Actually, Maybe There's Only 1 Game of Tic-Tac-Toe

[@marcevanstein]

In case you want some very silly merch: shop.marcevanstein.com/ I also made an announcement video featuring some epic Tic-Tac-Toe background music. kzbin.info/www/bejne/hWLKi6ujq9hrhcU

[@Turkaryotic]

O goes first btw

[@evgenkhersonets880]

I wonder what are those 4 times O can win (on 8:50)

[@william3371]

POV: You've never seen the movie "War Games"

[@william3371]

Also, I found the optimal play when I was 12 or so: Top left corner if you go first. Unless someone has brushed up on their tic-tac-toe theory, they'll probably mostly pick their first move at random, which is a guaranteed win for 7 of the 8 remaining squares, the center being the safe one. If they pick the center, you can either pick the square that is a "knight's move" away from the corner or the opposite corner. [Just based on nimbers] The former leaves you with a roughly 94% win rate and the latter a roughly 91% win rate.

[@greendsnow]

Are you in the spectrum?

[@kikones34]

This was on my mind the entire time while watching your other video. "But wait, isn't tic-tac-toe solved and always a draw?". But your way of framing the problem as two non-perfect humans playing using a reasonable heuristic seemed sensible too. In the end, with perfect play, there is indeed only one game of tic-tac-toe which ends before it even begins.

[@LethalLuggage]

Tis why I refuse to play with my daughter

[@Afish8me2china]

This game is rigged

[@diabl2master]

Yeah obviously it just depends on what you assume about the players..... In the other video, he made looser assumptions. In this, he assumed stricter assumptions.

[@diabl2master]

I like the idea of two perfect logicians sitting down in front of a piece of paper and two pens, looking at each other and saying "aha, well played sir, a respectable draw" , getting up and leaving

[@notoriouswhitemoth]

It doesn't _always_ end in a tie, there is a win condition that's possible to achieve, in fact, only about 18% of all possible move sequences result in a tie. It only "always" ends in a tie _IF_ both players are 1. trying to win, and 2. playing optimally toward that goal.

[@strawburst1001]

Next video: Tic-Tac-Toe don't exist

[@lorenzorafael4600]

What’s a tic tac toe

[@eyesicecold]

@@lorenzorafael4600 x o o o o x x x o

[@nanamacapagal8342]

Oh, it very much exists. It's just that there are exactly 0 games of it.

[@caked3953]

​@@nanamacapagal8342or a puzzle

[@mr_crazydude]

Tic-Tac-Toe is the matrix xD

[@dymaxion3988]

A strange game… the only perfect move is not to play

[@TimmyRiordan]

How about a nice game of chess? kzbin.info/www/bejne/qWqWfHZqdqx-pLs

[@sutirk]

Turns out that Tic-Tac-Toe is indeed a stupid game. Only a fool would engage in a such an activity, knowing that the result of your actions, no matter how well thought or well planned they be, will certainly lead to a draw.

[@hhhhhhhhhhhhhhh-Mikel.Montalat]

​@@sutirkno, that is only assuming your opponent knows how to play well too. If they're not as good as you, you may still win instead of tying. However, it still isn't fun.

[@zotaninoron3548]

How about a game of global thermonuclear war, instead?

[@ThePCguy17]

@@zotaninoron3548 Personally, Joshua, I think I'll stick to that game of chess you offered.

[@theultimatetrashman887]

I absolutly love the little sounds the tic tac games do when they are moving. Makes them so lively

[@EEEEEEEE]

E‎ ‎ ‎

[@fen6300]

makes them creepy imo, with the music and the noise. Maybe because it makes me think of Petscope. And also maybe the fact im watching this at midnight

[@hushedupmakiki]

I wish there was just a video of all the permutations of the similar games in audio only.

[@john_hatten2862]

It helps understanding how different 2 games are, without have to pause to analyze. Genius.

[@Mrflipflops_w]

And then the weird and ominous background tone continues to play

[@TriflingToad]

Even the background music is tic-tac-toe. This man is INSANE when it comes to content that's multi skilled.

[@suyunbek1399]

a very shrewd and nitwitted detail indeed, but it still falls into a music skill category i'm afraid

[@v0id_d3m0n]

Great profile pic

[@suyunbek1399]

@@v0id_d3m0n thank you. i will think about it and when i reach my conclusion i will contact you about the resolution of this situation.

[@suyunbek1399]

@@v0id_d3m0n i did get a profile picture. do i deserve your respect and acceptance now? will i ever?

[@suyunbek1399]

@@v0id_d3m0n wait, you wrote great? not get? oh well, i regret nothing.

[@quinndirks5653]

9:48 Another strategy is to always go center as first move. If 2nd player goes on an edge, first player can win the game 100% of the time. If 2nd player goes in the corner, 2nd player can cause a draw 100% of the time. BTW, I did not specify X or O because whenever I have played, either shape was allowed to go first.

[@nonmagicalwitch]

the sequel we didn't know we needed Also, in history class, a friend of mine and I came across the corner middle opposite corner strategy and we were absolutely stumped to find out that we, in fact, didn't solve the game since there is really obvious counterplay to it

[@RosieDump]

nice pfp :3

[@blasphemer_amon]

As a historian it makes me simultaneously pleased and baffled that kids these days are suddenly interested in the study of Charlemagne, but only one of his paladins and not the other eleven.

[@legitplayin6977]

@@blasphemer_amonIt’s very funny, I wonder how he would react if he came back to life and discover that this is his most popular representation in media.

[@nonmagicalwitch]

@@RosieDump :3

[@bluechromata6976]

@@blasphemer_amonOh don’t worry, that same franchise puts a lot of focus on Roland, Bradamante, and even Charlie himself.

[@jagobot1487]

Mad respect for censoring your children’s face before putting it online, some people just do not respect their own children’s privacy and it’s crazy to me

[@jnmarshmello2728]

Tf they gunna do about it? Cry

[@TheAechBomb]

​@@jnmarshmello2728and sue you for unpaid wages in a decade

[@Tdg_fun]

@@jnmarshmello2728duh

[@eindeed]

​@@jnmarshmello2728 youre a pleasure at parties aint you?

[@orimoreau3138]

@eindeed You really ran that phrase to the ground, it's nowhere near applicable in this instance

[@notoriouswhitemoth]

Tic-tac-toe is a zero-sum territory control game about the futility of competition. In the movie 'War Games', it was used as an object lesson about mutually assured destruction for a machine-learning AI.

[@DiamondAppendixVODs]

That's an interesting way to look at it

[@fujster]

What a reference. Yes the calculation in the end stated the only way to win is not to play

[@HolloMatlala1]

I'm so watching this movie in future thank you for the ChatGPT version in 1983

[@HolloMatlala1]

kzbin.info/www/bejne/Z6fQn6NtnM16hs0

[@GameRoMan]

The best game is: [ ][ ][ ] [ ][X][ ] [ ][ ][ ] [O][ ][ ] [ ][X][ ] [ ][ ][ ] [O][ ][ ] [ ][X][ ] [ ][ ][X] [O][ ][ ] [ ][X][ ] [O][ ][X] [O][ ][ ] [X][X][ ] [O][ ][X] [O][ ][ ] [X][X][O] [O][ ][X]

[@AlanKey86]

*Tic-Tac-Toe Poem* I played a game of Tic-Tac-Toe Against AI - a mighty foe Every one of my attacks Was undermined with minimax Every game we played - a draw Has this program not one flaw!? Offended by its swift ascendance I resolved to have my vengeance "Grids of 3x3 are easy, They're for babies, don't you know?" I draw a board, 19x19 "Come computer, let's play Go"

[@TejasKunduru]

ai generated?

[@ryanh7167]

I like this poem, especially the reference to alpha Go at the end. It's pretty interesting the stochastic optimal policy algorithms that get developed to solve systems where the action space is just too cumbersome to explicitly optimize over.

[@Foam_Woa]

nice dude

[@hiimemily]

This needs to be pinned.

[@an000n]

The former world Go champion is gonna have a word with you

[@vivienamare2231]

Mr Campbell I see you. I know you watch these. Mr Campbell stop assigning these as assignments in class please I'm begging

[@wiktorszymczak4760]

Hahahhshsgsg

[@Nphynite]

Brovhad to turn to KZbin

[@The_Hashbrown_Guy]

Mr. Campbell I know you don’t know me but just keep using these there fun 👍

[@michaelcarlton1484]

The largest solved game so far is Pokémon. Someone has mapped out the exact combination of button presses you need to win, regardless of the RNG.

[@Trivial_Man]

Not quite. If you are referring to FireRed then there is still a small chance that the run ends on Route 1 due to a Pidgey outspeeding the starting Charmander. It's nearly solved, but unlikely to ever be completely solved without exploiting some sort of glitch to bypass at least that segment

[@psymar]

Not sure how exactly one would define largest, nor which version of pokémon you mean, plus I would consider Pokémon a single-player game of chance rather than a 2-player game of perfect information. For the latter, the most complex that's been solved without being the result of a mathematical proof that generalizes to infinity is probably Antichess, aka giveaway chess, a chess variant where the goal is to lose all your pieces. It's been proven that 1.e3 leads to a forced win for white, however the winning tree of moves is several gigabytes in size, so this doesn't impact human play that much aside from maybe contributing to the popularity of 1.e3 among human players -- paradoxically making alternatives maybe more attractive as opponents will have less practice against them!

[@AlexanderTersakian]

I don't know if Pokemon even counts as a candidate for solving. You don't have an opponent that will play optimally, just an unoptimized computer.

[@featherofajay4667]

Said computer may not play optimally, but given enough knowledge of the engine, it’s always possible to figure out its next move (or, in some cases, the couple moves it sees that all lead to the same result).

[@michaelcarlton1484]

@@Trivial_Man Small update: the same guy found a 100% method for Platinum version.

[@Mr_Pastries]

In response to 9:53 I traditionally start with the corner because if they don’t respond with the center there is a guaranteed way to trap them and even if they do there is still one more possible trap they can fall into. The only other starting move I use sometimes is the center because if they choose an edge you can guarantee a trap win, and if they choose a corner, you can choose the opposite corner which sets up a possible trap if they happen to choose an edge. (For example using the grid at 0:23 the game 51947 uses this trap)

[@medleyshift1325]

I would recommend a healthy rotation of openings to keep you on your toes, every tic tac toe master can win with the X's when it counts. It's holding the draws with the O's where the real players cut their teeth. I find building up your opponents courage to be very important to a slip up later in the match.

[@gacrux-ni7hw]

I think you meant 51947 with a 3/8 fork? 51943 is a win for "O" at 7

[@Mr_Pastries]

@@gacrux-ni7hwyou are totally right. That was my intention but it appears I envisioned the board wrong and wrote the wrong numbers. Thank you.

[@GoFastLily]

Your kid is gonna find this in, like, a decade and have a huge revelation as to why he wasn't winning 😂

[@AirWick694]

his dad was a certified tic tac toe researcher

[@EEEEEEEE]

E‎ ‎ ‎

[@lewa_j]

Or why he was

[@iuqk]

@@EEEEEEEE iuqqqqqqk

[@Kaiasky]

I really like this update and particularly the pruned tree at 8:34. I think what you've done is defined the "plausible tic-tac-toe mistakes", and that's a really cool thing to see. If you spent some time trying to make the gametree graph as planar as possible (minimizing crossing edges) I think it'd make for a really beautiful poster.

[@marcevanstein]

Thanks! I'm considering doing this 🙂

[@kookaburrakai8026]

Yeah I love the implication at 8:34 that if x moves the same move means y wins I'm also trying to figure out what that Circe Winning game at 3rd move is, I suppose it's a "Corner->Center->Side adjacent to Corner" game

[@Kaiasky]

@@kookaburrakai8026 I don't think it can be corner center side, because 8:52 we get that "move 1 corner" is the topmost node, not the middle node. Looking at it, I think it's likely to be (labeling the squares 1-9 in reading order): X4, O2, X6. O5 is forced, X8 is forced, O plays any corner and has a fork, winning. I'm gonna try some ascii art: __| O |__ X |__| X . | |

[@nivolord]

In my memory, the classic way to win at tic-tac-toe is to start in the middle, and hope the opponent plays on an edge, not a corner. If you then respond with a corner on the opposite side, victory is assured. This strategy became too obvious however, which is why the meta shifted to the corner first play.

[@pgpython]

I use to think that was the best strategy but my usual tactic is to use the corner centre corner strategy as most people think the corner is op and so will fall for taking it on their turn then you just take the third corner and you have a guaranteed win

[@Linck192]

I think corner as the first move is objectively better than middle. When you play middle, the opponent has 4 positions they can respond where they don't lose: The four corners. Technically, all the corners are the same game, just rotated versions, but normal people don't think about it that way. However, if you play corner as the first move, the opponent has only 1 position they can respond: Middle. So corner is better

[@__christopher__]

@@Linck192 Even if you take symmetry into account, corner is better: With middle, the opponent has only one losing move: edge. However with corner, the opponent has four losing moves: Adjacent edge, adjacent corner, far edge, opposite corner. With only one non-losing move in both cases, this means 80% losing moves in the corner case, versus 50% losing moves in the middle case.

[@Linck192]

@@__christopher__ you're absolutely right

[@Twisted_Code]

@@Linck192 What is this, people on the Internet reaching an agreement? Preposterous, inane, UNACCEPTABLE, every interaction must devolve to something that resembles the intellectual quality of a tic-tac-toe championship! (I just saw a typical Internet argument, or at least one comment out of it, in one of the other threads. The irony was palpable)

[@aceofnothing7469]

this is the worst video to listen to in the background while doing homework, it's so engaging and the sounds the board makes just tickle my brain this is a compliment btw

[@SteinGauslaaStrindhaug]

I remember me and a fellow neurodivergent classmate spending the lunch on figuring out the optimal strategy of corner center opposite corner. We didn't do any particularly systematic symbolic maths, we just reduced the number of games by noticing the symmetries and testing every option and backtracking each time we had an obvious win or draw.

[@cristianyahirmejiacruz5495]

Neurodivergent 😭😭😭😭😭😭

[@Red-yt2dk]

@@cristianyahirmejiacruz5495 Is this a problem somehow?

[@slop599]

@@cristianyahirmejiacruz5495 grow up

[@VestinVestin]

​@@Red-yt2dk It's annoyingly euphemistic. It just means "crazy".

[@Red-yt2dk]

@@VestinVestin Rude.

[@conza1989]

It's not clickbait, watch the whole video - loved it, well done.

[@JannPoo]

9:13 I would argue that since the game never started to begin with and no move was made, the conclusion should be that there are 0 games of Tic-Tac-Toe. "The only winning move is not to play"

[@nixel1324]

He wouldn't be a true programmer if he didn't make the occasional off-by-one error.

[@orangereplyer]

I think it should be 1, for the same reason that, say, there is only one way of permutating 0 items. The game has length of 0 (it lasts 0 turns) but it is one game.

[@orangereplyer]

Sheesh, sorry, the send message button on mobile didn't work and when i spammed it it suddenly sent the message a ton of times

[@gacrux-ni7hw]

"The only way not to lose"

[@moralized]

Play EDGE first move! Most Tic-Tac-Toe players understand the "corner-start" fork trap. They'll think you're a fool for starting on the EDGE and will underestimate you! X: LEFT-EDGE, O: MIDDLE X: TOP-RIGHT, and if O chooses the sensible-looking option of BOTTOM-RIGHT to set up a win, X: TOP-LEFT wins by fork! (The other option for O was BOTTOM-EDGE, which ends in a draw.)

[@OMGclueless]

The XOX diagonal play is not the strategy that gives your opponent the most opportunity to make a mistake. But many people quickly learn the heuristic, "Middle > Corner > Edge" for cases where there's no obvious play (i.e. if you can't win or block a win). And the corner opening I think is the unique strategy that exploits this and wins, where otherwise that heuristic always achieves at least a draw -- this makes starting in the corner uniquely exploitative and gives it merit.

[@medleyshift1325]

I've long known that if x starts in the corner and o plays anywhere but the center then x can force them to lose. That's what makes the corner the best place to start. The addition of the corner center corner is a potent weapon on Italian restaurant table cloths the cousins will not see coming....

[@Tzizenorec]

If you ignore the possibility that the opponent will make a losing move with their first move (non-center in response to your corner opening or edge in response to your center opening), the opening that gives the opponent the most losing moves on their _second_ move is the OXX diagonal play, which gives the opponent a 4/6 chance of losing if they move randomly.

[@Droid29]

​@@Tzizenorec I think the reason this strategy works so well is because it confuses players who only expect their opponents to try to win. Going opposite corner seems like a waste because that diagonal is already blocked off. This is the only strategy I've ever used that people haven't thought through how to counter.

[@triacontahedron]

@@Droid29 This is exactly why I love it. I saw a video where a machine educable noughts and crosses engine started to settle on this as one of its strategies. I then thought about it and fell in love with it diabolicitiy. Plus, if you start center and their response is edge, you win.

[@arturdias8462]

1. Play X in the center. If he plays O in the edge you win if you play X in the opposite corner. 2. If he plays in a corner, you play in the opposite corner. His only move is to play O in one of the other 2 corners. Thats the strategy I use if corner doesn't work. A good second strategy.

[@Susul-lj2wm]

we could actually use this to generate those mentioned strategies. Instead of always allowing "bad" moves, we allow one heuristic move and from then on play minimax. On the pruned tree, we can then see where you can set up a trap by splitting into a winning node and a draw node

[@laytonjr6601]

My thoughts exactly. A position that allows for a trap is better than a position that is a guaranteed draw

[@kaynight64]

This can be made objective to generate the perfect game by the following heuristic: Always play the non-losing move for which a greater proportion of the opponent's replies (accounting for symmetry, and assuming the opponent will always win or block an immediate win if they can) lose. If you can't, then play the non-losing move that minimizes the opponent's ability to do that. That will certainly result in the corner-center-corner strategy. For the first move, there are two replies to center (1/2 draws), five to corner (1/5 draws) and five to edge (3/5 draw). So edge is optimal. Then center is the only non-losing reply. Now the first player has four moves. Two of these force a single non-losing reply. Let's look at the other two, opposite edge and opposite corner. For opposite edge, there are 6 replies (4/6 draws). For opposite corner, there are only two replies (1/2 draws). So again it is the best move. Now assuming that the non-losing move (any edge) is played, all moves are thereby forced - due to the need to block immediate wins - until the game is drawn.

[@justfellover]

Even though I was a fan of the corner corner opening in my youth, I believed your previous video and didn't notice you'd omitted it. I like your statement that the game occupies a sweet spot in complexity, which is probably why nearly everybody learns it, even though it's so famously easy to master.

[@BigStrap]

You have got to be my favorite tic tac tuber on the entire platform right now

[@EEEEEEEE]

E‎ ‎

[@mAny_oThERSs]

There are more than 1?

[@cymberciara]

For tricky strategies i enjoy mixing up the corner, centre corner strategy with centre corner corner. Go centre and if they go in they go corner, you go in the opposite corner if they then go for an edge you take another corner setting up a similar fork. I like it because in the corner, centre corner strategy they have to take and edge to secure the draw but now they have to take a corner to secure the draw and its slightly less famous so it catches people who prefer edges off guard

[@ldx8492]

I am losing it at the squeaky sounds for each tic-tac-toe game, it's brilliant!

[@EEEEEEEE]

E‎ ‎

[@PratikGharat1472]

NGL, i was gonna close the vid, but stayed just for those sound effects. lol.

[@uwoowoayaya]

Can't wait for the times when there's only 1 game of chess.

[@nixel1324]

There already is, we just haven't found out which one it is yet.

[@eclipserepeater2466]

@@nixel1324 Imagine that we find out that the one true game of chess is not a draw, but a win for black or white. Thus making tic-tac-toe the more balanced game~

[@bblunder]

@@nixel1324 The existence of safe and aggressive openings in chess actually sheds light on that. Chess is a game that can be shaped in many different ways. Every chess master has a safe opening that he plays on the day which he doesn't want to take any risk it.

[@bblunder]

@@eclipserepeater2466 There are certain openings with forced paths which when both sides play the optimum moves the game always ends with a draw.

[@alsatusmd1A13]

@@eclipserepeater2466 at least we know that if chess is sound, the one true game of chess should not be a win for black. Although we have enough computer power to solve chess itself right now, we may not have the will to devote the necessary computers to the solution. After all, we used humble desktop computers to solve English draughts between 1990 and 2007.

[@moonjae-in12thpresidentofr20]

At 7:40 the 2 in a row can force X to for a fork later down the line. If O goes for the 2 in a row with the bottom edge. X has to block it in the bottom left corner. Which O now has to block X with a move in the left edge. X can now force a fork by going in the top right corner. Leaving the board looking like this ❌🟦❌ ⭕️🟦❌ ❌⭕️⭕️

[@furiousdemon5713]

seven days later: *Actually, There Are No Games of Tic-Tac-Toe*

[@Hadeeen1]

Thanks for including the corner way. I used to play with 2 of my friends in 8th grade often and after a ton of games we'd settled on the corner move, but after we figured out how to block the corner move we stopped playing, because noone could win. Playing O edge then center consecutively or vice versa after the 2 corner X's (whether horizontally or diagonally) would always end in a draw

[@sillyking1991]

if O ever plays edge on their first move then they lose regardless of what X's first move was, assuming X knows what they're doing. because no matter what X's first move was, if O plays an edge then X can control O's second play, while also setting themselves up for a fork on their 3rd play. center is mathematically the best first play period. because the center affects half of the possible wins. edit: slight correction. if X's first move is an edge, and O's first move is specifically the opposite edge, then its a draw with perfect play

[@singed420snowinit9]

If X plays corner and you play edge then X wins no matter what, you can't block that.

[@Twisted_Code]

The amount of effort put into those videos only for The Algorithm to say "nah bro, I'm good", vs. just putting your best foot forward and getting enough attention that someone else helpfully points out your "mistakes" for you. This has some surprising applications to the perfectionism I've been struggling with lately. Didn't expect that from the follow-up video to something I just clicked on randomly earlier this month... Thanks for this rather serendipitous bit of insight!

[@marcevanstein]

Yeah, it's funny with KZbin in particular, because it seems like making mistakes actually causes engagement. So like, it might even be a good plan to have mistakes on purpose. I'm not going to do that, but I definitely think that there are times that I can allow things not to be perfect

[@myhamxd9692]

I came into this video knowing that the one true game was drawn at move 0. Ive played easily over a thousand tictactoe games with my friend, and we came to the conclusion that anything past move one leads to a draw so we started implementing more unique ways to play the game, i would love to see the same video but on 3d tic-tac-toe, a game that is for now not solved. At least in me and my friends' heads. Great video, I hope you can make it big.

[@DudeMan1620]

Yeah 3d tic tac toe is the way to go once you get to the always draw place. Playing with three boards at once is alot of fun

[@OkieWanKedokie]

I love playing Ultimate Tic Tac Toe, but rarely find someone to play it with. 😅

[@pferdsteiger5785]

Hi Marc, a few more notes on tic-tac-toe. Although many commenters have mentioned the corner-center-opposite corner as the optimal play pattern for X, if we consider players of different skill levels, it might actually *not* be the best strategy for a skilled X player facing off against an unskilled O player. Let me explain. I refer to the numbering of the tiles at 0:23 I'm going to assume the X player starts, and always plays optimally. However, the O player is a novice. They will always move to block an immediate three Xs in a row, but will not necessarily block an opportunity for X to make a fork, which would guarantee X the win on a subsequent move. With these assumptions, with the sequence (X1)-(O5)-(X9), then O has six possible squares for their second move. If O plays in 3 or 7, then X is guaranteed a win with perfect play. If O plays in 2,4,6, or 8, then the game is guaranteed to end in a draw. At each point, X will move to block, and O will be presented with a two-in-a-row from X that they must block. Even a novice O player will get to a draw every time. Assuming O's second move is completely random, X will win about 1/3 of the time. Consider instead the sequence (X1)-(O5)-(X8). Now the board isn't symmetric, and O has some more complicated choices. If they play in 2 or 3, then X is guaranteed a win with perfect play. If O plays in 6, 7, or 9, then they are guaranteed to achieve a draw with their skill level. However, if O plays in 4, then X responds with 6, then O is once again faced with a situation that they can allow X to create a fork if they haphazardly play in 2. As a result, X will win slightly more than 1/3 of the time assuming O's second move is completely random. In summary: X's optimal first move is corner. O must respond with middle or they lose. X's optimal second move is actually not opposite corner, but rather opposite side. No matter O's next move, X can always get to a draw. However, this play pattern maximizes the chance for a novice opponent to make a mistake.

[@NMS127]

Yeah, this is the only strategy I ever saw someone older than 7 or so lose to. I beat a very smart friend with it in high school once.

[@SgtSupaman]

This video is actually exactly why I didn't watch the previous video you did. I saw the one about 14 games in my suggested videos, but I already knew Tic-Tac-Toe was solved and always ends in a draw for anyone that knows the game. This was a good correction to go back and make.

[@schwingedeshaehers]

even if it is drawn, there are different ways to draw.

[@DudeMan1620]

Yeah the original video, had the assumption that no player plays towards a draw. Glad the author looked at the math again.

[@devilbob]

My fav oppening: X- Centre O- Corner (Non corner is losing) X- Opposite corner (Gives O one last time to make a mistake) O- One of the 2 corners (Non corner is once again losing) And from this point agree to draw, since every next move will be 3-in-a-row threat by X and block by O

[@skaruts]

Seems to me that in checkers it's also always a draw, if no one ever makes mistakes. I prefer calling it something like _"perfect plays"_ rather than _"perfect players"_ (or _"zero mistake plays")._ Because a player's skills are never perfect, but an imperfect player can still possibly make no mistakes, and thus have a "perfect play". That is true only in games of merit, where merit is the decisive factor for winning. As opposed to games of luck, where luck is the decisive factor for winning (like minesweeper or poker). In a game of merit, the player that wins is always the one that made the least mistakes (or the least severe mistakes). But it's always about mistakes.

[@johncochran8497]

Yes, checkers was announced solved by a paper published in September 2007.

[@tiagobelo4965]

I wouldn't say minesweeper is mostly a game of luck, although a bad opening or seed might force you into clicking a random square (a play of pure luck), once you become aware that there is a method to the madness, it becomes 99.9999% skill

[@calvindang7291]

@@tiagobelo4965 While no guessing minesweeper is cool, many purely random games of minesweeper end up with a 50/50 guess at the end and aren't that difficult in other places.

[@skaruts]

@@tiagobelo4965 No. That distinction isn't based on how most of the game is played, but on which factor is decisive to whether you get to win or loose. Your very first move in Minesweeper is 100% down to luck. And you'll be in that situation two or three times per game, depending on board size. In other words, it doesn't matter how good you are at it, you only ever get to beat minesweeper when you are lucky those two or three times. That's luck being the decisive factor. That is unlike Monopoly or D&D, where luck isn't the decisive factor. Each dice roll has no effect on the overall outcome of the game, it's how you decide to play with them that does.

[@TheAechBomb]

​@@skarutsthe good versions of minesweeper generate a new board if your first move is a bad one - windows vista minesweeper was great

[@RaRa-eu9mw]

Playing in the corner is only "the best move" because relatively few people know about the trick with the opposite corner. There's no real way in which it's better than playing in the centre and hoping the opponent plays on the edge.

[@space_kat1]

dude the little tic-tac-toe sounds gave my brain so much happy chemicals omg, they just sound so silly 🥺

[@PierreCarrier]

If you'd like slightly more complex than Tic-Tac-Toe but a lot deeper IMHO, I recommend Teeko.

[@nathanfeldman9510]

I maintain two things: 1) My favorite opening is corner-center-opposite edge. It maintains a 2/6 possibility (with a random opponent) of setting up a fork and is lesser-known than corner-center-corner. 2) This is the best opener. Let us assume that our opponent plays random moves, but blocks every two-in-a-row when possible. Let us also assume we play the best moves (i.e. fork when possible, block opposing threats). Let us also treat, as you do, symmetrical moves (with rotated and reflected boards) as identical. If we calculate the probability of our opponent making a mistake at some point in the game, the corner is better. This is because the corner is "trickier". The opponent, on the first move, has 5 possible plays: opposite corner, adjacent corner, adjacent edge, opposite edge, and center. Only the center survives. And on the second move, after I go on the opposite edge, they still have two losing moves. However, if I go in the middle, the opponent has only two possible plays: corner and edge. If I remember correctly from being bored in AP World History, with the random parameters I set up, the corner->center->opposite edge comes out to 1/96 superior to the second best move (corner -> center -> opposite corner) and vastly superior to the first-move-middle play.

[@Ari_Is_AriAriAri]

I think it can either be 1 game, 2 games, or 3 games! 3 games: either X wins, O wins, or draw 2 games: either you play or you don’t 1 game: you play the game

[@Wack..]

I LOVE videos that go into the details of a game as simple as Tic-Tac-Toe, solved games and subjects adjacent to it are just so interesting to hear about that I could watch another hour of this.

[@hunacean]

You know the added backstory of a Dad teching his son the game oonly to go on and make this analysis makes this saga so much better.

[@kathras]

there is truly only a single game of tic tac toe, where a player wins, and simultaneously a player loses.

[@EEEEEEEE]

E‎ ‎

[@kathras]

@@EEEEEEEE i really disagree with your opinion. how can you be such a shameless creature.

[@TheLadysAtelier]

What about ties

[@JoMama-b3k]

All other games at least have 1 “blunder”

[@JoMama-b3k]

Edit:the blunder is playing a move

[@JoMama-b3k]

Edit:the blunder is playing a move

[@JoMama-b3k]

Edit:the blunder is playing a move

[@JoMama-b3k]

Edit:the blunder is playing a move

[@AlphaPizzadog]

Edit:the blunder is playing a move

[@JamesWuellner]

The title of that XKCD comic, XKCD #832, is actually "The only winning move is to play, perfectly, waiting for your opponent to make a mistake." So I'd bet they hold a pretty similar opinion of how people go about playing tic-tac-toe to you, even if their chart is pretty standard.

[@jkid1134]

This is a wonderful follow up. It feels like you read my comment personally and addressed everything in it and more. I am glad you are making videos. (And again, I recommend Connect Four 😊)

[@rhmb1019]

I would like to point out that picking the corner as the first move wins you the game unless the opponents first move is in the centre. For example if the first move is the top left corner and if the opponent picks any of the sides the optimal move is alway to pick the adjacent corner to your first move without an 0 in the middle of them, this forces the opponent to place an 0 between your 2 Xs and for your move you put an X in the centre creating a fork and winning the game. If the opponent picks any of the 2 adjacent corners the optimal move is to place your X on the side that is next to your first X but on the opposite side to that of the 0, this forces the opponent to place an 0 in the other adjacent corner, which in turn forces you to place a X in the centre which coincidentally causes a fork and wins the game. If the opponent puts the 0 in the opposite corner, the optimal is to place your X in an adjacent corner to your first X, forcing the opponent to block on on a side, the next move is to place an X in the last remaining corner creating a fork and winning the game.

[@jessehng1896]

I feel like this video is overrated. There is really one optimum move both player can play, first player corner, second player play center and so on to the draw. That's it. Python code is unnecessary. Because most optimum move 1st player can play is the corner and 2nd player goes center and the game is basically done.

[@railmastergaming]

The only game simple enough for me to play as a kid now has the most intricate/complicated lore of anything I've ever seen.

[@somerandomweeb4836]

That divided by 8 code is truly well written

[@tizanelul]

Rock Paper Scissors > Tic-Tac-Toe

[@HyperionCasting-gg6vm]

There is only 1 game of rock paper scissors, there is the highest chance someone plays scissors. Do just play rock. Works 1/3 of the time

[@i_am_lambda]

Connect Four > Rock Paper Scissors Tic-Tac-Toe > Connect Four

[@cidlunius1076]

You play gun. It always wins.

[@HelloHumans1234]

@@cidlunius1076Exactly!

[@thegamingbanana8679]

you can go middle, (they cant go corner), you go ny corner, they block, you go corner in the same line and set up a fork

[@michaeltennant8312]

9:40 I think the best alternative to corner centre corner is center edge corner. As X can then set up a fork, either along the diagonal or the edge of the board, by placing a corner.

[@Tzizenorec]

Center edge corner isn't an "opening". It's just O making a blunder with their first move.

[@mrbeardbee4538]

13749 and 12749 are my favorite. You automatically win if opponent goes in an adjacent edge or corner second move

[@mimumi3723]

We are so back

[@kaynight64]

Here's an interesting variation of Tic-Tac-Toe with some fun dynamics: Play is on a 4x4 board. 4 in a row, column or diagonal win. A square of four connecteds also wins. There is one particular opening position (first player plays on a center square, second player plays on the diagonally opposite center square, first player plays on an edge square orthogonally adjacent to their first move) where the second player has a ton of natural looking possibilities but only one of them is good enough for a draw. I find it pretty fun, though once you get the hang of it it's a draw.

[@seazeiscool]

i love the songification of the tic-tac-toe games so much its so cute, curious if you would want to make an analysis like this in the future with variations of tic-tac-toe which are a bit less unfair, like having Only x's or having 3 separate boards or 3 in a row actually making you lose or all 3 of those combined (3 boards X's only Misere variation) also how good is your kid in playing the game

[@ordinaryshiba]

The strategy I always play is center, if your opponent plays edge, you win. If your opponent plays corner, you play the opposite corner (so you don't threaten a 3 in a row) and the edges are still free for them to play in and lose.

[@gloweye]

I remember solving this game when I was like, 15. That was fun. Any bored teen with a slightly mathematical mind can do it, as soon as you start eliminating boards by symmetry, and stop playing out decided games. Corner start is best move IMO, because you force your opponents move into the middle (or you have a guaranteed win), and even if they do that, there's the corner trap for them. Starting in the center has the edge trap, but most people rightly don't play edges anyway, because they're just not as good.

[@sillyking1991]

even if they play in a corner you can preserve the edge trap by playing the opposite corner from them. corner first has no real mathematical advantage over center first. Its strength lies in the relative obscurity of corner first play.

[@Last_Resort991]

Mathematically any first move you make leads to a draw. The only way to win is to trick your opponent so he does a mistake. Argunmenting mathematically is bogus in this case.

[@Tzizenorec]

@@sillyking1991 The mathematical advantage of corner first lies in its ability to defeat players who haven't yet figured out that the center is good.

[@sillyking1991]

that isn't a mathematical advantage...its a strategic one. that doesn't make it less significant, just making sure we're using the terms correctly@@Tzizenorec

[@Tzizenorec]

@@sillyking1991 There is no correct use of the term. "Mathematical advantage" is not precisely correct for any part of this topic. But... I can say that the corner first play has a 11/12 chance of beating a clueless player, while the center first play has a 5/6 chance of beating a clueless player. The first number is bigger, so there is a "mathematical advantage" here... arguably.

[@dagamerboi]

I have a strat where I take the center and if they take a corner I can take another (not opposite) corner and make them block a loss, allowing me to play the edge next to my corner not blocked by their corner, forking them (lesson: if they take the center, go for an edge)

[@ChrispyChken]

im glad the last vid got picked up by the algorithm, this was a great sequel and im looking forward to whatever you make next!

[@dxc5698]

I do have an alternative to the X in the corner strategy which similarly tricks players. You start by placing X in the middle of the board. Next your opponent will inevitably take one of the corners (If they don't you win). Then by placing your X in the corner on the same diagnol as the corner they took you place the opponent in a situation where they can either take the opposite corner or an edge piece. If they do not take a corner, you win. The reason I find this works is that it is a natural opposite to the X in the corner starting strategy because the conclusion to solve the board state is the opposite rather than taking an edge you need to take a corner. Additionally, it will always allow you to make a lightning bolt on the tic tac toe board if it ends in a draw and I like lightning bolts.

[@canaDavid1]

0:59 this is false, as some positions have fewer symmetries. Consider only having one corner. This has only four reflections, not eight. Most extreme is only one in the center, having only one symmetry. This means that dividing by 8 would give too low a number.

[@cannot-handle-handles]

Agreed! Came to the comments to point this out, but you were here 45 minutes earlier. 😀

[@LearningFast]

I really enjoy your videos. The rules in Tic Tac Toe are fixed. What would happen if the rules weren’t fixed? What if two squares in a row was a win? What if instead of your placement being the only factor for winning the game considered sequence as well for determining the winner? What would happen if the players didn’t know the rules? How many games would it take for them to figure out what the rules are? The ultimate challenge would be what would happen if the rules changed randomly each game. What would the winning strategy be then?

[@Verymusician193]

What a sequel!

[@free2play-previouslyanvesh508]

Finally, the vid we’ve been waiting for

[@seheyt]

I adore the sonifications. Since music is very primary to me I've actually afford something similar to help me learn chess openings and board visualization. I'd love to see the code you use to synthesize these quirky sounds

[@TalonhawkGaming]

There are actually 8 unique games of tic tac toe. I figured that out a long time ago in middle school because winning at tic tac toe was more fun than history class lol. 1. Is a tie which as stated with 2 perfect players will always happen. What I figured out was every mistake that o can make and guarantee x a win. I count this as 1 and don't consider all the unique ways to tie. 2. When x goes center and o fails to take a corner there is 1 way to win. next x forces o's next move by o's fist move. X goes to block and creates a double win. This also only creates 1 unique board as it will rotate to look the same. 3. X fist move is on the side and o does not make a move that fall in line with x's first move. This leaves 4 open spots that guarantee's an x win by forcing o's next move and creates 2 unique boards. 4. Finally when x's first move is corner and o fails to go either middle or opposing corner creates 6 ways to win and 5 unique boards. I am not going to list all the plays but I will say like all of the previous games I listed X's next move forces O to block and guarantee's a win. I will also say it is impossible for O to win without several mistakes from X, what I did was figure out all the guaranteed ways to win as X by the placement of the fist 2 moves anything other than scenario 2, 3, or 4 by players that know how to win will always be a tie.

[@KayrBayr13]

Oh interesting! From my experience, Tic-Tac-Toe is only losable by making a mistake, which corresponds with your data.

[@nexivy]

What you could look at to find the most optimal play is to have the player get score after every turn based on how many potential plays lead to wins if the opponent makes a bad move, deriving the best moves chancing a mistake from your opponent.

[@TitusRex]

There only one game of tic-tac-toe: a draw

[@maxurmon]

the reason the corner is considered the optimal move, is because there is only one answer to it, because of symmetry you win in all posible situations EXCEPT if they play in the middle, and even if they play the only possible answer to your starting move, then you can use the corner trick so there is still a possibility of you winning corner start pretty much has only 3 possible ways it can go: you win turn 1 (opponent doesn't play center) you win turn 2 (opponent plays corner after center) or you tie (opponent doesn't play corner) as you said, a perfect player vs a perfect player will always tie, but a perfect player vs an unperfect player, the optimal route is the one that has you winning in every combination but 1 center creates 2 possible moves to your opponent because of symetry, and one of them is a insta win, but corner creates 5 possible answers and 4 of them are insta win you give your opponent more options, but don't increase their chances of winning, so instead you increase their chances of making an error, and at the end of the day that is the only way to win in tic tac toe, for your opponent to make an error so thats why is the better move, more possibilities for your opponent to make an error, thank you for comming to my ted talk

[@sir_ox6735]

Now do one of these, but with Ultimate Tic Tac Toe!

[@ir0ispro923]

tic tac toe is a game in which you play the same combination 100 times before someone messes up or tries something new which is play a bad move cause we know all good moves

[@Robbyrool]

People are confusing “games” with “outcomes” and “final positions”. These are distinct things. To say the games are the same as the outcomes is to say the journey is the destination. We all arrived at Times Square, therefore there is only one route to Times Square. Outcomes are win, lose, and draw. There are 3 possible outcomes. Final positions are the final diagram or locations of the pieces. The various paths or ways you can arrive at the final positions and outcomes are the possible games. Having one or three outcomes does not mean there are that many games. I’m speaking about both chess and TTT. Each game has exactly one outcome and one final position. But each final position has one outcome and multiple games. Each outcome has multiple final positions and many games.

[@garythemoth8049]

There are exactly 2 games of tic-tac-toe, one where I win and one where I don't

[@ertugkaya919]

Doesn't that mean there are no games of tic tac toe?

[@chaoticcar6231]

My favourite part of tic tac toe is agreeing to the fact it's a draw before playing and not playing

[@xE92vD]

2:07 yeah well that looks like something.

[@XxXNightcoreQueenXxX]

My classmates and I played a version of this in the woods when we were younger. We used sticks, stones, and other stuff to make the game board. But we only had 4 pieces we could place. So there was always 1 open square open. We could move the game pieces we have to an adjacent square if it was open, either up/down or sideways but never diagonally. Looser of the last game would get first move in the next game. So it became a battle thinking smart and outwitting your opponent, by moving the right pice in to the right spot for a 3 in the row. While also blocking your opponent or tricking them. I once won a game by giving up the middle to my opponent as that would give me the winning move.

[@aze4308]

This is an incredible video! Can you do something on chess? Not necessarily solving it, but maybe talking a little bit about how many legal board positions there are? It is a very interesting and similar topic!

[@thatchapthere]

en.wikipedia.org/wiki/Shannon_number

[@wokencs330]

I don’t think it’s similar dude after 2 chess moves there’s already 400 potential moves and distinct positions After 6 moves there’s over 9 million potential positions for the board to be in

[@wokencs330]

I don’t think it’s similar dude after 2 chess moves there’s already 400 potential moves and distinct positions After 6 moves there’s over 9 million potential positions for the board to be in

[@wokencs330]

I don’t think it’s similar dude after 2 chess moves there’s already 400 potential moves and distinct positions After 6 moves there’s over 9 million potential positions for the board to be in

[@shoeshiner9314]

I love the sound effects their goofy Brilliant vid when you reach clarity after spending my full day moving lol

[@Damini368]

So what is the win percentage of X and O in game states that reach the point of inevitability? Is the game more balanced than you thought or less? Also have you considered making a game that uses these models in it's decision making?

[@rajaryan52]

There is only 1 type of draw... notice how every one of them will always end up forming a capital 'Y' like shape, now this shape can be diagonal (i.e., the base of the 'Y' can start from the corner just like it starts from the centre side blocks)...so basically you either make a 'Y' (horizontal or vertical) or you win.

[@justinsemple7454]

It would be cool if you did the same analysis of either 4x4 tic-tac-toe or 3D 3x3x3 tic-tac-toe and compared the complexity.

[@soupisfornoobs4081]

3d tictactoe is a win for the first player after they play in the center

[@somebodylikesbacon1960]

why does the sound design feel like it was made for a horror game

[@confuseatronica]

wurp wurp wur barp bwurp bop bwooooow

[@ButterscotchBread]

werb wurp bwomp bwerp werp bur wuaoow

[@Chuck.1715]

I remember playing Tic-Tac-Toe in school and we were evolving the rules, until we have played on a full A5 5mm grid page where the goal was to connect at least five in a row, to score a point, and extra move. with potential to connect up to 9 in one move, where each additional symbol in a row would be worth extra point (point only). Once you scored a point on any symbol, you could not score another point using the same symbol in the same direction. If you managed to fill 2 five in a row with one symbol at once (one horizontally, and the other diagonally/vertically), or any variation on it, it would count according to previous rules for each row completed (so 2 points, and 2 extra moves in this case) Generally the game played with altering short bursts of power over the other player scoring 3-5 points in a short span of time, with highly defensive play to not allow runaway effect for the winning player, the game would end either if loosing player concedes, or we run out of space. We also tried this rule set with more players, where at 3 players the game was less defensive, and it was hard to get more than 1 point at a time. 4 players were too many to score any points.

[@laploutre9409]

A strange game. The only winning move is not to play.

[@Pants4096]

How about global thermonuclear war?

[@Verbindungsfehle]

0:15 are the Xs "worm" and the Os "book" (=bookworm?) lol

[@creativitybyabhigyan]

Hehe

[@Mqrius]

I like playing blind tic tac toe where we both play in our heads, and for that the corner start is great. The reason it wins so often is that the second player is screwed if they play _anything_ except the center, but it's not so obvious this early on that their _first_ move is a forced move. So they'll often make a mistake. Even if they play their only safe move, the center, they'll often mess up later like you said. Other openings don't have this effect. Center opening is always a draw, and for side opening I can't set up a fork, because their blocks give them 2 in a row forcing me to respond. So corner start wins most often.

[@calinacho7704]

There is exactly one game of tic tac toe. It's called tic tac toe. You learn it in like 2nd grade. There is no one on Earth that plays it differently. There is a single game of tic tac toe in existance.

[@larryrobx]

That game tree @3:43 is a useful strategy visualization, Marc, although it misses an important draw path for O at move 3. From this diagram, I think you could argue there are really only 3 draw games for O in Tic-Tac-Toe: 1. If X corner => Then O center. 2. If X corner => Then O opposite corner. (This is the missing strategy from the diagram.) 3. If X center => Then O corner. All other optimally-played games are force wins for X.

[@NMS127]

X corner, O opposite corner is a win for X if they take a third corner. O blocks, X takes the fourth corner for a fork.

[@larryrobx]

@@NMS127 Ah, I stand corrected. Thank you, NMS (Nat'l Merit Scholar?). Even simpler, then. So, there are really only 2 mirror-image ways for O to draw in Tic-Tac-Toe, both occurring at move #2: 1. If X corner => Then O center. 2. If X center => Then O corner. All other optimally-played games are force wins for X.

[@joe_z]

I was in high school or maybe a college freshman when I discovered that center-corner-opposite corner was a pretty good trap. In order to prevent a loss, O has to make the super-counter-intuitive move of playing on one of the remaining corners. 4 of 6 squares are losing for O, compared to 2 of 6 for corner-center-opposite corner.

[@The_Story_Of_Us]

Those Tic-Tac-Toe sound effects you use hit my brain the same way a hit of gigantic cabbage spliff might. Well done on picking that out! Also nice game analysis btw

[@MercuriusCh]

How can i assume playing against not ideal opponent, if my friends and I solved this game in 7th grade, during a week... But! We created another game back then. We called it "Just crosses". Via brutforce we eventualy considered 7x5 is good enough board. Game for two. On your turn you put a cross on the grid(7x5). The loser is one who can't put a cross. The only restriction is you can't put a cross which form 3-in-row (horizontally, vertically or diagonally) with other crosses on the board.

[@rhvette]

Starting with center is interesting because it's 100% win or draw, no lose conditions. If they respond with an edge position, you can force a block by choosing an adjacent edge, then fork using those last two moves to set up either an edge win or diagonal win for mate in three. If they respond corner, you simply close one of their lines of play with an adjacent corner, forcing them to block the diagonal. Then you block the edge win they set up, which forces them to block your line through the center. This leaves only the orthogonal center line open as a win condition, but with only three spaces left, this is also obvious, which means it will invariably be a draw. But the center move, if played correctly, cannot lose.