How many chess games are possible? - Numberphile 

Lol

🤣🤣🤣

This comment deserves soooo many more likes.

and both players are still in their home preparation

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

Alex Pătraru that was my joke

No he smokes A TON OF METTHHHHHHH

Alex Pătraru pls dont comment again

top illin you might be onto something

Alex Pătraru that, was just totally pathetic.

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

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

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

mircea tim true

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

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

i bet your opponent's king doesnt :D

@@mikezinj BURNED!

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

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

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

Agreed. Awesome.

Wow, I didn't notice that ! Thanks!

castling woud work

You can`t castle out of check.

lol how is this not top comment

I don't get it. Please explain.

It took me 0.29 minutes to get

MLG Gaming so a little under 20 seconds?

Yes

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.

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

Oh no my queen

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

It is a very known mate pattern

Agadmator has covered the game. I recognized that checkmate!

Thanks.

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.

Absolutely gorgeous

@@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.

then its Bishop A5

@@KanishkMalkan You bet

*B5

and A6

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

Erik István Fejes..... gg

hahahaha, lol

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

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

Same,

I see a man of culture

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

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

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

Who needs theory when you can russian roulette pawns? 😎

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

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

Gond question

F

F

F

F

F

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

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

🤓

Coley Amos 😂😂😂

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.

Was looking for this comment LOL 😂 a true chess fan

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

That’s a great sentence thank you sir!

@@tarabinsurzo You are welcome.

Underrated comment

hahaha

I usually sacrifice my king for the win.

You sacrifice your king ummmmq

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

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

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

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

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

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.

"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?

9:15

en crossaint

r/anarchychess losing their minds

EN PASSANT

Nicolas Terbeek unoriginal

cocaine*

pop9095 Er, did you respond in the right thread?

woo hoo I take honey baby 😘

uk

I take cyanide in my tea.

Mine too...

Mine too...

Mine too...

+Anonyymi same

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

Xqc is still recovering from that day

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

2021

@@guts1859 Someone is burnt

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

No its nontrigintillion

Nvm

Tflolhahafacts

r/iamverysmart

@@MetalRaydown Yes, it was. Google owns RU-vid, and RU-vid makes a net loss.

I am the 69th like

@@henryambrose8607 Google doesn't own RU-vid. Alphabet owns both.

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

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

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

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

anapolis HA lol I love you already XD

what are the chances? Blessings

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

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

I thought that the first time I ever saw him

I was thinking; Pee wee Hurmans brother

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

No wonder his face's familiar

🤣🤣🤣🤣

Or League of Legends :0

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

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

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.

BrackenWood I wonder how many ARAM combinations there are?

Me too:')

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

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.

Don’t worry i’m back, oh wait

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

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.

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

It's really hard to calculate everything precisely

Agree

Plus music

Cheth

Chess ⊆ Math

Is chess related to science?

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

Did someone say Ruy Lopez?

And most recently against Caruana.

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

Thats because any playstyle can be countered.

kingscrusher many thanks - and great quote

kingscrusher Yes, KC!

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

kingscrusher Lots of chess players watching Numberphile, methinks!

kingscrusher KC my man. best chess channel on youtube

Pls no

SilverHound 7 En passant?

Buddy Clem Yep it’s En Passant

@@visorkatossa pls yes

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.

There are no matter enough in the universe to do it

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

Sicky 😂😂

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

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

Noticed that too! Lovely!

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

Fleshcut He's a robot from space

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.

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.

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?

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

One

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.

@@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".

@@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.

@@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.

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

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

You still play Hearthstone, right?

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

Oooh.

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

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

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.

how many "wololo's" are possible?

Go back to 2006, injun

Chuck Norris wins before the game even has started

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.

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

Hahahahhahahahahhahaha

Your picture fits great with your comment

Max Meraz I know right?

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

My boy

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

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

Killian Defaoite That's right

Close to π

@@evetheeevee2977 seems Legit

Maths is the new meth

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

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.

It's already been calculated. :)

Or the telescopes we use.

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 .. ?

100x100x100 Rubix cube: You under estimate my power

@@ottlight hello fellow cuber

"Almost"

laughs in scholar's mate

Tell that to the berlin drawers

asdf hjkl 🤷‍♂️

Haha a meme

Anston Music when was that? i was JUST in Helsinki

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

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

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.

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

@@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...

@@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

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

blake yes I think

Great comment. :)

You forgot Gauss and Euler.

@@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

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

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

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

Joshua Pearce Tip: Do not use markers on paper

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

Chess Master That's just mean.

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

4D chess