How many chess games are possible? - Numberphile

Dr James Grime talking about the Shannon Number and other chess stuff.
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[@severed6s]

in the distant future: "and it is as of move 11,000 we have a completely new game." -agadmator

[@UpperCrustthe3rd]

Lol

[@mirceapintelie361]

🤣🤣🤣

[@crazypomp927]

This comment deserves soooo many more likes.

[@clivethereddevil3178]

and both players are still in their home preparation

[@pawelwrzesinski7954]

@peter Solomon it is almost correct, 50 moves without taking any piece. After 50 moves without it it is a draw.

[@blue_genes]

this guy looks like he smokes math

[@blue_genes]

Alex Pătraru that was my joke

[@kuusik100]

No he smokes A TON OF METTHHHHHHH

[@LuWiigi21]

Alex Pătraru pls dont comment again

[@aspectoftheyeti1232]

top illin you might be onto something

[@ColdFishMus]

Alex Pătraru that, was just totally pathetic.

[@MackyBclips]

My chess skill is so low that i have most likely played games of chess that will never be repeated by another human being

[@owenmckenzie962]

Mac Boulden actually Everyone probably has, by the middle game the game is unique usually

[@sergifernandezmiranda1311]

Most likely. For two players to play the same game of chess is as unlikely as two people hitting the jackpot at same time

[@mirceatim3274]

@@owenmckenzie962 also in the start when he really does not study some openings

[@owenmckenzie962]

mircea tim true

[@apollyon1]

It is highly unlikely that any two games of chess have ever been repeated beyond a certain amount of moves. If your chess skill were truly awful you would have been caught out by fools mate on multiple occasions! :P

[@psilow7789]

7:34 "Some of those games are nonsense games, you can win in one move but you move other pieces" - I feel personally attacked!!!

[@pierQRzt180]

don't worry, the opponent will move other pieces the next move, it won't be checkmate.

[@mikezinj]

i bet your opponent's king doesnt :D

[@SKyrim190]

@@mikezinj BURNED!

[@mattk4758]

haha, when he said that, i was like "So you mean most chess games?"

[@reyanshpadhi9210]

Here's a co-incidence: As i was reading ur comment, the same line came up on the video

[@adrian5b]

That queen sacrifice at 3:40 was delicious.

[@CapAnson12345]

+adrian5b The immortal game Anderssen-Kieseritzky June 21, 1851.

[@JohnWTolbert]

Agreed. Awesome.

[@Kenneth_the_Philosopher]

Wow, I didn't notice that ! Thanks!

[@lorekeeper685]

castling woud work

[@casimirwallwitz8646]

You can`t castle out of check.

[@undera3014]

0:27 how to get extra sentences on a test

[@KawasakiOnly]

lol how is this not top comment

[@dmitriyk1857]

I don't get it. Please explain.

[@ryanxin1848]

It took me 0.29 minutes to get

[@darthbricksempire3606]

MLG Gaming so a little under 20 seconds?

[@ryanxin1848]

Yes

[@FrancoisTremblay]

197 742 possible games after 4 moves... and only 36 of them are possible Bongcloud openings. We really need to have more opening theory.

[@jhm8614]

I see a man of culture

[@okabekun844]

Two men of culture and one of them is 1 day ago? Wonderful

[@occultsymbols]

how is it only 36 games? Should be much more no?

[@HM-yq3cn]

@@occultsymbols it s always e4 (or e3) first, so...

[@guven3625]

Who needs theory when you can russian roulette pawns? 😎

[@orangenasa]

3:39 Can we just appreciate this queen sacrifice

[@Bartooc]

It's the most famous checkmate in history. The game is called the Immortal Game and was played between Adolf Anderssen and Lionel Kieseritzky in 1851.

[@chidzhustle3570]

Yeah I was watching and thinking “???” until the magic moment

[@sarahdumby]

Oh no my queen

[@ibbossb705]

@@sarahdumby c h e c k m a t e

[@BrazilianImperialist]

It is a very known mate pattern

[@Terry-nr5qn]

Move 4 there are 197000 different possible games. 90% of games I play 1. e4 e5 2. Nf3 Nc6.

[@KanishkMalkan]

then its Bishop A5

[@Terry-nr5qn]

@@KanishkMalkan You bet

[@KanishkMalkan]

*B5

[@KanishkMalkan]

and A6

[@dajanacoric1241]

I like playing king's and queen's gambit, any1 else?

[@MaxwellTornado]

... I almost said depends on the size of the board. I'm an idiot sometimes.

[@jsd4574]

Erik István Fejes..... gg

[@cidkagenoh9181]

hahahaha, lol

[@lincolnpepper816]

Technically it does but there is a standard size they are using in this video.

[@emilwallin1176]

no it doesnt. no matter how big/small the chess board is the number of squares are still the same

[@753238]

Same,

[@user-ek4ic2ip9e]

The game being played is “The Immortal Game” Adolf Anderssen v. Lionel Kieseritzky, London 1851

[@shreshth231]

Agadmator has covered the game. I recognized that checkmate!

[@dancrane3807]

Thanks.

[@KedarOthort]

Oh is this what it is? They use it for the game in Dragon Age Inquisition, I wasn't aware it was based on another one.

[@johncorn7905]

Absolutely gorgeous

[@hector9586]

@@KedarOthort It's also used in the original Blade runner. I used to play a lot that opening too, it's the bishop gambit and it's a lot of fun in lower levels.

[@SteveBakerIsHere]

The interesting question is - as the game goes on - the number of pieces goes down (as some are captured) - but the number of spaces they can move into without some obstruction INCREASES...understanding which of those two things happens to the greatest extent would inform us as to whether Shannon's number is an over-estimate or an under-estimate.

[@salahabdalla368]

We may never know most computers will crash with all of this info, and we need a super genius to code thus

[@adiboy010]

@darknightoftroy you sir have started to explore the code.. would love to crack the real answer with you 👍👏

[@jeanmoise9570]

Gond question

[@pizzashark7067]

There are only two possible chess games, actually. The one where I blunder my queen, and the kind that occurs much less frequently.

[@alexandersamuel5638]

hahaha

[@Fassle]

I usually sacrifice my king for the win.

[@braydenguy907]

You sacrifice your king ummmmq

[@ucLe-wg2wp]

de minimis OMG, that's actually a brilliant tragedy lul

[@jorriffhdhtrsegg]

Yeh the kind where i look three moves ahead and the other where i get bored/distracted and give my queen accidental suicide by move 5

[@GMPranav]

Me: How many are possible games? Doctor Strange: 10^120 Me: In how many I won against my dad? Doctor Strange: None

[@thomashorne2607]

F

[@spoont9544]

F

[@hamzatamim8379]

F

[@hannesye1541]

F

[@boombam3028]

F

[@dominikwagner9768]

The game he shows is the immortal game between Adolf Anderssen and Lionel Kieseritzky 1851, btw.

[@rohannayak3865]

Was looking for this comment LOL 😂 a true chess fan

[@divangibran8007]

Damn i really thought like wtf why does white just lost the Bishop and both rooks completely unprompted And I was gonna say the queen but then.. Bishop e7 mate

[@mynameisjeremy]

3:12 "it was only IN PASSING" that had to have been a purposeful choice of words

[@benJamin-bf4nu]

9:15

[@howiestillgamez5326]

en crossaint

[@whocan_duncan]

r/anarchychess losing their minds

[@ID10T_6B]

EN PASSANT

[@nelsonnicholson6175]

"This was in passing." Or... En passant?

[@coleyamos]

Weird Stuff I wonder how many chess players don't understand that. 😏

[@trevorrogers95]

Coley Amos Normal people won’t. Chess nerds like us... we’ll smile.

[@coleyamos]

🤓

[@trevorrogers95]

Coley Amos 😂😂😂

[@Phlebas]

I remember learning this rule as a kid (I had a copy of some edition of Hoyle's Rules lying around the house). Unfortunately, game rules only really count when both players agree on them as I quickly found out, so I've gotten in the habit of asking people I haven't played against if they're familiar with _en passant._ If no, I explain it to them and ask if they want to have a game where it's a legal move or not. I'm happy to play either way.

[@ChessNetwork]

I wasn't aware of how 10^120 was guesstimated. :) Nice video... *shared*

[@craigferge4702]

What you're missing is that "possible chess games" do not exist in the physical world the same way water does. 99.9.....infinite 9s.....999% of these games will never be played and therefore do not exist in physical space, they are only theoretical possibilities. Therefore, it is possible for "possible" number chess games to exceed a number of mass in the universe

[@leslieandclash7030]

hey chessnetwork :) how did you enjoy the king's gambit as an example?

[@armandopiloto]

the video specified "observable universe." we have no idea how large the entirety of the universe is or if it is measurably large.

[@TheDrexxus]

Yeah... There is a big difference between the theoretically infinite expanse of space vs "the observable universe". The observable universe is absolutely finite because we can only see so much of it.

[@loganreece3263]

"The Universe, however, is infinite and spans far and endless, and therefore, there is no way there are more games of Chess possible than atoms in the Universe" He said visible atoms in the universe. Also, we don't know if the Universe is infinite, do we?

[@willfreese]

The universe of possible chess games includes some marvelous games that have never been played. Every so often, two people get together and try to find one of them.

[@tarabinsurzo]

That’s a great sentence thank you sir!

[@willfreese]

@@tarabinsurzo You are welcome.

[@davidf2281]

Underrated comment

[@nicolasterbeek3322]

7:33 is a pretty accurate description of my chess experience

[@zhengellen1491]

Nicolas Terbeek unoriginal

[@Cr-gf3gn]

This guy definitely takes sugar in his tea.

[@General12th]

cocaine*

[@General12th]

pop9095 Er, did you respond in the right thread?

[@TheVoidisEternal]

woo hoo I take honey baby 😘

[@martinmichalko4166]

uk

[@taylorport3463]

I take cyanide in my tea.

[@Skullmiser]

The captions misspelled "googols" as "Googles". I blame the company.

[@henryambrose8607]

@@MetalRaydown Yes, it was. Google owns KZbin, and KZbin makes a net loss.

[@chandrabitpal9151]

I am the 69th like

[@DaviniaHill]

@@henryambrose8607 Google doesn't own KZbin. Alphabet owns both.

[@timboyle2784]

@@DaviniaHill This video was uploaded before alphabet was a thing and when google owned youtube so the captions were probably generated then

[@Kes22497]

"Google" the company was also a misspelling of "Googol" so we've come full circle

[@Thoughtless427]

So many possible games, but only one of them has ever and will ever truly *THROBBED* .

[@sammylahmeda7271]

Xqc is still recovering from that day

[@guts1859]

@@sammylahmeda7271 yes by later winning 6 and 0 in pogchamps

[@riverancheta1616]

2021

[@Panjab_47_84]

@@guts1859 Someone is burnt

[@jonathanryals9934]

As the games approach the ~11,800 move limit the number of additional variations will be decreasing. So, you can count the number to the halfway point then mirror it to the end for a better estimate.

[@douggale5962]

My favourite numberphile guy.

[@luisrebelo7051]

Mine too...

[@luisrebelo7051]

Mine too...

[@freshrockpapa-e7799]

Mine too...

[@flvyu]

+Anonyymi same

[@NoriMori1992]

+Flavio Andrade C-C-C-Combo breaker!

[@EnerJetix]

10^120 is called 1 Novemtrigintillion btw.

[@cgopie1]

I just looked this up and it's actually true, haha!

[@ralphy1054]

No its nontrigintillion

[@ralphy1054]

Nvm

[@gonzalo4658]

Tflolhahafacts

[@ryanxin1848]

r/iamverysmart

[@TimothyLockwoodinMexico]

“If you had a computer trying to work out the the future of the game and all the legal moves and where the game would go, it would never make a move“ So that's why Windows 7 chess lvl 10 wouldn't ever do anything

[@Oliver-bn7jt]

Because computers were too slow at the time, do a virtual machine on your PC now and it might go

[@michaelempeigne3519]

30^80 = 10^x 80 * log 30 = x 80 * ( log 10 + log 3 ) = x 80 * ( 1 + log 3 ) = x log 3 is approximately 0.5 since sqrt 10 is approximately 3.1 80 * ( 1 + 0.5 ) = x 80 * 1.5 = x 120 = x Therefore, 30^80 = 10^120

[@shyamsarkar7199]

I am a physics undergrad and i play chess casually and this is the exact question that came to my mind today. So thanks to youtube algorithm for reading my mind and recommendation.

[@trollollollhi7992]

Same, but only 1 week after this was recommended to me. Rly how?

[@gonzalo4658]

anapolis HA lol I love you already XD

[@johnfast1015]

what are the chances? Blessings

[@jerryteh420]

KZbin read my mind many times... Really sometime i couldnt sleep thinking how KZbin know whats in my mind. I am sure I din google it at all!!

[@anonymousshitposter1743]

The odds of a single game of chess being played out of all possibilities: 10^120 Odds of KZbin algorithm getting something correct: 10^100000000000

[@copythatchannel]

This guy looks like Fred and George Weasley's long lost triplet

[@joeyhardin5903]

I thought that the first time I ever saw him

[@ADEehrh]

I was thinking; Pee wee Hurmans brother

[@miaouew]

Mixed with Michael Fassbender. He looks like a wimpy Fassbender.

[@ghulamphasap.3225]

No wonder his face's familiar

[@Kiwi94fdt]

🤣🤣🤣🤣

[@sravi81]

Fun fact: The chess game numberphile showed was in fact the immortal game played by Anderssen.

[@aidanwotherspoon905]

After the first two moves (where there are already 400 possible games) you can’t get an accurate number of permutations through simple multiplication because a position where - a Rook has an open file, or a Bishop has an open diagonal across the board, or a Queen has either - has more legal moves than a position where those pieces are smothered or pinned to the King. And you’ll occasionally get a position where a King is in check and there is only one or two legal moves

[@patrickheart9390]

True but die to quantum mechanics it actually increases the number because the game goes on for longer . But nice thinking .

[@cram6916]

And then you get into situations where a different move order produces the same board. 1. e4, e5 2. d4, d5 produces the same board as 1. d4, d5. 2. e4, e5... or 1. d4, e5. 2 e4, d5. etc.

[@luizfelipemedeiros7506]

So, in other words, the variables are so many and entangled that it would take aliens with some crazy technology to calculate that 😅

[@27182818284590452354]

Now imagine the number of possible StarCraft games.

[@JuancharroVlogs]

Or League of Legends :0

[@DrEvil-uw1ju]

27182818284590452354e-19 Gaming is not really incredible since it was a factor for all games in that get popular is replayability

[@JuancharroVlogs]

***** You could say the exact same thing for board games

[@Mcraisins851]

There are infinite variations of those games. Even when considering ticks for the server to register something and truncated float values that limit the number of inputs, hardware itself causes infinite variations to exist.

[@cainfft008]

BrackenWood I wonder how many ARAM combinations there are?

[@Dixavd]

Yay, I missed James!

[@oscaar_3985]

Me too:')

[@ZipplyZane]

Dixavd Have you subscribed to singingbanana, Dr. Grimes's KZbin channel? It's got tons of math(s) on it.

[@Dixavd]

ZipplyZane I have - but he uploads so infrequently... only 3 in the past 12 months! Nonetheless, every time I see him in my Subscription feed is a joy.

[@VenomOnPC]

Don’t worry i’m back, oh wait

[@santoshmishra121]

0:29 a paper"how to program a computer to play chess" and it was on how to program a computer to play chess, ... 😂😂😂🤣🤣🤣

[@lilith10182]

When calculating the number of possible chess moves, do you also consider that each board posititon can be repeated twice before the game ends by threefold repetition? It's interesting to think about how in any position, multiple repetitions can be made that result in the same board position, in some cases, you couldn't replicate all possible moves of a given piece since the board would repeat more than twice and subsequently end.

[@kelvinnueveanimeguitar1983]

It's really hard to calculate everything precisely

[@jonathancoy5542]

Yet Carlsen played almost the same exact game 10 friggin times against karjakin

[@elpocamadre9810]

The speedster You have said ALMOST,but not the same.

[@calebmauer1751]

Did someone say Ruy Lopez?

[@marcozapata6984]

And most recently against Caruana.

[@16thcenturynormie]

@@marcozapata6984 they should become artists, they are way better at drawing

[@matija01]

Thats because any playstyle can be countered.

[@Norwegian733]

He needs to prove it by taking picture of every possible different sets.

[@quantumfool9773]

There are no matter enough in the universe to do it

[@Phoenix-kv3ou]

Anigame He could do it with one board though I mean he would die first but

[@jaysan3004]

Sicky 😂😂

[@sietsejohannes]

@@Phoenix-kv3ou Never mind the boards. There wouldn't be enough matter in the known universe to contain all the pictures.

[@Brandespada]

@@sietsejohannes Ok, and I would order you to check if there's any set missing.

[@mr.admr1016]

its so cool to think that i have played one of those games and nearly each time i play a different game discovering more of these possibilities

[@uncledallytv2878]

I’ve seen two of the number phone guys speak live now and they’re absolutely brilliant and completely hilarious, an honour

[@saad1653]

'In passing' I see what u did there.

[@visorkatossa]

Pls no

[@buddyclem7328]

SilverHound 7 En passant?

[@XDR2201]

Buddy Clem Yep it’s En Passant

[@vgamerul4617]

@@visorkatossa pls yes

[@kingscrusher]

Thanks for this video Numberphile. I have recommended this video on my recent video comments. I have been addicted to playing chess for over 30 years!. It is a game that provides constant fascination to me. There is an old Indian proverb about the game which relates to this video a bit : "Chess is a sea in which a gnat may drink and an elephant may bathe". Cheers, K

[@numberphile]

kingscrusher many thanks - and great quote

[@cheeseontoast14]

kingscrusher Yes, KC!

[@travispetit2410]

OMG KC! Love your channel and numberphile's as well

[@FJohnson001]

kingscrusher Lots of chess players watching Numberphile, methinks!

[@valentijnraw]

kingscrusher KC my man. best chess channel on youtube

[@ALF8892]

Shanon is a goofy estimate but the number would be way higher than that because some games go 120+ moves and some positions there is closer to 40-50 legal moves. Also amazing to think about in many positions there is only 1 move that dosnt lose or get checkmated

[@michaellautermilch9185]

Agree - "all possible games" should include billions of games having 500+ moves. Seriously just run a simulation of 1,000 games where legal moves are selected at random. See how many moves it takes on average to complete a game.

[@shouldersofgiants4649]

What an excellent video! Loved it lads

[@matheusalcantara9021]

math + chess = perfect

[@kiwigamer1418]

Agree

[@projectmilk3267]

Plus music

[@cindyrichter17]

Cheth

[@proxyprox]

Chess ⊆ Math

[@timsonins]

Is chess related to science?

[@owenivor]

You had Anderssen-Kieseritzky playing in the background! (Anderssen's immortal). Nice choice of game!!

[@iiglassfaceii6370]

Noticed that too! Lovely!

[@larslowther1495]

Yeah I recognized it when kf1 was played... ingrained in my brain

[@ethang8250]

Love the play through of the OG Immortal Game, makes me want to watch agad...

[@jacoby7036]

Awesome video! It was very educational and entertaining!

[@alexfauble3235]

Most games of chess would be extremely long games, as the number of possible sequences increases exponentially with the length of the game. Consider games where players cooperate to maximize the length of the game, by advancing pawns and/or capturing pieces only every 49.5 moves, with the minimum 8 pawn captures to allow all the pawns to pass each other and advance, these games all last 5949 moves. If we assume there's an average of 20 non-capture non-pawn non-mate moves each ply during those games, the number of possible sequences would be ~20^5949 or about (10^1.3)^5949 or about 10^7740. Certainly Godfrey Hardy wasn't invoking the 50 move rule when he came up with his figure. I suspect his estimate was based on an estimate of the number of possible positions constraining the length of the game through the 3 move rule. That's a lot more difficult to calculate. One article I found cited 4.1529*10^40 possible positions. This caps the number of possible sequences below 10^(10^42).

[@Fleshcut]

And even more astonishing than the dead numbers: Magnus Carlsen (chess GM and current king of chess) said that he sometimes remembers a board and knows what to do because he played it already before.

[@Trias805]

Fleshcut He's a robot from space

[@tgwnn]

Yago Duppel Yes that's true, it's not at all unusual. I'm a 1700 player and I also parrot a lot of theory, sometimes into the 20's! In fact one of the most amazing recent preparations was David Navarra against Radoslaw Wojtaszek in which he apparently knew the whole game up until move 25 when he moved his king to f6 as white! Move 25 per se is not impressive for a GM but bringing your king to f6 as per said preparation is.

[@jaimesantos809]

Fleshcut That's because in reality chess games aren't as diverse as in theory, because there're strategies and counter-strategies in act which means the possible moves are greatly reduced. There are still many possibilities in this case and it's a great feat to recognize those patterns, but its humanly possible.

[@Sapiensiate]

tgwnn A lot of GMs, I'm told, when playing weaker opponents will make slightly inferior early moves in order to get off of well known lines in the anticipation that their opponent has memorised the theory. Not sure if that is actually true, but it seems to make sense. Have you ever encountered this?

[@Sapiensiate]

tgwnn Wow, that's an awesome answer, thanks. And grats on punishing that guy!

[@glowstonelovepad9294]

There is a maximum of 132 moves that can be made on each turn. If the 1000-turn rule is there, then the maximum number of games is 132^1000 = about 3.74913 x 10^2120

[@varimo9924]

My boy

[@secretunknown2782]

Dr.Bishop : I have seen trillions of possibilities of chess game but we win only one time

[@jasondoe2596]

Wow! I *love* both chess and Numberphile, so this was a pleasure to watch! I was already familiar with Claude Shannon's simplistic -yet eye-opening- calculation but I still learned a few things. Now Brady we want a companion Computerphile episode series(!) about all those Minimax/Negamax variants and chess engine optimisations ;)

[@jasondoe2596]

P.S. Cool and very "romantic" King's Gambit game. Does anyone know more details about it?

[@jasondoe2596]

***** Oh, so that's why I was sure I had seen it somewhere! Thank you.

[@Kolinnor]

Now, the number of possible games on Hearthstone ? With 889 cards, it must be a HUGE NUMBER !! Oh, wait, most of them are trash. About 3 possibles games against secret pally.

[@Wyti]

You still play Hearthstone, right?

[@trunghungpham9414]

Also. The example you used in the video is the Immortal game as well. Very nice!

[@cihant5438]

Here is a more interesting question: "How many games of chess are there where neither side makes any mistakes"?

[@jixster1566]

One

[@eoghan.5003]

Or maybe it's none, if we accept that if you do not win, you must have made a mistake. There will always be at least one player who did not win, and therefore has made a mistake.

[@cihant5438]

@@eoghan.5003 No, you misunderstood. By "making a mistake" I mean make a move that changes the optimal outcome from your perspective from "winning" to "draw", or from "draw" to "losing". So if you are already losing (with best play of your opponent), then by definition you cannot "make a mistake".

[@henryambrose8607]

@@cihant5438 To get that answer, one would have to mathematically solve chess as a game, which I think is several (or many) years away. Maybe quantum computing and AI will make it possible. The answer could well be one, assuming that there is never a situation where multiple moves can be considered equally correct, which I'm not sure is possible, given that you can have a knight in a position such that it can move to two different squares and still be "attacking" one common square, for example.

[@eoghan.5003]

@@cihant5438 Is that not the premise I work from in my first reply? The result would be many many games where neither makes a mistake.

[@punishedwhispers1218]

Very impressive....but how many Age of Empires games are possible?

[@Cleric775]

Oooh.

[@Lummerbummer115]

Infinite, or nigh infinite given that the maps are randomly generated and the odds for two maps of the exact same size having their trees, resources and everything in the exact same positions is already astronomically high. I'm not sure but I think medium maps are 500x500. I'm not a mathematician but I learned something in high school that was about ordered positions where one spot is selected, therefore the next spot has to be any other spot, and so on till the final spot. I can't remember if is factorial or XchooseY or XpickY (yes there's a difference b/w pick and choose). So for simplicity sake I'm just gonna pretend it's factorial. So, the amount of possible positions on this 500 by 500 board is 500*500=250000 250000! (! Is factorial) that means 250000*249999*249998...all the way down to 1. For reference 25! is 15.5 septillion. But let's say you only play on one custom made map that is the exact same every time and you also play as the same civilizations. Now you have to deal with game ticks, which generally are about 60hz (60 times per second). Now in order to count the amount of possible games you would need to determine the exact location of each unit, number of units, health of each unit, etc. 60 times every second for the entire game, which, from what I have seen, most competitive games last b/w 45minutes to 1h30minutes. Maybe you can say screw the tick rate for the position, given that the units cannot "land" between tiles at the end of a move. Keep in mind that I'm still missing variables such as building locations and the number of potential matches is already incalculable. Even if it were a chess game on a 500x500 board with no obstacles (trees, water, etc. As so in age of empires) it would already be a preposterously large number. googolplex to the power of a googolplex or something insane like that. But to add in multiple tens or hundreds of specific variables that change potentially 60 times a second (speed of creating units for example), and multiply that by say 1 hour average? ... Although infinity is not achievable, this number would be indistinguishable from it. Probably something like (Planck time of the universe to the power of the Planck length of the universe) factorial

[@PianoGamer64]

Ye but the RNG is likely seeded with a single 32 or 64 bit number

[@patrickberbon3135]

Like 10 until the enemy attacks you while your still spamming villagers to gather resources because they just spammed temple units the second they got to the second age and then you quit the game.

[@HardCorn12]

how many "wololo's" are possible?

[@frankhaugen]

My head is rejecting input after thinking about these numbers...

[@MaxMerazMaxEmme]

Your picture fits great with your comment

[@ChessdumyTV]

Max Meraz I know right?

[@amandavo8668]

Frank R. Haugen I I have been in touch to Dragonite I am so sorry you

[@prismarinestars7471]

I was just thinking about this problem yesterday, now I see there’s a numberphile video about it

[@HayashiManabu]

In case you were wondering, the chess scenes that were peppered throughout the video came from Adolf Anderssen’s Immortal Game. I highly recommend you watch this game. It’s a brilliant example of romantic chess.

[@KillianDefaoite]

I see you using the Immortal Game as your chess animation ;)

[@izanagigod2185]

Killian Defaoite That's right

[@nychold]

@1:22 Whoa...when was the last you saw THAT variation of the King's Gambit? Jeez, what is this, 1851?

[@nychold]

***** Well, that is the Immortal Game, which took place in 1851. :)

[@branseed3479]

I think the best way of analyzing this would be getting a chess database that analyses how many possible moves there are on average on each turn. For example, there are always 20 options on move 1. But after that it depends. If you play A3, you’ll still have 20 options on your next move but if you play E3, now your bishop and queen can move so you have 28 combinations. If you get a database that analyses every game played (which wouldn’t be even near complete but at least it’ll give a much better range) and you get a number for options for every game. In this case for example, on move two, one game will have 28 options, other will have 20, and then you take all these numbers and get an average for the move 2. Than we’ll know for example, out of all the games that lasted 100 moves, how many options did they have on average per move. Then you can get a much more precise estimate. Then you find games that lasted hundreds of moves and calculate how many options they had on average and then you can estimate the rate of which the options will lower (for the game to be that big you’ll need pieces to be captured lowering the options) even in a game with over 10 thousand moves, there’ll be many options anyways because the kings are likely going to be far from each other and that by itself means they can each move to 8 different squares. Considering you need to have at least a king and a rook or a pawn for it not to be a draw, you can have up to 14 other options just by having a rook. Totaling 22 options even with only a rook and a king.

[@uuproverlord8324]

Longest chess game is like 8k moves also losing a peice doesn't necessarily lower options either

[@Geegs]

​@@uuproverlord8324The longest chess game possible is 5898 moves.

[@JavierArveloCruzSantana]

I love Dr. Grimes ever-present smile while talking about math.

[@simon.jacobs.0709]

Now let's see him calculate the number of atoms in the observable Universe.

[@sebastienpaquin4586]

Its surprisingly easy to calculate, we know that a cubic meter of empty space contains on average about 6 protons and that the observable universe has a radius of 46 billion light years (en.wikipedia.org/wiki/Observable_universe) for a total volume of 4,0772e32 cubic light years. One light year equals 9.461e+15 meters, so one cubic light year equals 8.468e+47 cubic meters, giving the observable universe a total volume of 3,452573e80 cubic meters. At 6 protons per cubic meters on average, you end up with approximately 2.07e81 proton in the universe. Now since only about 75% of all matter in the universe is Hydrogen (1 proton per atom), the total number of atoms will be a little lower, so perhaps around 1.5e81. The thing that really struck me calculating this is that even if we add all the mass of all the stars in the universe, the number barely goes up.The problem is that although a star's density is much higher than empty space, they are so minuscule compared to the vastness of empty space filling the universe that their combines total weight is almost insignificant. There are about 2e11 galaxies in the universe, each containing about that many stars, giving 4e22 stars in the universe. Our sun is a little bigger than the average star in the universe but we can still use it as a reference point. With a weight of 2e30 kg and mostly made of hydrogen, we can calculate that it contains about 1.2e57 atoms. Multiply that by the number of stars in the universe (4e22) and we get 4.8e79 atoms in all the universe's stars. Although this seem very close to the number 2,07e81 we had for all the mass of empty space, adding them both together bumps that number up by 0,048e81, which is about as small as the error margin for the calculation.

[@lilak-4741]

It's already been calculated. :)

[@simon.jacobs.0709]

Or the telescopes we use.

[@louisfranz1941]

i always wondered how the observable univers can be more billions light years in radius big then the universe is old because the the groving of the univers must have been faster then light or did it .. ?

[@portgasd.shanks356]

Chuck Norris plays all variation twice a day

[@miaouew]

Go back to 2006, injun

[@kinuux]

Chuck Norris wins before the game even has started

[@dominicgallagher8930]

But the only person capable of playing so many games is chuck norris which means he must be playing against himself which means he must have lost the most number of games in chess history.

[@martinet1985]

@@dominicgallagher8930 chuck wins even if he loses. such is life.

[@robinkhoury5579]

Hahahahhahahahahhahaha

[@derekliu4917]

this is why you should play chess. you'll almost never end up with the exact same game

[@ottlight]

100x100x100 Rubix cube: You under estimate my power

[@shezacuber6092]

@@ottlight hello fellow cuber

[@SanxBile]

"Almost"

[@antonpogorevici]

laughs in scholar's mate

[@skyerisma4627]

Tell that to the berlin drawers

[@NStripleseven]

0:35 ...it was about how to program a computer to play chess. Hmmm... The floor here is made out of floor.

[@NStripleseven]

asdf hjkl 🤷‍♂️

[@igorz4582]

Haha a meme

[@Infinite_Omniverse]

I love this kind of stuff

[@ThrawnTheater]

Look at how bright his eyes are, the passion is flowing out of Dr. Grime!

[@thecoolring6431]

3:11 *MATHS IS THE NEW WEED*

[@evetheeevee2977]

Close to π

[@thecoolring6431]

@@evetheeevee2977 seems Legit

[@BianLee]

Maths is the new meth

[@HooyahPeacock]

Scientifically speaking it would be the new cocaine since high functioning professions etc prefer cocaine... not weed

[@komstratyxspiele9613]

I want these numbers for our game Bollwerk 178. You have over 2000 options for the first move. It is great fun and very exiting!

[@truth1901]

I ate my chessboard, it was stale mate. " No it was NOT ! ! ! " Yes it was, check mate.

[@tohrulol]

The example game being played, by the way, is Anderssen vs Kieseritzky, 1851. Anderssen's Immortal Game. I liked his Evergreen Game better, though.

[@TheDigiWorld]

For everyone who might not have known, the game shown at the beginning of the video (the queen sac at 3:35 ) the game is called "Immortal Game" and it is a real game played by Adolf Anderssen vs Lionel Liezeritsky back in the era when there was no idea of chess computers and players were never afraid to make sacrifices that seem unimaginable today because apparently the computers can refute it

[@blipmachine]

Recorder guy said “that was the most wishy washy!” just as I thought the same.

[@General12th]

I like how one of Godfrey Hardy's biggest contributions to mathematics is discovering Ramanujan. Forget all his other achievements, he's famous for introducing the greatest mathematician of all time to the world!

[@cloerenjackson3699]

Great comment. :)

[@noblerkin]

You forgot Gauss and Euler.

[@changenoways9555]

@@noblerkin Ramanujan did what Euler did in a shack in India at the time of Colonial Rule. I think in this instance, we have to award 1 point to the Indians

[@skoto8219]

I recall reading somewhere that Hardy himself said that discovering Ramanujan was his greatest contribution to mathematics.

[@dhruva8538]

@@changenoways9555 yeah also India started calculus trigonometry geometry navigation etc Even chess invented in India Mostly later appropriated by west later

[@AhrkFinTey]

6:42 The rule states that if both sides have insufficient material to do a checkmate, then it is automatically a draw.

[@szczur0192]

Most of the games would be just a ton of blunders

[@FreeZeon1]

Szczur01 but if you think about it, every game that is not drawn contains some kind of blunder. Although I get your point - most of these games would be all silly moves

[@hermannihietalahti4818]

Jonte Friedrichsen thats actually not true, otherwise when Googles alphazero played against itself (best chess entity in the world) it would have always drawn, but thats not the case.

[@henryprickett5899]

@@hermannihietalahti4818 even alphazero plays inaccuracies, otherwise it wouldn't be getting verifiably better. Chess isn't solved in closed form yet.

[@TheVesper00]

@@FreeZeon1 drawn game also has a blunder (both players missed something) becouse you didn't won.. the main goal i chess is to win a game, so everything else is the blunder...

[@masaaki14]

@@TheVesper00 drawn games occur in 2 forms. If both players play the best move possible, it will always end in a draw. If both players fail to take advantage of blunders, mistakes and inaccuracies equally, it will also end in a draw. The only games where one wins is where one person takes better advantage of such mistakes

[@KedarOthort]

I just realized the game you're showing while talking about the moves is the game Iron Bull vs Solas play of mental chess from Dragon Age Inquisition.

[@TheTeddyZerg]

Maths is like crack for this guy :D

[@LoganBeck11]

7:18 Fit the set {(1, 20), (2, 400), (3, 8902), (4, 197742)} to an exponential fit of y=0.8995*e^(3.07x) with R^2=0.9999. So with your game limit of 11800, the number of games is y=0.8995*e^(36226), which google calculator confirms is infinity.

[@sleepful1917]

is this 10^8857.599?? i think right??

[@chasington5102]

blake yes I think

[@janmachacek4866]

That Andersen's game behind is just magic

[@dachijachvadze88]

You can't know exact number from third move, because after first move (and second also, you can't block opposite sides squares on first move), every next move played has effect on next moves probable max count, meaning I can move bishop or knight on third move and numbers will change drastically starting from next move, till the end of sequence mentioned in video.

[@oranmacphersonraffell8966]

8902/400 is pretty similar to 197,742/8902= about 22.13ish. This suggests a pattern. If you calculated one or two more steps to get a really accurate decimal, then would the calculation be: 197,742/8902(multiplier)x11,800!(possible number of games) Which equals: 2.06274285385227894242625743373618656671452552174656780709750617838687935295439227139968546394068748x10^42927 Or something like that.

[@kevinsandow5354]

The game shown is the andersson inmortal, which I just saw in Agadmators channel. Great youtube algorithms.

[@helloeveryone1512]

I just realized that this was the Immortal game of Anderssen where he sacced both his rooks and queen for mate

[@PaPapsters3294]

Wouldn’t there be an infinite amount of chess games because both players could choose to move a non-pawn piece back and forth any number of times before moving another piece to progress the game? Edit: Just to be clear, I wasn't aware of the threefold repetition rule when I typed this comment. I'll still leave it here though.

[@tiago9617]

It's a draw by repetition

[@nothinggood2696]

Not if you include the rule to not make the same moves 3 times

[@michaelcarr9032]

theres draw by three fold repetition and draw by 3 move rule ie both players move same piece same place over and over 3 times

[@brock2k1]

Geez, people take things so literally. Of course you could make a game last forever, even with the three-move rule. All you have to do is repeat the same four-move cycle endlessly. Make one of the moves a check, and you also evade the 50-move rule.

[@AnstonMusic]

It feels weird to remember that I actually met James Grime in person in Helsinki, got on stage too. =D He gave a great speech, although much of it was not new to me as things he discussed had been introduced on this channel.

[@j0nthegreat]

Anston Music when was that? i was JUST in Helsinki

[@j0nthegreat]

Anston Music cool beans. i'll probably never get to meet him

[@EtzEchad]

Back in the 70s, I wrote a program to play chess. Even if you are only looking a few moves ahead, those numbers grow incredibly fast.

[@zeezmusic7245]

I play the same opening which has the same principle moves and same goals which you try to achieve in the position, and lots of my opponent play similar replies for 10 to 13 moves and every single game is never similar to other, that's why I love chess.

[@Daniel-mb5qo]

Theres actually inffinite amount of moves, because they can go back and fourth with a slight variation every time over and over

[@petermueller3349]

6:31

[@joaquinplacides2]

threefold repetition rule

[@GamesFromSpace]

I could never be a mathematician. The sound of markers on paper drives me nuts.

[@gacorley]

Joshua Pearce Haha, well, there's no rule that mathematicians HAVE to make Numberphile videos.

[@wdsrocha]

Joshua Pearce Tip: Do not use markers on paper

[@SuperDipoleMoment]

Joshua Pearce Your low IQ would make it pretty difficult also, lol.

[@gacorley]

Chess Master That's just mean.

[@SuperDipoleMoment]

George Corley No, it's not just mean. It's also factual.

[@minecraftermad]

and THIS is where quant computing would shine

[@clansman89]

4D chess

[@glitchysquid1137]

I wonder if the estimation also considers conceding. In that case, you would have to add every move set with one another as well.

[@guidovrola5231]

Even if they only are very rough estimations, this number has to be hugely cut down, by the fact that a lot of variations can take you to the same position of the pieces on the board.

[@justinlewtp]

That first chess game, Brady sacrificed his queen and both his rooks and won the game!

[@MrCanadiandude1919]

+Justin Lew (MC Gamer) I don't remember from where but I swear I have seen that game from a famous grandmaster from history. He may have played it but I get the feeing it was borrowed from the romantic era of chess and it belongs to a GM of note (Andersson Maybe?). Still a cool video though!

[@justinlewtp]

Ryan Gonsalves yeah I recently realised it was a match between Adolf Andreessen and Kizertsky

[@ayylmao3480]

amazing game :D

[@oithornley7466]

Yeah, his "immortal" game was pretty sick

[@thenozar7603]

Shanon's estimate was so wrong simply because you eliminate pieces in the chess game, so the number of average possible legal moves should not be 30

[@jamespeter570]

The Nozar interesting thought might also create more legal more as would free up space on the board in some cases. The video would stand correct if the averages used stand for the whole game of chess with different combinations. but it would be hard to tell for sure if the guess is conservative

[@j0nthegreat]

The Nozar as soon as you open up the bishop, queen, and rook the number of legal moves increases dramatically. you can move each one 1 space, 2 spaces, 3, 4, 5, ... in multiple directions

[@twistedsim]

The Nozar Yeah, but near the end, the rooks and the bishops have more place to go since the board is less concentrated, so you need to count every case they can go on.

[@GraveUypo]

Simon Bouchard that's why it's an average.

[@twistedsim]

I know. Was talking to Nozar.

[@duckmeister5385]

The further along in a game one is, the fewer pieces are left on the board, so it would seem the law of diminishing returns would apply.

[@JoaquimAMagalhaes]

I wonder what kind of data would be possible if every single computer in the world analysed chess combinations for a few minutes everyday and organized them

[@michaellautermilch9185]

The number of computers in the world wouldn't be enough, due the the exponential nature of the problem. If you want to look into 10^120 permutations and can use 10 billion computers, each computer gets to solve for 10^110 permutations.