It is fun, but not as much fun as that guy’s ^ mom. If you don’t believe me, you can ask any other man in town (and most of the male horses). They all know it’s true, the same way I do-from experience. Trust me. Mrs. Tanirwar is the best!
Since the first player is one move ahead (making the game asymmetric), is there the same amount of winning games as of losing games (considering the point of view of the first player only) ?
Check links in the description for some pages with the guys who really know their stuff.... Including some great stuff about different sized boards, etc.
@@Some.username.idk.0 it realy isnt... "perfect play" means the player does, at any given moment, the objectivly best possible move given the current board state, and any given possible future boardstates
@@weberman173 so when player 2 can't win, the best move is to prolong the game as much as possible? Because some people could say if no winning or drawing possibilities are possible and you know the opponent will pick best possible moves, ending the game as quickly as possible is better
@@Some.username.idk.0 if you cant win, the best play is to "ensure to not loose" aka, a draw, whatever the draw is after 5000 Plays, or 100 Turns, is irelevant, however if you can not win at all, for whatever reason, and a draw is impossible, "optimal play" would be to ensure that every turn you take will be the least bad one, aka the one that brings you less close to ultimate defeat. While for a human, and in Real life, especialy in tournaments, yes ensuring the game ends as quickly as possible is prefeerable, its however not the "best move" inside the confines of the game as an isolated construct. While under time pressure in tournaments may make you want to end a game you can not loose quickly. That is however once again, inside the game, not optimal playing. Its prefeerable playing given outside circumstances however
+jiminybb What do you expect, He's English, not French... But then I'm American which is probably worse. Please help cure a small part of my ignorance. Is it pronounced "grace" as in "Hail Mary full of grace" or does it rime with "paw". OR is it sound like "Grassy".
I spent about 3 months in 10th grade designing and perfecting a game of Connect Four in Actionscript 3... Turned out awesome, it had fully featured AI so you play against the computer (with different difficulty levels). Every now and again I sit back and have a fiddle :)
i like the alternate name for connect for they listed as "fourplay" that way you could safely ask "you down for some fourplay?" and surprise them with a board game or sex. depending on their response....
Try this definition from the WR dictionary: cause: 2 a principle or movement which one is prepared to defend or advocate. A "movement" can often mean both the principle and the people and the organization taken together to promote a particular viewpoint or course of action. Uppermost in my mind is the principle that is being promoted -- but without people and a little organization, nothing's going to get done. :)
I actually lost a game and the other player won in 7 moves because at that time, I didn't know any rules and I just took my friend's phone and started playing😂
It's weird, isn't it? Numberphile was my first exposure to Brady and I've been with this channel since it's very beginning. Brady was a faceless, voiceless man behind the camera, and he's been coming out of his shell these past 2 years :)
Ummmmmmmm... I am seeing those omniscient Gods playing this game right now. *God 1 places piece in the middle* God 2: Goddamit, not again!! GG, dudegod, GG.
@@TaIathar No, the vowel sound in "de" is a schwa, the same as the second vowel in "lemon". "Des" is proounced a bit like "day", though it's a pure vowel, not a diphthong.
I love the topic, but the biggest pleasant surprise to me was how well Brady plays the role of the "professor". Usually he's just the voice behind the camera, or in front of the camera only briefly to talk about the channel in general. In this film he's the fount of knowledge, explaining the subject on his own, and in my opinion he's extremely good at it. Perhaps it's rubbed off from spending so much time around good teachers, combined with his experience as a BBC reporter in years gone by. Whatever the reason, I hope that this becomes a regular activity. Well done, Mr. Haran, well done.
Tic Tac Toe is solved, 4 in a row is solved, pretty much any game that is turn-based is probably solveable at some point, complexity is just bigger (in case of Chess, so big that fully solving it is a problem in itself). Kinda frustrating to think about it, that this games really only make "fun" because you cant fully understand them. If you solved such a game, it totally loses any appeal. To combat that it would require some form of additional randomness, so even the worse player "can" win (not on the long run, but at least not guaranteed all the time).
There is an interesting chess variant out there called Arimaa, invented by Omar Syed. While I suppose it is technically solvable, it is a game designed to be difficult for computers to play whilst being easy enough for human players to understand and get started. Its creation was inspired by Kasparov's defeat in chess at the hands of Deep Blue. So far, no computer program has been designed that has been able to beat any existing Arimaa champion consistently and decisively. In this way, it is a much more interesting and open-ended game to play, no randomness required. I suggest you check it out, if you are interested in "virtually unsolvable" games - games that are technically solvable, but are so difficult to solve that the technology and resources to do it simply do not exist currently.
I think it is interesting that Go, one of (or the) oldest strategy board games very may well be one of the last strategy board games to be solved. This is of course mostly by chance, because of how many potential moves there are. Then we'll have to add dice rolls to all of these games in some way so that we can still beat the computers some times.
Checkers is also solved. There must be a way to always win in Chess, but the game is so complex that I don't think anyone's gonna find it any time soon. Go may be a little bit simpler, but no one's solved that one yet. This is part of the fun of mathematics, but it's also the end of the fun for these games!
I'm not the best player ever in connect 4 but from a quick glance at your video and the variations shown it seems perfect. I was wondering if you could create a video about strategies to win in connect four from a mathematical perspective. I'm applying some empirical methods in my games (which i found alone, haven't read any connect four book; if that even exists) and i would be delighted to know the underlying ''laws''. Maybe you could ask the guys you mention in the video. Thx anyway great video as usual
I like that the perfect game starts by filling up the middle column. I played this game a ton in high school and after a while me and my buddy would always do that since we realized how massive of an advantage middle row gives.
I love this channel sooo much. but do you know what'd make it even better? If you actually showed the equations used to derive the solution to each topic. Sometimes you do this, but not often. It's a real shame that we weren't able to see the equation(s) that show how to find the number of total games, and winning games. The reason the equation is fun to see is because it exposes us to maths we may not be familiar with, or it exposes us to a more advanced version of the maths we're already on, or better still; it exposes us to new applications of the maths we've already learned! Doing this would greatly improve the interactivity and utility of an already interesting channel.
Dude, you're underestimating the complexity of showing such a thing for this game. The game has been shown to have 9 rules you have to obey while "in control" to guarantee a win. But even complying with these rules requires searching out moves in a way humans aren't that capable of. To play perfectly, you basically have to search out all possible futures of the current game and compare them against these 9. It's too complicated for any human to do in practice unless he treats it like chess and spends hours on his moves.
doodelay In real complex games, yeah, that is my impression. Game theory tends to be mostly about simple games since complex analysis of even those is complicated enough, and more complicated games tend to not yield any simple truths. That being said, I don't know game theory:)
I like what the both of you just said. That being said, I thought I had this game solved until I started playing top people from around the globe. I quickly learned either they had the whole board memorized, or knew how to play a perfect game. As I was once unbeatable, I'm now not. I don't think it's possible to memorize every possible outcome so now I'm left with "how do I play a perfect game" and was left thinking the same thing, "why doesn't he show the equation?"
SeniorXJ SeniorXJ Look up connect 4 on wikipedia. You will find a link to the paper I mention somewhere where the 9 rules that guarantee that you play perfectly are mentioned. I doubt you'll be able to follow them properly though.
"The Septuple Check" did not make any sense unless someone is toying with the other b/c they could have finished the game 2 moves earlier but decided not to.
Yeah, you're right. There's obviously no logical incentive to play like that - they're just showing you some of the more interesting/trivial aspects of the game
Reminds me of a story about Bobby Fischer examining a chess position. He said, "Not even God could avoid a loss as White here." After a brief pause, he says "Well, wait. If I move here, God goes there. And then if I go here, then maybe God could move there. and then if I . . ."
2:15 - 2:25 was cool. Also sixtysymbols did a video along time ago on "what confuses a physicist?" You guys should do a similar video for mathematicians.
This video gave me quite a flashback. In Italy we call this game forza quattro ("force four"), I remember when I was a kid, and my dad explained to me that it's called like this as a reference to the way sailors warn each other of incoming storms. Now that I've made some quick research, it seems to be the Beaufort scale, a measure of wind speed at sea. A forse four wind would be a "moderate breeze"
Kai Widman no, what I meant was red had no way to win on that turn. the win the guy is referring to was blocked previously. move 38 gave no chances for red to win.
When I was 13 my 20 year old brother introduced me to a game called "Marienbad" which involves picking up sticks from a start pattern according to a simple set of rules and trying NOT to have to take the last one. He knew a couple of winning 'leaves' so he won the first few games. That night I analyzed the game from start to finish and learned how to win from the start position if I went first (or was it second?), and what combinations to avoid if I went second (1st?), and never lost another game. (Of course, if he had known the same combinations, whoever went first (or was it second?) would have won. My 2 brothers and I were all very smart for kids in very different ways, and we were constantly being underestimated by each other, and even more often by others.
basically for each turn you assume the next move the opponent will play will be the best they can play, which is the move on his turn that assumes the best move you could play and so on until the end of the hypothetical game from that turn.
When I played football in high school we would have very intense connect four championships before practice and games. We developed some pretty rock solid strategies over time. The most famous was the “Deadly Seven” In which you would play three at a diagonal and three across so that the across would force a move and lead to an easy victory by playing the last chip in the same slot in a diagonal. The most disgraceful way to lose was on a vertical, because they are the most obvious and easiest to defend against, showing the player’s ineptitude at the game.
So wait... 1:24 is the end of the description, saying if you play a perfect game you are assured a win by dropping your disk into the center column - in this case, yellow disk would win. 2:25 shows no winner (draw). 2:32 yellow is in the center, yet red wins. What, then, actually is meant by a perfect game? If the "perfect player" knows that the first drop in the center is an automatic win, how do you get a draw with a full board? How do you get a loss? Seems to me that, short of there being a particular set of steps you have to know following that first drop in the center to get a "perfect" game and thus a win, it's still a wide open game within the three-trillion possible moves. Which then begs the question - what are the subsequent steps you'd have to follow for the perfect game and how many different ways can you follow those perfect steps for an assured outcome each time - as it doesn't seem reliant on the placement of the first disk...
I was the master of this in my primary school. I love this game so thank you so much for this video, Brady! And the middle slot was ALWAYS my first move. Even then I knew it was a sure win.
That only leaves Go as the last big one. You don't hear much about Shogi in the AI sphere though, so maybe that one is to come too. How about doing mini-max and nega-max algorithms and alpha-beta pruning? Maybe one for Computerphile.
I found this video especially relevant. I just programmed a connect-x game, where the players can decide to play any variant between connect 3 and connect 8 (an epic and tedious game).
I remember doing this in gcse maths circa 1991 . I remember there being a formula of the person who played second would be the winner. I won money this way in my twenties!
You make a mistake on The Septuple Check on move 12 Red moves right of centre making a possible diagonal win bottom left, yet yellow ignores it and red doesn't take the win, so this game would never happen.
+Roli Rivelino It's not the point. The point is showing a state of the board where you can win by putting a piece in any collumn. Of course it's not a "natural" state, it's implied.
The real mistake is during "The Perfect Game" with move 16 if red played in column 3 instead of column 5 it would have 3 in a row with no way for yellow to block. Unless that's not the point of this one either.
I figured this out when I was about 7 years old. I was king of connect four in elementary. Granted, I didn't really grasp the concept, I just knew how to win.
Loved this game as a kid. I soon worked out that without having a counter in the middle you we very unlikely to get 4 in a row. So the first move has to be in the middle.
unfortunately they do not define what is meant by "play perfectly"; Does it mean preventing your opponent from winning? Or does it mean something more elaborate than that requiring the fist player to fit into some prearranged template or rubricks for playing.
+FotisCanada I think play perfectly is actually based on every possible outcome and then choosing the one that takes the longest to lose(vs funnily enough, another perfect player), so yea, no human could do it.
Perfect play is when each side is making the best possible move, i.e. the move that brings the player either closest to winning or furthest away from losing. It so happens that in Connect 4 the first player can force a win by perfect play by starting in the middle column, and all the second player can do is delay the inevitable by choosing the move that's furthest away from the first player's win. In Chess they've discovered positions where one side can force a checkmate on the other side, but it can take as many as 500 moves to force against a perfect opponent.
Captains mistress and fourplay sounds fun.
It do
Yes sir
Pervert shut up
It is fun, but not as much fun as that guy’s ^ mom. If you don’t believe me, you can ask any other man in town (and most of the male horses). They all know it’s true, the same way I do-from experience. Trust me. Mrs. Tanirwar is the best!
@@chriswebster24 HAHAHAHE YOU'RE SO FUNNT
COMEDY GENIUS
I call it, "The game that broke up my relationship because my girlfriend is a sore loser"
MORE LIKE FORE LOSER
For*
Sore*
*Fouré
Dude it's called FourPlay, it doesn't mean you have to treat it like that.
My mom always called it, "Quit Fighting With Your Sisters."
Pretty sneaky sis.
My mum called it "stop fighting with your sisters" she'd always told us to quit
i was expecting some rules as to how to play perfectly :'(
exhaustive search?
Just tell the other person that "trying is what matters" you'll get a win
Centre when possible. That's my advice.
Just slip 2 in when your opponent is distracted lol
@@laurasanchez7105 Wow really
Hah. "Fourplay". Hoh, I'm immature.
「S」 thought the same
kevin calvanese me too
Actually if you get it you are mature.
well i play connect five
Also the name of a band.
Since the first player is one move ahead (making the game asymmetric), is there the same amount of winning games as of losing games (considering the point of view of the first player only) ?
e-penser mais quesque tu fou la
:'(
J'avoue, c'est une bonne question
First player has advantage due to there being an odd number in the central vertical column, the only line that allows you 4 left, right and diagonal.
Check links in the description for some pages with the guys who really know their stuff.... Including some great stuff about different sized boards, etc.
I'm surprised there's no explanation of what perfect playing means. I wouldn't expect numberphile to miss an opportunity to talk about game theory.
because "perfec playing" don't have room for explanation, i mean a Perfect play means that the player don'T make any mistakes
@@weberman173 yeah, but that description is subjective
@@Some.username.idk.0 it realy isnt... "perfect play" means the player does, at any given moment, the objectivly best possible move given the current board state, and any given possible future boardstates
@@weberman173 so when player 2 can't win, the best move is to prolong the game as much as possible? Because some people could say if no winning or drawing possibilities are possible and you know the opponent will pick best possible moves, ending the game as quickly as possible is better
@@Some.username.idk.0 if you cant win, the best play is to "ensure to not loose" aka, a draw, whatever the draw is after 5000 Plays, or 100 Turns, is irelevant, however if you can not win at all, for whatever reason, and a draw is impossible, "optimal play" would be to ensure that every turn you take will be the least bad one, aka the one that brings you less close to ultimate defeat.
While for a human, and in Real life, especialy in tournaments, yes ensuring the game ends as quickly as possible is prefeerable, its however not the "best move" inside the confines of the game as an isolated construct.
While under time pressure in tournaments may make you want to end a game you can not loose quickly. That is however once again, inside the game, not optimal playing. Its prefeerable playing given outside circumstances however
Haha Brady, "coup de gras" means "fat move". The word you're looking for is "coup de grâce".
my bad - the worst thing is that I just made a video about the term on wordsoftheworld (my words channel)!!!
Coup - Words of the World
Numberphile Way to recoup, Brady. Good on ya!
Numberphile Yeah I saw it yesterday, that's why I commented. Shame on you :) haha
To be phair, that move was pretty phat.
+jiminybb What do you expect, He's English, not French... But then I'm American which is probably worse. Please help cure a small part of my ignorance. Is it pronounced "grace" as in "Hail Mary full of grace" or does it rime with "paw". OR is it sound like "Grassy".
You should do Chess next just because there's at least 318,979,564,000 possible ways to play the first 4 moves.
Connect 4 has 14 times more positions than that. Were you paying attention to the video?
Gaming Turkey maybe pay attention to his comment of “first 4 moves”.
@@beri41381head
I spent about 3 months in 10th grade designing and perfecting a game of Connect Four in Actionscript 3... Turned out awesome, it had fully featured AI so you play against the computer (with different difficulty levels). Every now and again I sit back and have a fiddle :)
"Fourplay"
m8 r u srs
Thank you for seeing that ahahahaa
I had thought of a "wait, what?" to that one as well
0:35 fourplay... really
hahahaha
***** lol perfect
AYY MUM!!!! WANNA HAVE A GAME OF FOREPLAY B4 SCHOOL? :D
I love fourplay 😂
i like the alternate name for connect for they listed as "fourplay"
that way you could safely ask "you down for some fourplay?" and surprise them with a board game or sex. depending on their response....
how about both?
Adam Miller Have you ever asked someone this exact question?
Except a game Fourplay leads to the game of Life, where you now have to get a job and have a kid to take care of. You're better off playing Solitaire.
the 7 ways to win scenario is hilarious, at that point you hand the opponent your disk and tell them to put it wherever they want.
Try this definition from the WR dictionary: cause: 2 a principle or movement which one is prepared to defend or advocate.
A "movement" can often mean both the principle and the people and the organization taken together to promote a particular viewpoint or course of action. Uppermost in my mind is the principle that is being promoted -- but without people and a little organization, nothing's going to get done. :)
I actually lost a game and the other player won in 7 moves because at that time, I didn't know any rules and I just took my friend's phone and started playing😂
I know it as 'Vier Gewinnt' or "4 wins"
"Vier gewinnt" is the german version
Vier gewinnt, ja Mann :D
Auf deutsch halt XD
David Birkenmayer I'm german :D
Schon klar, sonst würdest du es ja nicht als vier gewinnt kennen :D
in France : Puissance 4
e-penser Tiens Bruce je savais pas que tu regardais Numberphile
Salut !
bonsoir mdr
Connect cœur
In Quebec too! :)
Wait a sec... Brady did his own video, where he actually explains everything? Have I landed in an alternate dimension or something?
He did it before. For instance his Yatzee playlist. It is rare though...
It's weird, isn't it? Numberphile was my first exposure to Brady and I've been with this channel since it's very beginning. Brady was a faceless, voiceless man behind the camera, and he's been coming out of his shell these past 2 years :)
Great video. Awesome channel!
Tru operators performing real operations erry day.
dude I see you on a ton of the channels I am subbed to. either that makes me really operator, you it makes you a stalker. maybe both.
***** That makes me operator and YOU a stalker!!!
Bro, I am pretty operator. Real operataz dont die! #OperatorLyfe
Used to love that game. Completely logic based, but not so overwhelming like chess that you can't play it over a beer.
Nice cinematography BTW.
You can literally play chess Over a beer
@@laskurtanceixixiiYour beer will get warm, chess games drag onnnn
@@soupisfornoobs4081 yeah bullet is soooo long, like 2 minutes max
@@laskurtanceixixii you'll find that "logic based" and "bar bullet" do not go together
@@soupisfornoobs4081 it does but you know nothing about chess soooo...
Ummmmmmmm... I am seeing those omniscient Gods playing this game right now.
*God 1 places piece in the middle*
God 2: Goddamit, not again!! GG, dudegod, GG.
How about "Youdammit, not again"
M Hanson Haha... or "Idammit!!!"
M Hanson Doesn't "Medammit" work just as well?
The real question is. If both of them are omnipotent, Which one will be player 2? Because both of them could Make themselves be player 1.
BlokenArrow No because God 1 made the move, not God 2.
I assume God 2 didn't damn himself.
"Coup de Grâce" is french and is pronounced "koo de grass" not "coup de gras" which would infer that you'd hit someone with fat... Yeah I know.
And I should know better after uploading this a month ago... Coup - Words of the World
:)
And you just got another follower on your other channel, well done on the mispronounciation ;p
Awesome videos by the way
It's more like coo day grah for pronunciation
@@TaIathar No, the vowel sound in "de" is a schwa, the same as the second vowel in "lemon". "Des" is proounced a bit like "day", though it's a pure vowel, not a diphthong.
I call it "The Kind of Boring Game That Still Manages to Capture Your Attention"
I love the topic, but the biggest pleasant surprise to me was how well Brady plays the role of the "professor". Usually he's just the voice behind the camera, or in front of the camera only briefly to talk about the channel in general. In this film he's the fount of knowledge, explaining the subject on his own, and in my opinion he's extremely good at it. Perhaps it's rubbed off from spending so much time around good teachers, combined with his experience as a BBC reporter in years gone by. Whatever the reason, I hope that this becomes a regular activity. Well done, Mr. Haran, well done.
Tic Tac Toe is solved, 4 in a row is solved, pretty much any game that is turn-based is probably solveable at some point, complexity is just bigger (in case of Chess, so big that fully solving it is a problem in itself).
Kinda frustrating to think about it, that this games really only make "fun" because you cant fully understand them. If you solved such a game, it totally loses any appeal.
To combat that it would require some form of additional randomness, so even the worse player "can" win (not on the long run, but at least not guaranteed all the time).
The question is: Will chess or go be solved first?
Or just involve so many moves that trying to mathematically solve it isn't feasible. Like Go.
There is an interesting chess variant out there called Arimaa, invented by Omar Syed. While I suppose it is technically solvable, it is a game designed to be difficult for computers to play whilst being easy enough for human players to understand and get started. Its creation was inspired by Kasparov's defeat in chess at the hands of Deep Blue. So far, no computer program has been designed that has been able to beat any existing Arimaa champion consistently and decisively. In this way, it is a much more interesting and open-ended game to play, no randomness required. I suggest you check it out, if you are interested in "virtually unsolvable" games - games that are technically solvable, but are so difficult to solve that the technology and resources to do it simply do not exist currently.
I think it is interesting that Go, one of (or the) oldest strategy board games very may well be one of the last strategy board games to be solved. This is of course mostly by chance, because of how many potential moves there are.
Then we'll have to add dice rolls to all of these games in some way so that we can still beat the computers some times.
Checkers is also solved. There must be a way to always win in Chess, but the game is so complex that I don't think anyone's gonna find it any time soon. Go may be a little bit simpler, but no one's solved that one yet. This is part of the fun of mathematics, but it's also the end of the fun for these games!
In Brazil: Lig-4.
And Coup de Grâce is NOT pronounced coup de gra, which means fat move as opposed to fatal/final move :)
Se chama Golpe de Misericórdia na verdade.
but who's counting ?!! NUMBERPHILE !!! NUMBERPHILE IS COUNTING !!!!
aah aah aah...
I'm not the best player ever in connect 4 but from a quick glance at your video and the variations shown it seems perfect. I was wondering if you could create a video about strategies to win in connect four from a mathematical perspective. I'm applying some empirical methods in my games (which i found alone, haven't read any connect four book; if that even exists) and i would be delighted to know the underlying ''laws''. Maybe you could ask the guys you mention in the video. Thx anyway great video as usual
I like that the perfect game starts by filling up the middle column. I played this game a ton in high school and after a while me and my buddy would always do that since we realized how massive of an advantage middle row gives.
"Hey kids, you up for some Fourplay?"
How did they not see that...
Delete the comment
I call it Vier op een Rij.
That's Dutch
Inderdaad
LOL
It’s taken 3 years to crack this down without using a calculator....
Four in a Row.
"Fourplay" I wounder why that name didn't stick.
Is there something I'm missing?
Magiphart 'foreplay' ;)
Magiphart A few years on your age, maybe.
It didn't stick because fourplay(foreplay) results in slipperiness.
What's wrong with the word? I don't get it.
Thank you for bringing back all of those lovely childhood memories of playing Connect Four.
I love how a simple game I played in childhood can be solved mathematically!
In France, the game is called "Puissance 4" ("Power 4").
Admit it Brady, this is the best job in the world.. :D
In Italy we call it Forza Quattro! :)
"The Septuple Check" - another way to say overkill
It's really surreal but really fun to see a video presented entirely by you!
That is called Forza Quattro in Italian.
I probably had a clone... called "Formula Quattro" :D
I love this channel sooo much. but do you know what'd make it even better? If you actually showed the equations used to derive the solution to each topic. Sometimes you do this, but not often. It's a real shame that we weren't able to see the equation(s) that show how to find the number of total games, and winning games.
The reason the equation is fun to see is because it exposes us to maths we may not be familiar with, or it exposes us to a more advanced version of the maths we're already on, or better still; it exposes us to new applications of the maths we've already learned!
Doing this would greatly improve the interactivity and utility of an already interesting channel.
Dude, you're underestimating the complexity of showing such a thing for this game. The game has been shown to have 9 rules you have to obey while "in control" to guarantee a win. But even complying with these rules requires searching out moves in a way humans aren't that capable of. To play perfectly, you basically have to search out all possible futures of the current game and compare them against these 9. It's too complicated for any human to do in practice unless he treats it like chess and spends hours on his moves.
***** oh I didn't know, thanks lol so basically game theory is almost useless in terms of real time decision making?
doodelay
In real complex games, yeah, that is my impression. Game theory tends to be mostly about simple games since complex analysis of even those is complicated enough, and more complicated games tend to not yield any simple truths.
That being said, I don't know game theory:)
I like what the both of you just said. That being said, I thought I had this game solved until I started playing top people from around the globe. I quickly learned either they had the whole board memorized, or knew how to play a perfect game. As I was once unbeatable, I'm now not. I don't think it's possible to memorize every possible outcome so now I'm left with "how do I play a perfect game" and was left thinking the same thing, "why doesn't he show the equation?"
SeniorXJ SeniorXJ
Look up connect 4 on wikipedia. You will find a link to the paper I mention somewhere where the 9 rules that guarantee that you play perfectly are mentioned. I doubt you'll be able to follow them properly though.
Only Chuck Norris can win Connect 4 in three moves.
or six
Buenomars you mean one
"The Septuple Check" did not make any sense unless someone is toying with the other b/c they could have finished the game 2 moves earlier but decided not to.
Yeah, you're right. There's obviously no logical incentive to play like that - they're just showing you some of the more interesting/trivial aspects of the game
Wonderful episode, Brady! I've always loved the mathematics behind games.
Those shapes on the disk are so aesthetically pleasing
I call it "Vier Gewinnt" what means "Four wins".
Good to see Brady presenting for a change.
Reminds me of a story about Bobby Fischer examining a chess position. He said, "Not even God could avoid a loss as White here." After a brief pause, he says "Well, wait. If I move here, God goes there. And then if I go here, then maybe God could move there. and then if I . . ."
I love the sound when the stones fall each time
Me too - it was the first song we played at our Wedding reception.
Numberphiles need to be stopped. Always prowling around the calculator section at Best Buy acting creepy.
Yes. That's me.
I almost died of shock at the end. Thanks!
2:15 - 2:25 was cool. Also sixtysymbols did a video along time ago on "what confuses a physicist?" You guys should do a similar video for mathematicians.
You know Brady also runs the sixtysymbols channel?
tdfj95 I did know that. Although my comment does imply that they are run by different people, when they aren't.
Me, approaching a friend: Want to do some fourplay?
Friend: *immediately turns and walks away at a brisk pace*
I'd call the last one the anti-zugzwang. You're forced to win.
This video gave me quite a flashback. In Italy we call this game forza quattro ("force four"), I remember when I was a kid, and my dad explained to me that it's called like this as a reference to the way sailors warn each other of incoming storms. Now that I've made some quick research, it seems to be the Beaufort scale, a measure of wind speed at sea. A forse four wind would be a "moderate breeze"
2:24 move number 38 is wrong. Red had a win if it went third from the left. Granted, it is a legit combination.
u right, u right
It wasn't their turn though
lev1t1cus yes it was. Look more closely.
Kai Widman no, what I meant was red had no way to win on that turn. the win the guy is referring to was blocked previously. move 38 gave no chances for red to win.
you're wrong
An awesome account, thank you i like to whatch every video and i hope you will keep it on.
One day we will solve chess.... One day...
When I was 13 my 20 year old brother introduced me to a game called "Marienbad" which involves picking up sticks from a start pattern according to a simple set of rules and trying NOT to have to take the last one. He knew a couple of winning 'leaves' so he won the first few games. That night I analyzed the game from start to finish and learned how to win from the start position if I went first (or was it second?), and what combinations to avoid if I went second (1st?), and never lost another game. (Of course, if he had known the same combinations, whoever went first (or was it second?) would have won. My 2 brothers and I were all very smart for kids in very different ways, and we were constantly being underestimated by each other, and even more often by others.
So how does one play perfectly? Is this supposed to be obvious?
I was kinda expecting the answer to that in the vid too
basically for each turn you assume the next move the opponent will play will be the best they can play, which is the move on his turn that assumes the best move you could play and so on until the end of the hypothetical game from that turn.
That last sound when the coins were dropped scared the crap out of me!
Damn i love that sound
I've been watching Sips play connect fouuuur and now I'm getting this video in my recommendations.
There's a 3 dimensional version of this game which is surprisingly complicated.
It's nice to see brady appear on this channel
Here in America, i call the game connect four.
On a random RUclips roll and this is pretty amazing
I've only ever heard connect four and four in a row.
Will Federowic In Germany its called "vier gewinnt" (four wins)
This is exactly what I was looking for. If you play perfectly and so does your opponent, you win in your last move.
Ah, I loved this game, but we call it in German "Viergewinnt" (Four wins^^)
Gender Neutral Chibi Thing
Ok.
Swiss Man 18 Yeah.
+Swiss Man 18 Viergewinnt :))
Travis Rivera Petit
Yeah, I don't really get what's so funny about it, but okay.
But you don't win four times...?
When I played football in high school we would have very intense connect four championships before practice and games. We developed some pretty rock solid strategies over time. The most famous was the “Deadly Seven” In which you would play three at a diagonal and three across so that the across would force a move and lead to an easy victory by playing the last chip in the same slot in a diagonal. The most disgraceful way to lose was on a vertical, because they are the most obvious and easiest to defend against, showing the player’s ineptitude at the game.
Even with all this information, I cant win a game of connect four to save my life
I saw this in mathematical structure checkers, chess (former high school player) and go when I was in middle school. It's good information!
So wait... 1:24 is the end of the description, saying if you play a perfect game you are assured a win by dropping your disk into the center column - in this case, yellow disk would win. 2:25 shows no winner (draw). 2:32 yellow is in the center, yet red wins. What, then, actually is meant by a perfect game? If the "perfect player" knows that the first drop in the center is an automatic win, how do you get a draw with a full board? How do you get a loss? Seems to me that, short of there being a particular set of steps you have to know following that first drop in the center to get a "perfect" game and thus a win, it's still a wide open game within the three-trillion possible moves. Which then begs the question - what are the subsequent steps you'd have to follow for the perfect game and how many different ways can you follow those perfect steps for an assured outcome each time - as it doesn't seem reliant on the placement of the first disk...
a "prefect GAme" would be when neither of the two Players would make any mistake in witch chase the Center player would always win
+Madamegato Those are not perfect games with perfect players. He was still talking about how many games you can play (not perfect games, just games).
I was the master of this in my primary school. I love this game so thank you so much for this video, Brady! And the middle slot was ALWAYS my first move. Even then I knew it was a sure win.
Why would a perfect being play a game if that being knows he/she/it will loss?
They wouldn't. It's a mental exercise.
It makes sense. You have the most possible ways to connect 4 if your disk is in the middle
That only leaves Go as the last big one. You don't hear much about Shogi in the AI sphere though, so maybe that one is to come too.
How about doing mini-max and nega-max algorithms and alpha-beta pruning? Maybe one for Computerphile.
I love math and I love Numberphile
Thanks for all the hard work.
I call it something different, but I speak a different language. For me it's "fire på rad" (Norwegian for "four in a row")
***** Really? It seems you have a different word for EVERYTHING !!
***** Het spijt me - I was making a joke: Of course Dutch has a different word for everything - that's what another language IS !
May the Four be with you.
Now do this for chess
i second that motion
Correction: it's impossible with the computing power we can ever have.
Yeah it's not like we could imrpove our technology or anything
Quanxiang Loo no, we are already developing things like quantum computers, we may already have the tech
Spathe it's*
I found this video especially relevant. I just programmed a connect-x game, where the players can decide to play any variant between connect 3 and connect 8 (an epic and tedious game).
lol find of ironic that there's 42 spots in the grid
thats not irony
Looks like connect four is the answer to life.
@@Arcyse 42 is the answer. But connect four is the question....
In German the game is called "Vier gewinnt!" which translates into "Four wins!"
"Fourplay" :D
I was expecting some professor explaining it but daaamn my boy Bradey
In Germany, we call it "Four wins"
In french, we call it
“Puissance 4” which means Power 4
In german it's vier gewinnt: Four wins.
I remember doing this in gcse maths circa 1991 . I remember there being a formula of the person who played second would be the winner. I won money this way in my twenties!
You make a mistake on The Septuple Check on move 12 Red moves right of centre making a possible diagonal win bottom left, yet yellow ignores it and red doesn't take the win, so this game would never happen.
+Roli Rivelino It's not the point. The point is showing a state of the board where you can win by putting a piece in any collumn. Of course it's not a "natural" state, it's implied.
The real mistake is during "The Perfect Game" with move 16 if red played in column 3 instead of column 5 it would have 3 in a row with no way for yellow to block. Unless that's not the point of this one either.
Sure, put red in column 3. But then Yellow also puts it in 3 and has 4 in a row...
Aesahethr Kind of like showing a chess board with every attacking piece on the board simultaneously checking the opposing King.
Missed that, thanks. Alas, I am not a perfect player
Was planning on buying Connect 4 for my siblings this Christmas but now this video has given me the mathematical edge haha.
you still didnt prove it was true.
you asume the apponent put a coin on top of the first one,
but what if he drops one beside you?
I figured this out when I was about 7 years old. I was king of connect four in elementary. Granted, I didn't really grasp the concept, I just knew how to win.
Yeah... there's a genius right there.
Fourplay lol sorry
Loved this game as a kid. I soon worked out that without having a counter in the middle you we very unlikely to get 4 in a row. So the first move has to be in the middle.
unfortunately they do not define what is meant by "play perfectly"; Does it mean preventing your opponent from winning? Or does it mean something more elaborate than that requiring the fist player to fit into some prearranged template or rubricks for playing.
+FotisCanada I think play perfectly is actually based on every possible outcome and then choosing the one that takes the longest to lose(vs funnily enough, another perfect player), so yea, no human could do it.
Perfect play is when each side is making the best possible move, i.e. the move that brings the player either closest to winning or furthest away from losing.
It so happens that in Connect 4 the first player can force a win by perfect play by starting in the middle column, and all the second player can do is delay the inevitable by choosing the move that's furthest away from the first player's win.
In Chess they've discovered positions where one side can force a checkmate on the other side, but it can take as many as 500 moves to force against a perfect opponent.
I used to be the best connect 4 player in the whole school back in the day :D
in sweden it´s called : fyra i rad.