# Chess: The Big Picture - A Concise Mathematical Study by Lester Moore

## [A Mathematical Study] suggests that the number of possible chess positions after the first 6 moves is 62,854,969,236,701,747 (6e16).

## I cannot verify the calculation, but let's suppose that it is valid. Then, if we assume that a billion (1e9) people have played five chess games daily for the past 500 years to represent total participation in the history of modern chess, a very liberal (upper limit) estimate of chess activity, then 1e12 chess games (1e9 players x 5 games/day x 500 yr x 400 days/yr = 1e12) were played in that period. So at most only 1/60,000 (6e16/1e12 = 60,000) of those 6-move game positions could yet have been uncovered in real games, and that ridiculously assumes that there were no 6-move repeats in the history of chess (Occurences of candidate positions later than the sixth move are possible, but such positions become less likely or impossible as the games progress; at six moves, no more than eight pieces can be removed from the board; thus moves after more than eight pieces have been removed cannot manifest any of the candidate 6e16 positions). So it seems extremely likely that fewer than 1/60,000 of these 'potential' 6th-move positions have ever been seen on any real chessboard in the post-Columbian era of chess (1493-2016).

## If all of the FENs (a FEN is a concise one-line text descriptor indicating the positions of all the pieces, etc.) for these 6e16 positions were published in a single catalog with 60 FENs on each (double sided) page, the catalog would be about 50 million miles thick (more than 1/2 of the distance from the earth to the sun.) Assuming a page size of 6 x 9 inches, one could then publish the whole book as a 500 billion volume set and house a reference library here in Dallas. The volumes would be kept on pallets with 5 ft stacks of books on each pallet. The library would occupy 240 sq. mi. The city of Dallas is 386 sq mi, so this Chess Memorial Library would cover over half of the total city area.