursion. Where basically it all loops back on itself. There is no top or bottom board, because below the bottom board is the top one. The center tile of all 3 are equally important, and it means some all tiles simply have more options with which to win
As a speedcuber, seeing cube related maths makes my brain tingle
12:26 Minor correction: an edge lies on three lines.
ur content is amazing
That game is simple enough to implement the AlphaGo algorithm on a single GPU. Should produce a super-human AI ;)
A reminder: In AlphaGo, an evaluation function is trained from pair-wise match winners. And then, this function in used in Monte-Carlo tree search (MCTS) during inference (play).
Would love more such videos
If we aren't counting the middle most cube, isn't it just a 2D variation game of tic tac toe where we play on 6 grids simultaneously? 🤔
Thinking along these lines changing the assumption of the 'line becoming unplayable' to 'that whole face became unplayable' once you make three in a row, will make more sense coz X won on that game (or face) so that's only right that it should belong to him
"You might notice that 7 is more than 3"
Best quote
As an eldrich horror, I can confirm that enjoyment peaks at 6 spatial dimensions. These days I hardly play without an additional 4 temporal dimensiona and 3...oh actually that kind of dimension is unintelligible to the human brain.
4:30 This explanation is correct, but it can still be simplified. The number you give for possible games is not the number of possible end states of the board. If it was that, it would be 9!/4!/5! (for 2D) or 26!/13!/13! (for 3D), since if you swap around the circles or the crosses among themselves the end state looks the same. Instead the games you count are defined by where each subsequent move is made. This can be visualized better in a way similar to the plots of place/move you made in previous videos: instead of filling the board with crosses and circles fill each cell with the number of move that is being made. For example, if the first player draws their symbol in the central square, represent that by writing 1 in that square, and so on. At the end of the game the entire grid is filled with numbers from 1 to 9 (or 26 in the 3D case). Now the games that you count are distinct such grids. In this way you can see that no full game has any particular symmetry that you would have to take into account, since all the numbers in the squares are distinct. Therefore in order to take into account the rotational and reflection symmetry you just need to divide by 8 or 48 and only consider an appropriate subset of the games.
this series of videos is driving me crazy
Man do I love playing Tic-Tac-Toe with an octopus
Best trilogy of videos I've ever seen
finding optimal plays in this is just comparing tic tac toe to chess with extra steps. yeah it is a solved game in theory but only with infinite computing power. thats what makes tic tac toe so interesting, it's a solvable game that is so small that you actually can go through all options
The cube rotating around with cute music makes me nostalgic for game cube...
Very nice, thank you!
The only problem with this solution is having 9 squares in a grid allows 8 for the octopus and only one for the opponent.
i remember when i use to play tic tac toe² and tic tac toe³ with my friends
how many games of 5d chess (multiverse time travel)
His Tic Tac Toe videos get better and better everytime
LOL! Wow, I didn't think you'd actually try a 3D idea. And yet, here we are.
And I like this concept too. I once tried to make a game show concept that executed similar to CubeTacTics, except the center is still open. Answer questions to earn points, which you can use to buy squares. More powerful squares cost more points. Every TTT made nets cash, most cash when the board is full wins.
If you're going to do 3D, doing this or upping the game to 3 players are the fairest ways to do it, for the exact reasons you pointed out in the beginning. And the music is always fun.
PS 1: The game where your symbols can move around, I liked that electronic game. Take 3. I still have it buried deep somewhere, it's the ultimate in look-ahead strategy. Dare?
PS 2: There may or may not be invertebrate sea life involved in this, but I do remember another electronic TTT game I had as a kid called I Took A Lickin' From A Chicken. If you can bring animals into this, so can I.
3D tic-tac-toe *with* the center could also be a three player game, accounting for the extra freedom by having to account for *two* new marks between each player's turns
You can also force a win by starting in the corner, not just the center. Since there's six possible lines you can make, you're then able to put your opponent into a fork.
The arc continues!
Alternate title: how many games can stockfish play on 3D tic tac toe minus center
I played 3d tic tac toe but we didnt have any way to suspend the pieces, so you had to start at the bottom more like connect 4 (you should also do a video on connect 4)
You should make a combinatorial game theory video. I cannot imagine the raw power it would exude
SECONDING THIS
Nooo I wanted you to keep analysing. Great video, any chance you will explore more complicated algorithms?
Can you make the next video on octopus tic-tac-toe
I play 3d tic tac toe a lot in school, and the way me and my friend found to nerf the center was to allow for cirlcle to place a right side up triangle and x to place an upside down triangle in the case of a two-way fork from the opponent. Or we play with three people. But if your adversary manages to make a three-way fork, then you have to take the L.
That is a really cool addition to the game. Are the blocking triangles permanent or do you move them around as if a stone across the board and to block a new position is to free the square the triangle was previously on?
I orefer 3d connect 3, or 3d tic tac toe with gravity if you prefer. Pieces must be played on the lowest possible layer for a given column
It's interesting to see Marc Evanstein teaching Octopuses to play 4d Tic-Tac-Toe
We played 4x4x4 for years in school. after putting some effort into "inventing" it, completely ignoring the possibility that someone else probably alrdy did it.
Was fun tho, hundrets of games and about 1-2% of ties
If i'm not mistaken starts the edge ad 12:27 starts three linens instate of two.
I had the same thought
do you have any interest in combinatorial game theory? it's not perfect for this type of game because of the fact that in this type of game the one who win is the one that can still make a move but it can be interresting because your way of doing things looks a little alike.
Tic Tac Toe is so complex! 😮
At the end there would be at least 2 cubes that wont score into a line so we could remove them.
becuase 26 isn't a multiple of 3(the number of cubes needed to complete a line)
we end up with (26!/2×1)/48 => (26!/2)/48 => 26!/96
Idk what im trying to explain.
I get what you're saying; I do actually end the games when there are no meaningful moves less, but I didn't have time to get into it, and it was only possible with the few strategies where I could actually get to the end of the game before my computer couldn't handle it. :-)
At 12:27 you say an edge piece does 2 lines, but wouldn't it do 3 because of the one across the middle tile on the other adjacent face?
4:27 I don't know what the 4D stack of CubeTacTix is like so this may be irrelevant, but there are 384 symmetries of a 4D hypercube
but how many different types of octopi can play tic tac toe
Damn never knew you were actually an octopus
Just trying to comprehend that I now live in a world where "tic-tac-toe influencer" is a thing...
Smart people make me contemplate my existence more than anything else. Not anything they say, just the utter feeling of inferiority and mortality, knowing it's too late for me.
I wish I was an octopus so I could have great tic tac toe strategies
cool video but I'm not too sure why I saw an octopus playing tic tac toe
Honey, wake up. The tic tac toe math guy uncovered a new dimension
I just made 3D tic tax toe in Excel, but I only had to code in the 49 possible winning conditions
Who's ready to play the 3D Tic-Tac-Toe minigame in Octodad?
Cant eait till you get to Gomoku Narabe, 5 in a row, big ass board.
you're really getting all the value out of tha tic tac toe thing huh
Whats next, an infinity moves in 5 Dimension tic tac toe now?
MARC THATS ENOUGH
I will run this into the ground. ;-)
OH i didnt expect you to respond eheehehe @@marcevanstein it was a little joke i love your content
what octopus is everyone talking about?
And how many 4th dimensional variations?
sounds are a bit loud at 6:10
The microtonal sonification at the end is so yummy
cube tactix ytpmv
I am so disappointed that the app has no sounds.
Ok, but what if your players were octopodes?
Fun
Oh boy, here we go again.
Does this factor in the fact that 3d tic-tac-toe can have up to four players?
Can someone please paste the text that's there for 1 frame? I cant figure out how to pause at the right time. Also can you think of another way to do that without making it a pain in the ass to read? Unless you are trying to alienate a whole bunch of viewers.
Can someone please explain the octopus joke lol. I don't get it, there was no octopus? What's it a reference to?
Its a reference to the 1992 war on octopus conducted by the Zemfried Federation. They lost
2:46 there are 27 digits, almost 26...
you didnt say how your ai did against the built-in ai
The best possible (that doesn't take 5 times the age of the universe to compute) AI is probably something closer to AlphaGo, some kind of ML model learning to predict minimax, then instead of using the Board Position Evaluation Function you use the ML model
what about a 4d tic tac toe