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. ruclips.net/video/O1gZxmvs8Oc/видео.html
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.
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.
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.
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
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.
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.
@@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.
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
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.
@@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.
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
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.
*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"
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.
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"
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.
But we've disproved tic-tac-toe exists, and people believe it does. To cancel out the belief, there is actually -1 games of tic tac toe, the anti game: eot cat cit.
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.
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
@@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 . | |
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.
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
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
@@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 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)
Play tic-tac-toe with a child and you will quickly see games far outside these narrow guidelines. Oh you drew a strawberry in that box? Masterful play ma'am, truly inspired.
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
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.
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!
Yeah, it's funny with RUclips 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
@@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~
@@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.
@@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.
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.
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.
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....
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.
@@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.
@@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.
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
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!
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).
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
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.
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.
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
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
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.
@MichaelDarrow-tr1mn … did you not read the reply? Yes, generally x goes first, but it doesn’t have to There’s no hard and fast rule About a pencil and paper game like tic-tac-toe. Depending on personal preference or who you’re playing with, o can also go first
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.
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.
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.
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.
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.
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.
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 😊)
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
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)
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.
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.
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.
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
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.
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
@@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.
@@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.
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
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.
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
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.
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
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 ❌🟦❌ ⭕️🟦❌ ❌⭕️⭕️
@@correcthorsebatterystaple4831 yes! Only the states that are different in every orientation will be overcounted 7 times. Others are only overcounted 3, 1 or 0 times. Therefore we cannot simply divide by 8 :)
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.
The audio-ization of the tic-tac-toe game is godly. I'd love an hour long video that just plays an endless string of random games that we could listen to. Hell, just play every game in existence! I wonder how long that video would take.
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.
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?
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.
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.
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.
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
@@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.
Awesome video. I've been attempting to write, basically, this exact same thing using C# in Unity, to train a convolutional neural network. I haven't finished it yet, but these videos have been an inspiration. Thank you.
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!
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
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
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
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.
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.
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.
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)
![Felix "Unfair" | [Stray Kids : SKZ-PLAYER]](http://i.ytimg.com/vi/Oswujxm2Ag0/mqdefault.jpg)
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. ruclips.net/video/O1gZxmvs8Oc/видео.html
O goes first btw
I wonder what are those 4 times O can win (on 8:50)
POV: You've never seen the movie "War Games"
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.
Are you in the spectrum?
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.
Tis why I refuse to play with my daughter
This game is rigged
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.
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
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.
Next video: Tic-Tac-Toe don't exist
What’s a tic tac toe
@@lorenzorafael4600
x o o
o o x
x x o
Oh, it very much exists. It's just that there are exactly 0 games of it.
@@nanamacapagal8342or a puzzle
Tic-Tac-Toe is the matrix xD
A strange game… the only perfect move is not to play
How about a nice game of chess?
ruclips.net/video/s93KC4AGKnY/видео.html
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.
@@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.
How about a game of global thermonuclear war, instead?
@@zotaninoron3548 Personally, Joshua, I think I'll stick to that game of chess you offered.
seven days later:
*Actually, There Are No Games of Tic-Tac-Toe*
Even the background music is tic-tac-toe. This man is INSANE when it comes to content that's multi skilled.
a very shrewd and nitwitted detail indeed, but it still falls into a music skill category i'm afraid
Great profile pic
@@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.
@@v0id_d3m0n i did get a profile picture. do i deserve your respect and acceptance now? will i ever?
@@v0id_d3m0n wait, you wrote great? not get? oh well, i regret nothing.
I absolutly love the little sounds the tic tac games do when they are moving. Makes them so lively
E
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
I wish there was just a video of all the permutations of the similar games in audio only.
It helps understanding how different 2 games are, without have to pause to analyze. Genius.
And then the weird and ominous background tone continues to play
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
nice pfp :3
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.
@@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.
@@RosieDump :3
@@blasphemer_amonOh don’t worry, that same franchise puts a lot of focus on Roland, Bradamante, and even Charlie himself.
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
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.
That's an interesting way to look at it
What a reference. Yes the calculation in the end stated the only way to win is not to play
I'm so watching this movie in future thank you for the ChatGPT version in 1983
ruclips.net/video/1vmnp7ghGPk/видео.html
The best game is:
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[ ][X][ ]
[ ][ ][ ]
[O][ ][ ]
[ ][X][ ]
[ ][ ][ ]
[O][ ][ ]
[ ][X][ ]
[ ][ ][X]
[O][ ][ ]
[ ][X][ ]
[O][ ][X]
[O][ ][ ]
[X][X][ ]
[O][ ][X]
[O][ ][ ]
[X][X][O]
[O][ ][X]
Mr Campbell I see you. I know you watch these. Mr Campbell stop assigning these as assignments in class please I'm begging
Hahahhshsgsg
Brovhad to turn to RUclips
Mr. Campbell I know you don’t know me but just keep using these there fun 👍
*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"
ai generated?
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.
nice dude
This needs to be pinned.
The former world Go champion is gonna have a word with you
It's not clickbait, watch the whole video - loved it, well done.
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"
He wouldn't be a true programmer if he didn't make the occasional off-by-one error.
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.
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
"The only way not to lose"
But we've disproved tic-tac-toe exists, and people believe it does.
To cancel out the belief, there is actually -1 games of tic tac toe, the anti game: eot cat cit.
1:08 that's so incredibly funny to me.
Your kid is gonna find this in, like, a decade and have a huge revelation as to why he wasn't winning 😂
his dad was a certified tic tac toe researcher
E
Or why he was
@@EEEEEEEE iuqqqqqqk
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.
Thanks! I'm considering doing this 🙂
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
@@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
. | |
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.
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
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
@@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.
@@__christopher__ you're absolutely right
@@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)
Play tic-tac-toe with a child and you will quickly see games far outside these narrow guidelines. Oh you drew a strawberry in that box? Masterful play ma'am, truly inspired.
You have got to be my favorite tic tac tuber on the entire platform right now
E
There are more than 1?
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
Tf they gunna do about it? Cry
@@jnmarshmello2728and sue you for unpaid wages in a decade
@@jnmarshmello2728duh
@@jnmarshmello2728 youre a pleasure at parties aint you?
@eindeed
You really ran that phrase to the ground, it's nowhere near applicable in this instance
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.
Neurodivergent 😭😭😭😭😭😭
@@cristianyahirmejiacruz5495 Is this a problem somehow?
@@cristianyahirmejiacruz5495 grow up
@@Red-yt2dk It's annoyingly euphemistic. It just means "crazy".
@@VestinVestin Rude.
I am losing it at the squeaky sounds for each tic-tac-toe game, it's brilliant!
E
NGL, i was gonna close the vid, but stayed just for those sound effects. lol.
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!
Yeah, it's funny with RUclips 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
Can't wait for the times when there's only 1 game of chess.
There already is, we just haven't found out which one it is yet.
@@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~
@@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.
@@eclipserepeater2466 There are certain openings with forced paths which when both sides play the optimum moves the game always ends with a draw.
@@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.
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.
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.
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....
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.
@@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.
@@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.
bro is creating neural networks
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.
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
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!
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.
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).
@@Trivial_Man Small update: the same guy found a 100% method for Platinum version.
4:50 One of my friends and I figured this out in middle school when we sat and thought about it for a minute after we had like 10 draws in a row.
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
My thoughts exactly. A position that allows for a trap is better than a position that is a guaranteed draw
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.
Bad ending:
You have no friends
There's 0 possible games of Tic Tac Toe :(
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.
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
I love playing Ultimate Tic Tac Toe, but rarely find someone to play it with. 😅
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
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
If X plays corner and you play edge then X wins no matter what, you can't block that.
0:34 sounds like spider dance
no... no it absolutely does not.
dude the little tic-tac-toe sounds gave my brain so much happy chemicals omg, they just sound so silly 🥺
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.
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.
no, x goes first
@MichaelDarrow-tr1mnnot always, I’ve also had games starting with O
@TheFlamingSlayer no, x goes first
@MichaelDarrow-tr1mn … did you not read the reply?
Yes, generally x goes first, but it doesn’t have to
There’s no hard and fast rule About a pencil and paper game like tic-tac-toe.
Depending on personal preference or who you’re playing with, o can also go first
Thank you for making another video with minmax and mentioning that the game is solved!
Thanks for the support!
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.
even if it is drawn, there are different ways to draw.
Yeah the original video, had the assumption that no player plays towards a draw. Glad the author looked at the math again.
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.
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.
I’m in awe…… I never realized there were that many forks set-ups… I’m gonna be invincible now.
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.
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.
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.
there is truly only a single game of tic tac toe, where a player wins, and simultaneously a player loses.
E
@@EEEEEEEE i really disagree with your opinion. how can you be such a shameless creature.
What about ties
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.
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 😊)
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
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)
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.
I think you meant 51947 with a 3/8 fork? 51943 is a win for "O" at 7
@@gacrux-ni7hwyou are totally right. That was my intention but it appears I envisioned the board wrong and wrote the wrong numbers. Thank you.
That divided by 8 code is truly well written
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.
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.
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.
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
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.
Yes, checkers was announced solved by a paper published in September 2007.
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
@@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.
@@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.
@@skarutsthe good versions of minesweeper generate a new board if your first move is a bad one - windows vista minesweeper was great
There are 0 games of tic tac toe
There are -1 games of tic tac toe
There are games of tic tac toe
There are games
There are people who've played these games of tic-tac-toe before.
All other games at least have 1 “blunder”
Edit:the blunder is playing a move
Edit:the blunder is playing a move
Edit:the blunder is playing a move
Edit:the blunder is playing a move
Edit:the blunder is playing a move
If you'd like slightly more complex than Tic-Tac-Toe but a lot deeper IMHO, I recommend Teeko.
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!
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
Rock Paper Scissors > Tic-Tac-Toe
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
Connect Four > Rock Paper Scissors
Tic-Tac-Toe > Connect Four
You play gun. It always wins.
@@cidlunius1076Exactly!
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.
We are so back
Next video: *"Maybe, actually there are no games of Tic Tac Toe"*
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
There are exactly 2 games of tic-tac-toe, one where I win and one where I don't
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.
Center edge corner isn't an "opening". It's just O making a blunder with their first move.
13749 and 12749 are my favorite. You automatically win if opponent goes in an adjacent edge or corner second move
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
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
❌🟦❌
⭕️🟦❌
❌⭕️⭕️
I love that the perfect player ties you showed, all end in a disappointed sounding progression. I love the way you represented the game sounds!
Finally, the vid we’ve been waiting for
Oh interesting! From my experience, Tic-Tac-Toe is only losable by making a mistake, which corresponds with your data.
You cannot simply divide by 8 to account for symmetries. You can use the polya enumeration theorem for the dihedral group of irder 8 though
Because game states can be both reflectionally and rotationally symmetrical in more than one way?
@@correcthorsebatterystaple4831 yes! Only the states that are different in every orientation will be overcounted 7 times. Others are only overcounted 3, 1 or 0 times. Therefore we cannot simply divide by 8 :)
Now do one of these, but with Ultimate Tic Tac Toe!
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
2:00: It's the other way around. A competent player would make one of these two moves and avoid the other four.
Both of those would lead to x forking them next turn though?
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.
There only one game of tic-tac-toe: a draw
The audio-ization of the tic-tac-toe game is godly. I'd love an hour long video that just plays an endless string of random games that we could listen to. Hell, just play every game in existence! I wonder how long that video would take.
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.
Agreed! Came to the comments to point this out, but you were here 45 minutes earlier. 😀
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?
What a sequel!
I'd like to think that this is the exact process that the computer in War Games goes through to reach this conclusion
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.
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.
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.
@@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.
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
@@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.
Awesome video. I've been attempting to write, basically, this exact same thing using C# in Unity, to train a convolutional neural network. I haven't finished it yet, but these videos have been an inspiration. Thank you.
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!
en.wikipedia.org/wiki/Shannon_number
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
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
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
The middle square?! The middle square!!!! What kind if charleaton begins tic-tac-toe with the middle?!
0:15 are the Xs "worm" and the Os "book" (=bookworm?) lol
Hehe
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.
Doesn't that mean there are no games of tic tac toe?
"When the only winning move is not to play"
- You've Been Trolled, Antony C
2:07 yeah well that looks like something.
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.
wurp wurp wur barp bwurp bop bwooooow
werb wurp bwomp bwerp werp bur wuaoow
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.
3d tictactoe is a win for the first player after they play in the center
My favourite part of tic tac toe is agreeing to the fact it's a draw before playing and not playing
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.
IT FEELS SO GOOD TO HAVE MY CONCERNS BE LISTENED TO. SILLY DRAKE!
A strange game.
The only winning move is not to play.
How about global thermonuclear war?
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)