Numberphile wrote:If you consider all of the games of chess ever played throughout history, that would only be a minute fraction of all of the possible games of chess there are to play.

Welcome to Chess2U - The Ultimate Computer Chess Forum!

If this is your first visit, be sure to check out the FAQ by clicking the link above. You may have to register before you can post and use all thefeatures of the Chess2U forums. To start viewing messages, select the forum that you want to visit from the selection below.

________________

Core_Engine_Tester_CCRL

https://en.wikipedia.org/wiki/Shannon_number

Shannon Number wrote:The Shannon number, named after Claude Shannon, is an estimated lower bound on the game-tree complexity of chess of 10120, based on about 103 initial moves for White and Black and a typical game lasting about 40 pairs of moves. Shannon calculated it as an aside in his 1950 paper "Programming a Computer for Playing Chess". (This influential paper introduced the field of computer chess.)

Shannon also estimated the number of possible positions, "of the general order of \scriptstyle \frac{64!}{32!{8!}^2{2!}^6}, or roughly 1043 ". This includes some illegal positions (e.g., pawns on the first rank, both kings in check) and excludes legal positions following captures and promotions. Taking these into account, Victor Allis calculated an upper bound of 5×1052 for the number of positions, and estimated the true number to be about 1050. Recent results improve that estimate, by proving an upper bound of only 2155, which is less than 1046.7 and showing an upper bound 2×1040 in the absence of promotions. Mathematician James Grime estimates that there are 1040 possible "sensible" games.

Allis also estimated the game-tree complexity to be at least 10123, "based on an average branching factor of 35 and an average game length of 80". As a comparison, the number of atoms in the observable universe, to which it is often compared, is estimated to be between 4×1079 and 4×1081.

________________

Core_Engine_Tester_CCRL

Numberphile wrote:If you consider all of the games of chess ever played throughout history, that would only be a minute fraction of all of the possible games of chess there are to play.

I subscribed to that channel, very interesting content.

The Longest Possible Chess Game?

http://www.chess.com/blog/kurtgodden/the-longest-possible-chess-game

http://www.chess.com/blog/kurtgodden/the-longest-possible-chess-game

________________

Core_Engine_Tester_CCRL

Related Topics