How to always win at Dots and Boxes - Numberphile

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this game is called Datsun boxes it's played by children in many places I learned it in the first grade in 1946 we're going to play a game and if you don't know the rules you'll soon learn them as you watch this play we have a board here it's when we end up will have 9 boxes and when it's your turn you can make a move I'll make the first move like this it's your turn you can join any two dots that are adjacent horizontal or vertical and it's in my turn I'll make a move here you play anywhere you want now the goal of this game is to make more boxes in your opponent the rules are if your move makes the fourth side of a box then you get to fill that box in it becomes your color and you you own that box so we get scores depending on boxes you okay so now I make a move well I just made the third side of box so Brady if he if he wants to he gets the fourth side of the box and he puts his initial on that and he owns that box that's Brady's box it's one point for him but he takes an extra move now he gets a bonus move for having made a box and he has to move and he must move that's right now you'd think well go ahead he'll make a move four and four looks like he may get I may get four and he may get four but let's see that done quite work so I go here and I make this box that's one box for all one I go here and I make another box that's a box for all it now if I wasn't a very bright player and I was sort of a beginner I would continue making two more boxes and then I'd give him a last four but I'm smarter and I give him a play here now I've completed my turn without making boxes I'm done it's his turn now and whatever he does if he goes there it's called a double cross that's probably his best move and he makes two boxes in one turn yeah but he gets only one extra move but having made boxes he gets an extra turn but now he has to take the extra turn give me the last four and so I win this game by a score of six to three so every time I make a box I get an extra turn and you go on like this then so the score is six for me and three for him did I lose because you're too good for me or did I do something stupid you lost because we got to a point here where there are two long chains and a long chain here's a chain of size four here's another chain of size four and the number of chains was even two and that's why you lost this little one is a chain of size one it's too short to matter long chains are very important and a long chain is one that has three or more boxes in it the first player wants an even number of long chains and second player wants an odd number of long chains how could you control the number of long chains well I couldn't if you'd have played really smart from the beginning but you had a chance even fairly late fee to cut one of these chains into two short chains than have been only one long chain and you've been okay second player strives to make an odd number of long chains and on this board he can do it and I'll explain how first player strives to make an even number wrong chains a key feature of this board is there's only one center square and if we look at this at the board we can decide okay there's some moves over here in the corners it's called these corner moves right so we have some corners we have some sides we have four sides right and we have some centers there's four centers and we have some spokes and these moves are okay that's all the moves there are if you can force all long chains to go through the center there will be only one so any chain that not go through the center necessarily has to be a side chain so for example let's just look here what is a side chain a side chain is a chain that goes off on some side C so this in the first game I played we got he wants something like this now I'm threatening to make a side chain over here see haven't done it yet but it's it's it's tempting so we go something like this like this something like this something like that something like this maybe here maybe here and I now have a side chain this chain is one chain there's another chain here so there's going to be two chains which means this is going to be a win for the first player now the second player could have won and the key to the second player is winning is to stop the side chain and the way to do this is to play spokes these are the moves you want I prefer to do it in a swastika pattern if you sew these these particular moves this set of moves is very good because they stop all side chains there's no way than a side chain today so let's look at it suppose the first player starts like this the second players you'd think aha he's threatening to go and make a side chain over here or at least get started and then there'd be very hard to me to stop it without sacrificing some things I'm going to break it up right away I break it I stopped that chain from coming into existence on that side right so he goes over here maybe he's threatening another one no I play another spoke I play one of the swastika spokes I play it perpendicular to his last move usually right adjacent to it if I can like this and now I can't make any side chains over here so he's in bad shape he will never get a second chain what about everyone what about the top and the bottom can these be today countess sidechains only if he can make a chain but how's it going to make a chain if he tries watch he tries he tries us see but I stopped that to second player goes here so now that we have two little chains they don't matter it's only the big chains account and so there isn't now maybe he succeeds in being no chains which would be good for the second player in the end game but the only way he can make no chains is the sacrifice he might do that he might give away two boxes right now but if that's the case there's no chains the little stuff will all be divided up evenly and I'll win on the sacrifice on a game that is four dots by four dots or three boxes by three boxes yeah play second play the spokes and you will do play they all in a spokes isn't a swastika you don't let him get Center in a site adjacent to each other because if he does that that's that's a threat to run a chain through here and the only way you're gonna be able to stop it as a sacrifice a box don't don't give away any sacrifice until you have to stop the side chains right away by playing the alternate spokes and play them adjacent whenever he makes the center or side he goes and moves in a corner that's no problem you just let that move be now if he plays a spoke fine that's the way that we like the more spokes the better should we play a game and see if I can beat you no okay oh my god so immediately the danger to me here is you pay up there that's for sure so I want to make a spoke yes right yes great idea okay now again that's good for me but from what you told me that's my danger now yes so I want to make another spoke yes oh I have not hope anymore this early in the game you're thinking I now have no hope true now again this is my this is my danger well first of all there's a box and if you don't take that box I will now there's threats on both sides does that scare you why well because even number of chains gives you the game yeah unless they're all small so you can stop there from being - just there to threats now you stop one the other is only going to be one so I play here that's fine these have both become small chains that's right and now we're back to only one big chain and that's good for me or maybe zero I mean I can make zero change but since you're already one point ahead that's right that's right you get both of those right and you give me to give you and I give you to you you ends normally and actually you got six two three because I sort of I played elwyn berlekamp and dots and boxes only after you talk oh I tell you the proudest thing a teacher ever does is when he gets students who are better than him this video was filmed at MSR eye in Berkeley California but perhaps fittingly for a video about dots and boxes it's also been sponsored by Squarespace if you're looking to set up a website or a blog or an online store I really recommend Squarespace in fact I recently got fed up with my own blog and I've started using Squarespace and I wish I'd done it a long time ago it's really enjoyable to use they've got these great startup templates you can start building with but then customize them as little or as much as you'd like really usable really good customer service and importantly the websites you make on Squarespace automatically look really good well on big grown-up computers but also on your handheld devices your mobile phones now you can just go to the site have a look you can even play around and build your own site no credit card details or anything like that just see what you think and then if you do like it and I think you probably will you can get 10% off by using the code numberphile it also lets the people at Squarespace know that you came from here in fact you can just go to the website squarespace.com slash numberphile find out the rest from there as I said I use them myself I'm a really happy customer and you might be too but regardless thank you to Squarespace for sponsoring this video about appropriately dots and boxes

Info

Channel: Numberphile

Views: 2,060,791

Rating: 4.9455357 out of 5

Keywords: numberphile, Dots And Boxes (Game), elwyn berlekamp

Id: KboGyIilP6k

Channel Id: undefined

Length: 9min 45sec (585 seconds)

Published: Mon Jan 12 2015

Reddit Comments

How does this strategy change for larger playing boards?

👍︎︎ 1 👤︎︎ u/jaguar_EXPLOSION 📅︎︎ Feb 18 2015 🗫︎ replies

Where was this 30 years ago!?

👍︎︎ 1 👤︎︎ u/sutiibu 📅︎︎ Feb 18 2015 🗫︎ replies

Man, the entire time I was waiting until he drew a swastika. Then he goes outright and tells of a trick with swastikas. Ridiculous.

👍︎︎ 1 👤︎︎ u/Juicysteak117 📅︎︎ Feb 24 2015 🗫︎ replies