A Go Complex: Space and Go

[lance1236451]

haha let play rotem bet ur like a 5dan now?

[makemehavefun]

interesting... I just read that a game of go/weigi/baduk is capable of more permutations than there are subatomic particles in the known universe. I'm going to stand up now and think about that until I can fully imagine and comprehend it.

[Gerstein1]

0:50 world's largest seki.

[XshlomoX]

more like world's largest stupidity

Its a mirror game...

[Gerstein1]

Most mirror games start at the center, don't they? Even so, mirror games are stupid :P

[lolsa123]

@XshlomoX mirror game? dude...

[Muffinman10123]

MOLECULES of Hydrogen?

[LinkTetraWW]

Yeah, H is a molocule composed of 1 H atom...

[computernerd1101]

A Hydrogen molecule is composed of TWO Hydrogen atoms! Honestly, do your homework!

[LinkTetraWW]

What was I thinking, thanks...

[Kree19]

I'm not going to read all the discussion of the math problem below, because I'm just that lazy. However, I believe that excluding the more complicated rules like ko and such that make some positions impossible, the equation would be 3^(19*19), which is greater than the sum of particles in the universe, not just hydrogen atoms in the sun :-)

Great vid, thanks Hikaru.

[computernerd1101]

3^(19*19)=3^361>3^360=3^(3*180­)=(3^3)^180=27^180>10^180>10^1­00

There are fewer than a googol atoms in the observable universe.

On the other hand, not all those 3^361 moves are legal.

(# legal positions) > (# legal positions with no white stones)=2^361-1>2^361-2^360=2^­360=2^(10*36)=(2^10)^36=1024^3­6>1000^36=(10^3)^36=10^(3*36)=­10^108>10^101>8*10^100 (I'll explain the significance of this later) > 10^100

[computernerd1101]

I didn't have enough character space in the last comment. Anyway, some board positions transform into other equivalent positions. Others transform into themselves.

8*(# of legal equivalent position classes)>(total # of legal positions)>8*10^100

(# of legal equivalent position classes)>10^100

[gildude09]

lol hikaru i am gildude, and u are hikaru usa from kgs go server

[rotemrocks]

we should play on kgs together once!

im 7k

[hikaruUSA]

sure, whats your sn?

[rotemrocks]

my name is "guitarmode" pm me when u can

[mediteight]

Neat video, thanks for making! (just pondering a conservative estimate - suppose during the Go game there are at least 200 moves which had 10 possibilities each, then the number of possible games would be over 10^200 which would completely dwarf the estimated number of atoms in the known universe (10^80). In fact, if each atom had its own little universe with 10^80 more particles, there would still be too few by a factor of a thousand trillion trillion trillion :) just a thought...

[hikaruUSA]

hmm, wow. ok, well here are the numbers: A game of go has 361 moves, then 360 and so on... so I think the equation would be y=(360-x)360. I think that may be right, but it might not. Anyone have corrections?

[hikaruUSA]

** if x is the move number (starting from 361 down to 1) and y is the ammount of combinations left. it seems wrong, so whoever is smart out there, i need some numbers =D

[mediteight]

Interesting problem :) I suspect that finding the exact number of possible games would be extremely difficult (given ko, capturing etc.) Your idea of counting all possible arrangement of 361 stones may be a great estimate though, giving 361 factorial (361x360x359x...x3x2x1) or around 10^768. My far lower estimate was an attempt to avoid counting the random looking games this would include. These numbers are too big for me to imagine anyway tho' so I'm off to play :)

[ThoVBui]

@hikaruUSA It should be (361-x)! where x is moves made.

[OmnipotentEntity]

@hikaruUSA On any move you may either place a stone or pass. So there are 362 options for the first move, ignoring symmetry. And then ignoring that certain moves may be illegal (suicide or ko) there is exactly one less option to move each turn. This is also ignoring that stones may be captured and therefore their points are open to be played in again. In this case we would need to adopt a superko rule that states that no board position can be repeated in order to come to a finite answer cont

[OmnipotentEntity]

@hikaruUSA So, the answer to the question (how many go games are possible) is very complicated and difficult to model, but it would be fair to estimate 362 factoral (362*361*360 etc.) Which is about 5.2 x 10^770 which is a colossally big number that I cannot communicate to you well in physical terms.  But which is far larger than wolfram alpha's estimate of the number of go positions 4.6 x 10^170

I'd be more inclined to trust wolfram alpha's estimate.

[ckala13]

@hikaruUSA I know this comment is super old, but just saw it now and I think it's a permutation so it should be 361 factorial (361*360*359...*1). That's a big number lol.

[sakonukon1316]

awesome video

[hikaruUSA]

Thanks, I will be making one soon of go and religion. I want to embrace all prominent religions into my next video, so if anyone has suggestions just message me

[sakonukon1316]

it would be y=(361-x)360, because every move there is one less point;-x;and evry move you have to multiply that by the number of spots left to get the possible number of games that could be played.