Perfect Information Game: On Chess • Hacker News Board

Re: Perfect Information Game: On Chess

#31

Post by eric_h » Sun, Jun 05, 2016, 1:26 AM UTC

Pamar wrote: post #12

dkbrk wrote: post #4

I don't mean to diminish the accomplishments or skill of chess players, but in my opinion being a perfect information game makes chess, like go, much less interesting. It means that, in principle, it is simply a matter of running Minimax on a sufficiently powerful computer, and the game can be solved. I do mean 'in principle': actually doing this is still well beyond the world's computational capabilities, though thi…

Regarding your surprise about chess being played as a sort of wargame: actually when used as such, they did include "fog of war": https://en.m.wikipedia.org/wiki/Kriegsspiel_(wargame) See also: https://en.m.wikipedia.org/wiki/Kriegspiel_(chess)

Blind chess sounds like an extremely difficult game. I really want to play it.

Seems as though it's most easily played as a computer game.

Re: Perfect Information Game: On Chess

#32

Post by ybird » Sun, Jun 05, 2016, 3:03 AM UTC

chongli wrote: post #20

ybird wrote: post #17

Earlier quoted context omitted.

> we can't in reality solve chess and go with computers I don't think this is correct. Both could be solved by determining the perfect move for each board arrangement, leading to a very simple, but very data-heavy solution (see: https://en.wikipedia.org/wiki/Shannon_number - number of chess positions somewhere below 2^155 - and also need to track for each position whether can empassant for each pawn like X-FEN does,…

I don't think you realize how large of a number 2^155 is. The number of atoms comprising the entire planet earth is on the order of 10^49 or 2^162 [0]. Thus, to store all possible chess positions using only the material available on planet earth you'd have only 2^7 or 128 atoms available to store each one. All of this is ignoring the amount of energy you'd need to operate such a device, which is even more staggering.…

A petabyte of storage would have been unthinkable 20 years ago. Think of the not too distant future.

Re: Perfect Information Game: On Chess

#33

Post by ybird » Sun, Jun 05, 2016, 3:19 AM UTC

omnigoat wrote: post #19

ybird wrote: post #17

Earlier quoted context omitted.

> we can't in reality solve chess and go with computers I don't think this is correct. Both could be solved by determining the perfect move for each board arrangement, leading to a very simple, but very data-heavy solution (see: https://en.wikipedia.org/wiki/Shannon_number - number of chess positions somewhere below 2^155 - and also need to track for each position whether can empassant for each pawn like X-FEN does,…

"In reality" means that the working set of memory and time complexity on solving Chess (let alone Go) is vastly too large for computers now and in the future. I don't get why you tacked on computers beating grandmasters/9-dans, since that has nothing to do with solving the game. Oh you added something on the end. Well, augmenting a human brain doesn't change the search space of solving Chess and Go (especially Go). Y…

I told you how many solutions you'd have to store. I don't see how that is underestimating.

Re: Perfect Information Game: On Chess

#34

Post by ybird » Sun, Jun 05, 2016, 2:15 PM UTC

ybird wrote: post #32

chongli wrote: post #20

Earlier quoted context omitted.

I don't think you realize how large of a number 2^155 is. The number of atoms comprising the entire planet earth is on the order of 10^49 or 2^162 [0]. Thus, to store all possible chess positions using only the material available on planet earth you'd have only 2^7 or 128 atoms available to store each one. All of this is ignoring the amount of energy you'd need to operate such a device, which is even more staggering.…

A petabyte of storage would have been unthinkable 20 years ago. Think of the not too distant future.

Using the following dataset of year to max drive size in bytes per year [1a][1b]: {1956,5.00E+06},{1979,5.71E+08},{1980,1.00E+09},{1991,1.00E+09},{1992,2.10E+09},{1997,1.68E+10},{2003,3.70E+10},{2005,4.00E+10},{2006,1.60E+11},{2006,7.50E+11},{2016,5.00E+12}

Linear regression provides the equation: year = 4.222874399 ln(numBytes) + 1896.534826

Assuming the average bits required to represent a board state is 160 [2], then: 2^155 positions x 160 bits = 9.13e47 bytes

4.222874399 ln(9.13e47) + 1896.534826 = 2362.87979

So, a projection shows that by year 2362, we could have a single storage drive holding every permutation of a board state, so it would be less than 2 drives to store the states along with the move to make for that board. Add more drives and you pull that date in.

References:

1a. http://www.pcworld.com/article/127105/article.html 1b. http://www.computerworld.com/article/2473980/data-storage-so... 2. http://codegolf.stackexchange.com/questions/19397/smallest-c...