Is it Possible to Always Win at Connect 4?

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Is there a strategy that could win the game Connect 4 every time? Let me show you how this question leads to a bunch of surprising patterns, unsolved mysteries, and connections to other games like Tic-Tac-Toe and Chess! (See below for timestamps of different subtopics)
0:00 - Introduction
1:06 - Basic Rules and Human Strategies of Connect 4
4:39 - Zermelo's Theorem about Solvable Games
5:58 - Tic-Tac-Toe, Tic-Tac-Two, and Adding "Gravity"
9:22 - The Solvability of Chess
10:57 - Strategy-Stealing Techniques
13:46 - Why "Connect 3" Wouldn't Be Fun
15:55 - Connect 4 on Different Board Sizes
18:42 - The Mysterious Landscape of Known Solutions
21:57 - How The First Move Can Determine Everything
23:54 - Philosophies about Humans and Computers
26:54 - Outroduction
Thanks for watching! I might analyze more games in future episodes from time to time, so let me know if there are any games you personally enjoy and/or would like to see me cover (I don't play video games much so I'm more likely to check out the math within board games or card games). A few games/puzzles I’ve written brainstorm notes about which might be parts of future episodes include: Tic-Tac-Toe, Checkers, Chess, Magic The Gathering, Poker, Sudoku, Othello / Reversi, Two Not Touch (a.k.a. Star Battle), Rock-Paper-Scissors (yes it actually has "strategy" haha), and some board games I invented myself.
Here's a website page from the computer scientist John Tromp that I quoted some data from in this episode: tromp.github.io/c4/c4.html
Slight correction about Zermelo's theorem: there's one extra restriction about which games it describes, which is that they must be "finite" games, as opposed to games that could continue for infinitely long.
Make sure you're also subscribed to my @Domotro channel for bonus content! And if you need to catch up on any Combo Class episodes, I've now made playlists of each whole "Grade" in chronological order: www.youtube.com/@ComboClass/p...
Special thanks to all of my supporters on Patreon. Supporting the show not only helps me keep improving my content, but also lets me avoid putting any product placements in episodes. Brands (not the company that makes Connect 4 haha) have offered me money for me to advertise them during an episode on this channel but I want to avoid that unless/until necessary, so thank you to all of these supporters who keep our Grade -2 episodes from having any product placements in them!
Evan Clark, Max, George Carozzi, Peter Offutt, Tybie Fitzhugh, Henry Spencer, Mitch Harding, YbabFlow, Joseph Rissler, Plenty W, Quinn Moyer, Julius 420, Philip Rogers, Ilmori Fajt, Brandon, August Taub, Ira Sanborn, Matthew Chudleigh, Cornelis Van Der Bent, Craig Butz, Mark S, Thorbjorn M H, Mathias Ermatinger, Edward Clarke, and Christopher Masto, Joshua S, Joost Doesberg, Adam, Chris Reisenbichler, Stan Seibert, Izeck, Beugul, OmegaRogue, Florian, William Hawkes, Michael Friemann, Claudio Fanelli, The Green Way, Julian Zassenhaus, Bailey Douglass, Jan Bosenberg, Brooks Boutwell, David Irvine, qe, George Sharabidze, Jack Dwyer, Fredrik, and Dave Brondsema!
If you want to help support this channel (and get your name on that list) and get some bonus content, check out the Patreon here: / comboclass
If you want to mail me anything (such as any clocks/dice/etc. that you'd like to see in the background of Grade -2), here's my private mailbox address (not my home address). If you're going to send anything, please watch this short video first: • You Can Now Mail Me Th...
Domotro
1442 A Walnut Street, Box # 401
Berkeley, CA 94709
Combo Class Discord server: / discord
Subreddit: / comboclass
If you want to try to help with Combo Class in some way, or collaborate in some form, reach out at combouniversity(at)gmail(dot)com
In case anybody searches any of these terms to learn about them, some topics mentioned in this video include: the mathematics of game theory, Zermelo’s theorem about two-person games without randomization and with perfect information, Connect 4 / Connect Four strategy and solvability, Connect 4 on various different sizes of board, solvability of chess, tic-tac-toe and strategy-stealing arguments, philosophy of computers vs. humans remembering data, fire, squirrels, and more!
This episode was directed/edited/soundtracked by me (Domotro) and was filmed by Carlo Trappenberg.
Disclaimer: Do NOT copy any dangerous-seeming actions involving fire, tools, or other chaotic activities you may see in Combo Class episodes. This is an episode of a show that is purely meant to provide entertainment and education. Also, do not copy the squirrel-feeding (my squirrels have a rare circumstance) without doing your own research first.

Опубликовано:

20 май 2024

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Комментарии : 522

@issholland 6 месяцев назад

Our ancestors fought and died for me to watch a guy in his backyard explain the math around connect four while I'm in my pajamas.

@MarloTheBlueberry 6 месяцев назад

Basically, yes

@ComboClass 6 месяцев назад

I think some ancient ancestors might actually understand my classroom’s vibe more than some modern people haha

@MarloTheBlueberry 6 месяцев назад

@ComboClass True, you do teaching pretty well

@iantullie 6 месяцев назад

Worth it

@issholland 6 месяцев назад

@@iantullie true, I'm actually in college right now learning programming to make games. Dude is giving me a relationship with numbers I've never had before

@makzs9626 6 месяцев назад

This looks so… whimsical? The squirrel, the clocks, the voice tone, excessive hand gestures, the sort of fall “aesthetic”, the fire, things just falling apart, pumpkins? Squash? And the random dragonfruit, it all just fits.

@CODDE117 6 месяцев назад

The squirrels really sold me here

@littlered6340 6 месяцев назад

RIGHT First I was like, why dragon fruit? Then I was like, wow squirrel Now I'm like, this all fits; 10/10 video, do recommend.

@matthewmitchell3457 6 месяцев назад

It's got some serious "mad scientist" energy.

@samamies88 6 месяцев назад

@@matthewmitchell3457i got heavy mad hatter vibe... all he needs is tea, hat and wacky guests for tea party - the chaos and scenery is already present

@TymexComputing 6 месяцев назад

Yeah - i didnt like it in the beginning, i especially dont like the GAFAM RU-vid last syllable accents... instead of standard sentence but i take it as some shakespeare' drama contrast.

@tylerowens 6 месяцев назад

I would legit absolutely love to see the game you made with your friend

@julianschondorf304 6 месяцев назад

Yeah it sounds so cool!!

@ChaosLierLen 6 месяцев назад

Agreed!

@patchoparadise8730 6 месяцев назад

kickstarter?

@themixedmaster 6 месяцев назад

agreed

@emilyrln 6 месяцев назад

Same!!

@Randomusername4124 6 месяцев назад

I've been researching social deduction games (like the party game mafia/one night werewolf, or the infamous among us), and the game theory is actually really interesting. It might not exactly fit the more mathematical (as opposed to psychological aspect of game theory) lean this channel has, but it might be worth a mention/a bit of discussion on a follow up video.

@ComboClass 6 месяцев назад

Yeah the mafia/werewolf games are cool. I enjoy psychology as well

@patchoparadise8730 6 месяцев назад

why is among us infamous D:

@prcr364 6 месяцев назад

⁠overexposure

@nindroid2042 6 месяцев назад

look up the game 'blood on the clocktower'. its like a combination of mafia and werewolf. i think u'd love learing about it.

@jakethejax 6 месяцев назад

Bruh I watch so much Town of Salem games over on PipeTrons channel, great social deduction and every game goes differently.

@rlstine4982 5 месяцев назад

The fact that you manage to clearly deliver your text absolutely fluently all while maintaining this mad professor tone is quite an impressive acting and pedagogical feat. Would love a video about chess.

@ComboClass 6 месяцев назад

Thanks for watching! I hope you all watch the whole thing, but in case it helps, here are timestamps of some different subtopics: 0:00 - Intro 1:06 - The Basic Rules of Connect 4 1:59 - Human Strategies and Double Traps in Connect 4 4:39 - Zermelo's Theorem about Solvable Games 5:58 - Tic-Tac-Toe, Tic-Tac-Two, and Adding "Gravity" 9:22 - The Solvability of Chess 10:57 - Strategy-Stealing Techniques 13:46 - Why "Connect 3" Wouldn't Be Fun 15:55 - Connect 4 on Smaller Board Sizes 18:42 - The Mysterious Landscape of Known Solutions 21:57 - How The First Move Can Determine Everything 24:22 - Philosophies about Humans and Computers 26:54 - Outro .... for more bonus content, make sure you're also tuned in to my @Domotro channel, and check this video description for more cool links and info. Love you all :)

@MarloTheBlueberry 6 месяцев назад

So it went from children's games to philosophy... of course it did.

@815TypeSirius 6 месяцев назад

Now try and solve hyper tictactoe.... wish I remembered the actual name, its a trip.

@Kwauhn. 6 месяцев назад

I watched the whole thing, but I love when creators include chapter timestamps. Good man.

@faland0069 6 месяцев назад

what about Connect 5?

@plaxy100 6 месяцев назад

Must be a very kind person. Squirrels are notoriously afraid of everything and the fact that trust you says a lot.

@davidklein8608 6 месяцев назад

Have you heard of "order and chaos"? It is a variation of a x number in a row to win where one player is trying to make either player have x number in a row (order) while the other player is trying to make both players not have x number in a row (chaos). There is no tie possible.

@AJLord 6 месяцев назад

Turning a traditional win into one player's win and a traditional tie into the other player's win, that's clever!

@HappyBeezerStudios 6 месяцев назад

Reminds me of that game where you have a triangle of matches and the players take turn removing matches, either a single one, or a complete row. the loser is one the that has to take the last match.

@TymexComputing 6 месяцев назад

What about repetitions??? oh ok - the board is not infinite

@ShandoGuardian 6 месяцев назад

This guy definitely has heard of chaos

@litigioussociety4249 6 месяцев назад

The most interesting games in my opinion are those like Risk or 10,000 point, dice games where players who are behind can still win, if they play a more risky strategy, or are forced to increase risk as the game nears the end. The worst games are those that are more or less luck based, and where the final fate of at least one player is essentially prederermined long before the game ends. That's why Monopoly is one of the worst games of all time, because after going around the board twice, there's usually a huge gap between the winning and losing players.

@ferusskywalker9167 6 месяцев назад

If you think Monopoly is one of the worst, wait till you learn about Candy Land and Chutes and Ladders

@thatscrub8351 6 месяцев назад

I will never like risk after an incident where someone had one piece of land left and by shear luck of the dice became un-killable and managed to win.

@litigioussociety4249 6 месяцев назад

@@ferusskywalker9167 Those are clearly luck, but the outcome can switch at any moment. No one is really more likely to win in those games, because you can be right near the end of Candy Land and draw Plumpy, or end up on the worst chute right before winning. In contrast, after all the properties are bought in Monopoly, the players with no sets can't win.

@JR13751 6 месяцев назад

@@ferusskywalker9167 Snakes and ladders is the worst game. Nothing you do matters and everything is luck based.

@ferusskywalker9167 6 месяцев назад

@@JR13751 candy land is worse because the outcome of the game is decided as soon as you shuffle the deck.

@jblen 6 месяцев назад

This set is so unhinged but so beautiful. I've never seen this channel before but I know this ia going to be hella interesting.

@sorin_markov 6 месяцев назад

Member of the professional Connect Four community here. AMA Also, yes there are people who have *essentially* memorized all strategies to win as player 1, although there's more complexity in that statement than most would first think, so we have some rules to make games more interesting between those kinds of players.

@ComboClass 6 месяцев назад

Cool! Can you clarify about what you mean by "essentially" (in a simplified way if necessary) there? Like, is it that they have memorized all of the most common board states but would have to make educated guesses in certain rarer situations, or what?

@sorin_markov 6 месяцев назад

@@ComboClass It is partially that. Usually a player will memorize early openings and trickier lines where it's very hard to intuit what the correct move is, then rely on good play and game knowledge to carry them through the rest of the situations. Also, most players only memorize one "branch" of the decision tree. ie if you play a specific opening and there are 4 correct moves that I can play that are winning, I'll only bother memorizing the position after 1 of those moves and just use that line every time. Why bother memorizing all 4 lines when I can choose to use the same one every time? So one of the things we do to increase the skill ceiling is after so many games of players trading games because they went first, we make them play different lines than they usually do. That way, players have to either memorize a *lot* more lines or they have to rely on having really good game knowledge. There are maybe 10 people I know personally (there are others out there I'm sure) who will win 99% of their P1 games playing the same lines, but only 1 who actually knows just about every single winning position and can play every single one of those winning lines. That dude's insane and will play things that make me, with years of experience, go "nah there's no way that's winning" and he wins anyway and I look it up later and he played perfectly.

@icycloud6823 6 месяцев назад

@@ComboClass Connect 4 is simple enough that you don't need to memorize the full tree of moves used to win. But instead only need to understand key strategies/patterns. So it's possible that if a player understands the strategy of connect 4 enough, that they could play a 'perfect game' without having necessarily memorized the full tree of moves to win. Chess is similar to an extent. Even the leading chess engine, Stockfish, that used to 'mostly' brute force solve positions has adapted to using a neural network, which essentially just learns the different sort of patterns of moves and strategies are better. There are other engines that are almost entirely based on neural networks that are on similar levels to stockfish. Though for chess, the patterns and strategy would get so complex that I doubt a human could ever memorize/learn all of it, even if it's easier than trying to memorize the entire tree of solutions.

@TymexComputing 6 месяцев назад

@@ComboClass 3 replies but i only see one reply with a question - probably this question is also an answer :)

@woolis697 5 месяцев назад

⁠⁠@@ComboClassI used to be apart of the the professional community despite not being one of the best players, so I think I can answer this in a digestible manner. Much like in chess there are very obviously good moves and very obviously bad moves for players that understand the positioning of the game. Because of this, you actually don’t have to memorize that many board states but rather the concepts that make a “good move” a good move. Much of the higher level revolves around player 2 playing off the theoretically “perfect” strategy to try and force player 1 into a position they aren’t familiar with and thus, getting them to mess up . A very simple example of this is the 4,3,6 opening. Many people just getting into connect 4 understand that the middle is extremely important, so when player 2 sacrifices the middle by playing 3, lots of players would assume that the next good move would be to take even more center control (4,3,4). This is actually a draw scenario though. For some more complex reasons I won’t explain here, playing in column 6 is actually the only advantageous response for player 1 (4,3,6). This is one of many different scenarios where player 2 can set up a deceptive situation. The players that have “essentially” every situation memorized means that they know these deception openings, all their variations, and why they are the way they are. This requires an insane understanding of the game, and tons of studying.

@jaxsolaris1177 6 месяцев назад

I would love more on Chess! You make the most entertaining mathematics videos I’ve ever seen

@MarloTheBlueberry 6 месяцев назад

I agree! He is doing so well. He is also massively underrated

@tristantheoofer2 6 месяцев назад

@@MarloTheBlueberry fr he is definitely. i first saw his channel when his tetration video fucking blew up lol. i think i caught it really early too and he was at only a few thousand subs (and exploding)

@TymexComputing 6 месяцев назад

The antichess has been solved - it has a 120 2x ply Watkins solution after 1 e3. But... the top players play at most 10 moves of the longest opening and later its complete madness and innovation :)

@MoonJellyGames 6 месяцев назад

This was a lot of fun. I dig your brand of chaos-- falling junk, fire, and the occasional squirrel-- all while barely skipping a beat. I've worked ik school-aged childcare for a long time, and Connect-4 has always been one of my favourites to play with the kids. It's quick, simple, and strategic enough that it gets my brain going a bit. Often, if I have a winning move, I'll let my opponent choose where I go next, but it's good to let kids lose sometimes too. Being a good "loser" is an important social skill. I remember reading about Connect-4 and how it's (unsurprisingly) solved, but I couldn't remember how complex it actually is. I think the best abstract strategy games are the ones that are too complex for a human brain to truly optimize, and it seems like Connect-4 might fit that category. I love to see you do a deep dive into my favourite game, Hive. Or another one that's newer to me (but may someday take Hive's throne), Homeworlds (from the Pyramid Arcade).

@conando025 6 месяцев назад

It is refreshing to see this topic in a rather relaxed manor after having spent an unreasonable amount of time sifting through winning ways, which while being totally awesome is also suffocatingly dense

@tomkerruish2982 10 дней назад

Have you watched Owen Maitzen's video on Hackenbush from #SoME2?

@gravitrax3287 6 месяцев назад

That's why math is also a game😂 A beautiful game of art and completly logical❤

@landsgevaer 6 месяцев назад

Actually..., you can consider math a single-player game. Applying logical deductive rules to previous theorems (or axioms) to generate new proved theorems are the moves in this game, and if you are able to reach the statement that you wanted to prove (or its negation) then you win or lose the game. It is a way to generate automatic proofs. en.wikipedia.org/wiki/Automated_theorem_proving

@gravitrax3287 6 месяцев назад

@@landsgevaer i know, that's exactly what I meant

@whannabi 6 месяцев назад

@@gravitrax3287they're just agreeing with you and expanding more eloquently I guess

@TymexComputing 6 месяцев назад

@@whannabi They only missed some theorems might be unsolvable (or need some other axioms if not linearly related) so its a n imperfect information game or some other Riemann Zeta related?

@soninhodev7851 6 месяцев назад

i absolutely love the vibe of the combo class, i feel right at home, especially with the squirrels and the cats. they are so cute, i love their inclusion in more recent videos!

@kentslocum 5 месяцев назад

I love how the set just randomly falls apart during the video; it perfectly reflects my brain falling apart as I try to wrap my mind around the theory of Connect Four.

@FireStormOOO_ 6 месяцев назад

How about nested tick-tac-toe? You get to mark the cell on the top level board only by winning the board nested in the cell, you play all nine nested boards at the same time (e.g. each turn choose 1 to make a mark in). Substantially more tricky. Could in theory recurse deeper than that and keep nesting boards for another interesting notion of how to "expand" the board.

@rixaxeno7167 6 месяцев назад

Haven't seen one of those, what happens when one of the nested boards is a tie?

@jofx4051 6 месяцев назад

I do sure it remains unclaimed .. the thing is 3X3 always ended on draw

@didntwantmyrealnameanymore 6 месяцев назад

couldn't you as the second player always move in the same board as the first player in a way that would draw that board, and easily make a draw?

@Lily-white 6 месяцев назад

I recall it being played on a weird reversal way, whatever tile you place on one board is the board that your opponent will play on, eg you play bottom left tile of the mid right board then they will play the bottom right board This forces much more strategy

@HappyBeezerStudios 6 месяцев назад

@@jofx4051 only of both players play perfectly.

@ShapesWithoutColors 6 месяцев назад

There are two key factors to an always win strategy for connect 4. The set up, and the block. You always try to set up a trap, and only deviate from that strategy when you have to block. It's still complicated, but it's not as complicated as the computer trying to figure it out.

@woolis697 5 месяцев назад

The game is actually as complicated as the computer makes it. I have played competitive connect 4 on and off for about 2 years now, and the game is not as simple as traps and blocking. A lot of the game comes down to obscure positioning for a win on a board fill that many would consider (luck). Playing against “trap” players is actually ridiculously easy because they always have a clear strategy they are trying to go for to win. You just block it ahead of time and set up your board fill win.

@murphthegangster 6 месяцев назад

I just found your channel the other day and it’s so awesome, my style of learning and I love your energy

@Creepyslandofdreams 6 месяцев назад

One of the machinations of my pals and I is Big Tac Toe. Played on a 4 by 4 board Players take turns placing X and Os If you have 3 in a row, place a line through them and score a point. You can not place lines, and thus score, through spaces that already have 3 lines through them. A player may use their turn to expand the board to 5 by 5, choosing a corner to expand on. This can only happen once When the board is full the player with the most points wins. Lemme know how u feel bout it if you play, It has a suprising amount of strategy. The 3 line limitation can be dropped to 2 to make it brutal, but that tends to make players think forever. It has a temporal element with the line limit, which makes it almost 2.5 d

@eroticbearvideos 6 месяцев назад

and me*

@ErikHalboth 6 месяцев назад

I had a math professor in college who studied game theory. He gave a colloquium about how adding wild cards to poker changes the odds of different hands in the game. Very interesting stuff. It would be cool to see how Domotro would present such a topic.

@Muhahahahaz 6 месяцев назад

I just watched a video about this the other day! If you add a single joker (wild card), then three of a kind actually becomes more likely than 2 pair. (The other hands stay in the same order, though the exact odds do change) But if you try to change the rules and rank the hands in order of their probability, then it leads to a paradox. Due to hands with one pair + joker When three of a kind was ranked higher, you would just make the joker match the pair to form three of a kind. But if 2 pair is ranked higher, then you make the joker match one of the other cards to make 2 pair The paradox lies in the fact that by switching these joker hands from being three of a kind to 2 pair, you end up adding a bunch more combos for 2 pair, which suddenly makes them more likely than three of a kind In other words, there’s no reasonable way to rank the hands by probability, because the rank directly affects what the joker becomes, so the definition of rank becomes a self referential contradiction (Hard to explain in words, but hopefully you see what I’m getting at. The video did a better job lol)

@HappyBeezerStudios 6 месяцев назад

How would Poker do if the ace can also work as 1, like in black jack? you could have [ace, 2 ,3 ,4, 5] straights.

@josephmozena7640 6 месяцев назад

@@HappyBeezerStudios That's already a rule. A2345 is a valid straight.

@3eve0n 5 месяцев назад

@@Muhahahahaz I would say a possible solution to that would be to have jokers able to make either 2 pair or 3 of a kind, and the 2 tie, with of course the tie being broken by card values as normal. so for example, 2 pair kings over 10s would beat 3 10s which would beat 2 pair 10s over 8s. This would mean you only get 3 of a kind from pair + joker hands when the pair is also your high card, overall making 2 pairs more common again, which makes sense because 3 aces beats any possible 2 pair.

@yllim3170 6 месяцев назад

I think it would be interesting to see a video like this about Uno I've already learned that each color card has 2 copies, aside from the 0 card, and started to use this to count cards. The main thing i learned is that, for you to switch colors without a wild card you'd have, in the whole game, assuming the color doesn't change, two chances to do so for every unique card of the color you wanted to switch to that you have in your hand. I wonder what other types of strategies can be formed

@HappyBeezerStudios 6 месяцев назад

So I guess counting cards less like in black jack were you count the value and instead for the colors? counting in black jack aims for the high value cards to increase the chance to get 20 (or 21) with two cards. The numbers in uno have no intrinsic value outside the limitation that you can only put them on a card with the same number.

@romasissues 6 месяцев назад

My favorite channel on the entirety of the internet.

@ComboClass 6 месяцев назад

Thanks! Happy to hear :)

@ethanmiller5105 6 месяцев назад

I would honestly love to see any content you make about board or card games. Thanks for the fun video!

@3eve0n 5 месяцев назад

Have you heard of Ultimate Tic-Tac-Toe? It's a version of Tic-Tac-Toe where each space is its own Tic-Tac-Toe board. You claim the space as yours by winning the mini-board, with draws not counting for either player. The big twist is that you can only play in the mini-board that corresponds to the space the other player played in last. So if the 1st player started in the middle space of the middle board, the 2nd player would then have to play in the middle board somewhere, let's say they play in the middle-top space in that board, the 1st player would then have to play in the middle-top board. This actually creates a dynamic quite similar to connect 4, where every move you make influences your opponents options. And, of course, it still has the 3 conditions for Zermelo's theorem, so it's solvable, but I don't know if it's been solved yet. Would love to see a video on it.

@MarloTheBlueberry 6 месяцев назад

I love your work! Keep up the great content!

@krazykilper 6 месяцев назад

I love your content! Keep up the great work!

@kristyandesouza5980 5 месяцев назад

I'm glad you made a video about this, i was actually wondering about this subject for a long time

@craftydoeseverything9718 6 месяцев назад

Thank you sooooo much for making this video, I've been trying to train an AI to play Connect 4 for the past 6 months just about and this has provided so much insight. Thank you so much.

@woolis697 5 месяцев назад

I have played connect 4 competitively on and off for about 2 years and would be happy to help you on the complex concepts of the game. Ideally if you just need a model to go off of, look up “Connect 4 Solver” on google, the ai already exists.

@stevenmorrison9052 6 месяцев назад

I clicked for connect 4, but I subbed for the theme. You have a very high effort and interesting way of presenting, and it's also concise and entertaining. I think i'd enjoy watching you present anything in a backyard, with your set falling apart around you.

@captainkyle1158 6 месяцев назад

the ambiance, the topic, the tone, it's all perfect. I'm hooked, and will be watching all of your videos, thank you for this, I love it

@Donutdunot 6 месяцев назад

best math youtube channel which makes learning actually fun

@pavonian7531 6 месяцев назад

I wonder whether either player can force a win on an infinity by infinity board. Obviously such a game could never 'end in a draw', but is there a perfect strategy that either player can use to just keep the infinite pile of pieces growing forever, or some crazy long sequence of moves where someone forces a win by turn 1,000,000. I'm almost not sure which one of those would be weirder? Or the weirdest option option, a game that one player is guaranteed to win after an ordinal number of moves (like what happens in some infinite chess games). e.g. One player places a piece at the 'origin', then their opponent places a piece an arbitrary distance away, then there's some sequence of moves the first player can use to push the two ever growing piles of pieces closer together and win when they meet. The second player can prolong the game as much as they want by placing the second piece as far away as they want, but since infinity isn't a number they have to place it some arbitrarily large finite distance away, and that decided how long the game will go until the first player wins.

@cullenlatham2366 5 месяцев назад

I have tried thinking this over multiple ways now. In its simplest form, the game would progress forever infinitely by expanding outward in the single bottom row with a pattern of (xo.ox.xo.ox.xo), with each letter representing a different player and expanding outward on either side from the first central move. When adding in verticality, the pattern has its first potential win state in row 4 from the bottom, but i cant fully wrap my head around just how complex and long lasting the pattern is. If the winning pattern does exist in this step, it is one player 2 cant stop, only delay (unless player 1 missed the move to start expanding upward with aggression, allowing player 2 to swap roles). Considering how the simplest form is an infinite loop and that the wins of connect 4 are defined by the limitations of the board creating unavoidable undesirable plays, adding infinity to the mix would logically only give players the option to "skip" their turn if they would otherwise be forced to make a bad move by playing their piece away from the center of action, likely never to be seen again. Heck, infinite possibilities means infinite ways to prevent the game from ending. Regardless of how i think about the question, i notice a pattern of momentum emerge. If a pattern exists in infinity, then an end to the pattern likely does not. If a win exists, it is dependent on the flow of momentum and who is in control of it when the board has reached a complicated enough state for win conditions to appear. My brain has started processing the problem as sand flowing down a hill. As the board gets taller, the "sand" at the top rolls down to the sides to create more space to work with. Any time a win is visible, instead of making the bad move that would allow it, the sand flows down as far as it can; no space in the active play area? then it falls to the side and makes the play area wider. It takes defined walls to stop the sand from falling to make a wider base.

@krzychxyz8358 5 месяцев назад

It's a theoretical draw according to "Advances in Computer Games. ACG 2011" and you can pay 30€ to read the chapter about this game and get to know why that is exactly.

@littlered6340 6 месяцев назад

Wow. This is the second video of this guy's I've seen. The first one was a long while back and then I started this and was like "oh hey, this guy!" I did not expect this to be so good. This surely took a long time to film. 😂 I'm only halfway through and I just subscribed. Also, my mind is blown that C4 is TTT + gravity (and some other stuff.)

@MarloTheBlueberry 6 месяцев назад

I really love your channel though. You make learning so fun

@louismyers8845 6 месяцев назад

This was a wonderfully interesting and entertaining video to watch - you've earned my subscription!

@sethparham5669 6 месяцев назад

What happens when you change the topological "space" of the game? Like connect 4 on a cylinder. There would no longer be a center column.

@ComboClass 6 месяцев назад

I think another viewer mentioned a game like that (like cylindrical connect 4) although I haven’t investigated it yet myself! Sounds intriguingly symmetrical

@MoonJellyGames 6 месяцев назад

Brilliant! I have no idea what the implications of this might be, but I love the sound of it.

@HappyBeezerStudios 6 месяцев назад

I was thinking on an infinite board.

@woolis697 5 месяцев назад

I love the idea of this, I may actually look into it myself.

@BlaBlaBlaInDaHouse 6 месяцев назад

What a fantastic channel, thank you for your efforts! Very interesting content

@QQueTV 6 месяцев назад

I absolutely love the very important pause to feed a squirrel

@eddie992 5 месяцев назад

Loved the vid man keep it up

@MilesIsReal 6 месяцев назад

I’ve been playing connect 4 the past few months so I was surprised when I saw this in my recommended. Will watch soon!

@Tomahaka 6 месяцев назад

Loving the content! More game stuff please! It would be interesting to see connect 5 or tic tac toe on a larger/infinite grid or tic tac toe with 4(aka connect 4 sans gravity)

@eek6764 5 месяцев назад

My college roommate and I played a lot (like a lot) of Connect 4, and we developed a 16 move opening pattern that we would always play. Later, we looked up this up and found out that we were one move off from a perfect opening. Love this video

@lucasmetzger1154 6 месяцев назад

First time ever seeing one of your videos and I just have so many questions, about so many things 🤣 already have like 7 more videos open in new tabs, everything sounds so interesting

@imonmahbub9515 6 месяцев назад

The background is so unique. Im hooked to this channel!!

@tensorride 6 месяцев назад

Surprisingly good video! It's clear that you had fun filming. But I would have liked to learn a little more about the underlying strategies. You always mentioned the results, but I would have been interested, at least superficially, in how one gets to these results (simply brute force, clever moves, abstractions, ...).

@ey3187 6 месяцев назад

in chess the importance of drawn endgames seems indicative that if ever solved it follows the third option in zermelos theorom. but most pro players tend to operate based off psychological edge rather than engine perfection. idk. this video was great, subscribed and liked.

@X3MgamePlays 6 месяцев назад

Came here for the squirrel. Loving that squirrel. And the squirrel loves its nuts. I will certainly come back for the squirrel. But also for the cat. That is a very lovable cat. Shared this video on a board game forum. So..... how about you show the game that you made with your friend? *** As for complexity of games. I always consider the possible (and sensible) moves per turn. Then see how it grows the first few rounds. (For RTS games, this is called practical balance, and has to end up in a tie. "The player with the most mistakes should loose", kind of game. That is the goal of the game designers. Tic-Tac-Toe has 9, 8, 7, 6 etc. Which gives 9! as a maximum possible moves. With possible being "possible". Since an outcome can come earlier. And if you indeed consider the only sensible ones. The game obviously has less sensible moves. Chess starts with 20 for white. Depending on the first move and the opponents move, white might be having a range of moves in the second turn. Around 20 still, but this can decline or increase rapidly, depending on what pieces are free and still on the board. A queen can have 28 moves at most in 1 turn. Personally, I like the 7x7 version of 4 in a row. Simply due to the fact that it can end up in a tie. But it is much more complicated than tic-tac-toe. And thus, more mistakes can be made. I say, this is the most fair for human players. Still, I like the original 7x6 version for the fact that the second player is forced to play better than the younger player who goes first. And can only win at the '41th' move if it is just as smart.

@devind585 6 месяцев назад

I feel like the patterns definitely repeat as you go up. The 2/1 alternating is probably just changing even and odd number of moves to depict who gets to go last, and the first two columns should always stay ties because changing height won't change the gridlock from not having the horizontal dimension for variability in setups.

@ultimatedbz2 6 месяцев назад

Would love to see future game theory vids and the game you made with a friend!

@di1848 5 месяцев назад

I hope you do a tic-tac-toe video, I did a research project on it in school and I found that the first player usually forces the tie by using the most common move of the center but if they find the best move (any corner) the 2nd player ruins it by playing the same center move which is the only move the 2nd player can make to save the game.

@een_39 6 месяцев назад

Fantastic video! Some other game suggestions of mine: Dots and Boxes or the similar version with triangles, sudokus, chopsticks I think it’s called (the one with the fingers), picross/nonogram puzzles, or boggle if you are feeling a bit wordy. Loved the dive into game theory, super interesting!

@ComboClass 6 месяцев назад

Thanks, and I love all of those games you mentioned, so they are definitely possibilities for future episodes :)

@didntwantmyrealnameanymore 6 месяцев назад

i feel like chopsticks has to be a forced draw. when i played it in school, once everyone got good most games ended in loops and metas started forming

@ShadowKestrel 6 месяцев назад

one variant of connect 4 we came up with at my old school, which seemed non-trivial as far as our 16-year-old minds could tell, had each player place 2 counters of their colour per turn, as opposed to 1. However, to avoid a similar situation to 'connect 3', creating a 2x2 square of all your own colour is forbidden. I wonder where that variant lies in Zermelo's theorem

@tylerowens 6 месяцев назад

Also I'd love to see a video on my favorite classic board game: 9 Men's Morris. It is a solved game, of the perfect play leads to a draw type, but I haven't looked into it much further than that.

@jmugwel 5 месяцев назад

With this epic music, strange scene and passion this man can talk about any theme and I will listen to it.

@fearstreak7462 6 месяцев назад

giving me mythbusters vibes. very satisfying personality Edit: also, just really nice background music. maybe this wasn't intentionally "halloween themed (??)" but i really noticed it at 23:00 when i'm just fully invested in your enthusiasm for this topic and am personally reciprocating and appreciating that, in the stakes of a "perfect information, perfect execution" strategy of connect 4 - which satisfies the theorem Edit2: 24:39 i actually chuckled out loud here. when i clicked on this video, i was perplexed by the thumbnail and title, tictac toe and chess. i didn't know there was a name/theorem to accurately describe these perfect information games, but i suppose that both of them and connect 4 could be on the same spectrum, but what makes connect 4 a comparable, as you visually implied. Half way into this video, i googled "games that follow zermelo's theorem" and to my surprisewikipedia and such top results don't even mention connect 4 as an example, just tic tac toe and chess. You giving us the gist of even the programing laying out the game tree and showcasing the winning paths and trying to identify an instinctual pattern showcases so much; your understanding of where you want to bring your narrative in conclusion to this lesson AND what has been building up in your audience's expectations, AND how you can reward that expectation/suspence. This is a VERY fun and very stimulating lesson you've produced here. Thank you ok final edit and i'm done: 9:22 i'm very interested in you doing a video on chess, everything from the solvability from a human to computer perspective and how that's been realized today with our technology, by programmers who COMPETE to make the best ai gamers in the TCEC. i've been on this rabbit hole for 2 hours help me

@kjetil1845 6 месяцев назад

small correction, in the zermelo's theorem the third trait should be "either player can always tie *at worst*". e.g if you have a game where neither player can force a win, you may still not be able to force a tie if your opponent is purposely trying to lose.

@3eve0n 5 месяцев назад

game theory in general usually looks at game strategy's where both players are playing optimally, so a case where 1 player is intentionally trying to lose would typically be ignored.

@pbjandahighfive 6 месяцев назад

I'm sure someone else has already noted this, but dude is like the Explosions & Fire of math.

@emilyrln 6 месяцев назад

Lmao I thought the same thing 😂 instead of hating yellow he loves clocks

@nicholasb8900 6 месяцев назад

8:53 perfect timing on “drop downward” and the lead (leaf) fallout from the tree.

@ComboClass 6 месяцев назад

Assuming that by "lead" you jut misspelled "leaf" (haha) yup that was a cool coincidence! One of the reasons I like filming outdoors with nature.

@nicholasb8900 6 месяцев назад

@@ComboClassyes I meant “leaf” awesome channel. Did you ever dissect checkers or is that also “impossible” given current computing power? Have you considered “Guess Who” to determine which set of clues eliminates people in the most efficient manner based on perfect play?

@tristantheoofer2 6 месяцев назад

when he got the chess board/triangle game thing thrown at him at the beginning of the vid and 26:46, i felt that lol

@heyvsauce8444 6 месяцев назад

This was the video I didn't know I needed to watch

@asherroodcreel640 6 месяцев назад

Lovely staghorn fern, fire on the glove was great along with everything falling appart, may I suggest action or ceramic figure heads possibly on a string or strings

@BridgeBum 6 месяцев назад

This video brings me back to my childhood. In high school I managed to convince my physics lab partner to bet me on tic-tac-toe. The bet was I win a nickel per game I win, but if I lose I give back double the total amount I won. I made a couple of bucks before he gave up. (And he finally understood how to always force a tie too, so it was boring.) 🤡

@TheOblomoff 6 месяцев назад

If chess players can identify mates in 10+, I have no doubt one can remember the whole tree in classic connect 4 1st player start. After all, there's just 7 possible moves each turn or less. Checkers have more. I heard they are computer solved. But are objectively harder to remember all positions. I like checkers. :)

@landsgevaer 6 месяцев назад

Let's see, you only need to know the correct reply to every move from your opponent. Say that on average they have about 5 columns to choose from (more in the beginning, less at the end) and the game would go about 15 moves deep for each player (some variations shorter, some longer), then you would need to remember about 5^15 = 30 billion branchings. Those seem conservative estimates, and still that seems like a lot. The mates that can be identified in chess tend to have narrow trees, where the vast majority of the opponent's wrong moves can be countered with a very quick mate according to typically recognizable patterns. Those are also positions that a computer would usually find the moves for very quickly, since they are good at tactics. I am not sure if that is equally the case for four-in-a-row. Add that a computer doesn't equally easily see the win from the starting position, that makes me less than entirely optimistic. Not saying you are wrong, but the "no doubt" is a bit strong to me. Addendum: I now read that solving four-in-a-row took 40,000 computer hours. They did get a bit faster, but you are still thinking about "can a chess player completely memorize a mate that took a computer, say, a year to solve?" Can you memorize an endgame tablebase with, say, six (64^6 = 70 billion) mixed types of pieces? Unlikely, even for a GM.

@pairot01 6 месяцев назад

I like chess' 50 move rule and 3 fold repetition. It shows these ganes have an entropy of sorts. In tic tac toe and connect 4, the board fills up, in chess pieces can be captured but you can never add a piece to the board, and pawns can't move back. But in chess not all moves have positive entropy, some are neutral, so we made up rules that if nothing irreversible changes in a while the game is just a draw.

@EPMTUNES 6 месяцев назад

Really Really awesome video!!!

@milokiss8276 5 месяцев назад

Greetings! I’ve never seen you before, But this was an intriguing and informative video. I generally prefer it when these sorts of videos go a little more into the math to show WHY things are, Rather than just how things are, But I understand not doing that. With that said, However, I do want to hear about this “Azundo”...

@theinternetis7250 6 месяцев назад

Yo yo yo my G finally another banger!!!

@falconplayz6118 5 месяцев назад

I had a computer science project once where we had to make a connect 4 ai and our professor linked us his thesis paper on computational and mathematical analysis of connect 4 and how to win using those ideas

@MowiWowi 6 месяцев назад

I'm so glad I picked this one

@vietnamgamer9490 6 месяцев назад

I don’t often hear “go inside” on the internet but it came to mind here

@PlanetXtreme 6 месяцев назад

I like the 3 player connect 4 staircase board you created @ 21:12

@soupisfornoobs4081 6 месяцев назад

A video on chess would be absolutely amazing

@soupisfornoobs4081 6 месяцев назад

Also the game you made!!

@kaiserping7996 6 месяцев назад

Nice video. I wasn't listening to what you said, but that squirrel was cute.

@Not_mera 6 месяцев назад

Thank you for the soupe opera decorations

@tav7630 6 месяцев назад

I'd definitely be interested in the Rubik's cube video

@-delilahlin-1598 2 месяца назад

I adore the chaotic environment with educated instructor vibes ❤

@colinothebambino 5 месяцев назад

This man is just a young Doc Brown. I'm sold this is who invents the time machine

@oliverniemann2541 6 месяцев назад

If your going to continue with game theory PLEASE talk about surreal numbers!!! They are so fascinating

@mrmuffins951 6 месяцев назад

I’d love to hear you talk more about other solved games like Chopsticks, Mancala, Dots & Boxes, Hexpawn, Gardner’s Minichess, Maharajah, and Anti/Losing/Giveaway Chess! Plus, I’d love to hear how long you think it’ll take computers to solve Chess and Go

@bananalegend194 5 месяцев назад

chopsticks was my childhood

@Nikioko 6 месяцев назад

I have been playing Connect 4 since I was 6. The first couple of days, my father won, but when I learned how it's played, I never lost against him again.

@morgangraley1049 6 месяцев назад

I loved this one Domotro! Do another one in this same vein, but with 3D Connect Four! 😮

@morgangraley1049 6 месяцев назад

Also, at 9:04, THANK YOU for setting up the chessboard correctly! I did an escape room recently where the chessboard was an integral part of the puzzle, and I couldn’t get the answer because they had put the dark square at the bottom right; but acted like that was fine! It was infuriating!

@edwardisaacs3663 5 месяцев назад

I love the 90's style cinematography.

@emilyrln 6 месяцев назад

I'm living for the unbridled chaos of this man feeding walnuts to squirrels and having things catch on fire 😂 for those 3 game conditions, is it assumed that both players make the same kind of moves (as opposed to in Hangman or another asymmetric game)?

@pimpsauce 6 месяцев назад

Just subbed. I want that chess video!

@KittenKatja 6 месяцев назад

In a Tic-Tac-Toe video, I saw that the chance of the first player is always 50%, where the second player has the other 50%'s 1 chance to be a tie. And that this margin drastically changes by how many dimensions are added. Basically, you didn't explore 4-connect in a 7x76 playing field, or in a 7x7x6x7 playing field.

@scotty3739 6 месяцев назад

this is really funny to see, since i just made connect 4 in monogame (xna framework) because i was bored lol. the game is essentially fully functional!

@alexrobinet7576 6 месяцев назад

There is an alternate strat I came up with playing on the handheld version against max dif computer. It always made you go first and blinded the board. Assuming the opponent does not play optimally take the turn 2 def spot on left first then check the middle spot. If you land on mid spot height 2 then play off the left side for the diagonal only checking mid when blocked.

@alexrobinet7576 6 месяцев назад

The reason this works is you only need 1 block before you get diagonal on mid set up. Once the left side is done simply wait for right 1 height 4 to be yours. Or the comp to tie.

@JosaxJaz 5 месяцев назад

16:32 the way he goes "...5 by 4 boaaaarddddd..." as the stop sign falls off and then just continues like nothing happened is so funny to me

@JanJeronimus 6 месяцев назад

You could also change the game rules to put first a different color piece in the middle that is not from one of the two playes.

@silviocupica2521 6 месяцев назад

What was the scramble of the cube at 27:09? Or was it random?

@ComboClass 6 месяцев назад

That cube was scrambled randomly. But I did used to like rubik’s cubes (could solve them in 1-2 minutes back in middle school) and will probably make an episode about them someday, at which point I’ll try to refresh my skills and see if I can still solve it quickly-ish haha

@nitehawk86 6 месяцев назад

"If you are a parent, do not try to train your kid to become a computer." Well, suck all the fun out of parenting, why don't you?

@qwerty11111122 6 месяцев назад

How does the game change when we add a third player? Does fair-share turn order actually give Player3 onwards a shot at winning?

@ComboClass 6 месяцев назад

I wondered a similar thing but I haven’t investigated 3-player versions (yet)

@MarloTheBlueberry 6 месяцев назад

3 player connect four sounds interesting

@landsgevaer 6 месяцев назад

That makes it tricky because it depends on players' strategies. Suppose that I am lost no matter what, but I have a move that decides whether either the first or the second other player can win with optimal play. What do I decide? And do the other players know for sure how I decide? How do they deal with that uncertainty in their calculations? With two players that doesn't happen.

@MarloTheBlueberry 6 месяцев назад

@@landsgevaer That's why you just decide better

@landsgevaer 6 месяцев назад

@@MarloTheBlueberry ❓