What is the number of legal positions in a chess game? There have been several questions regarding the possible number of chess games. for example; Database of every possible move in chess. However,can there be an estimate on the number of &quot;allowable&quot; chess positions?
For another example, White pawns cannot occupy the first row and Black pawns cannot occupy the eighth row. If a given chess piece is occupying a square, then another chess piece cannot occupy that. Using simple elimination rules coded, can we have an estimate on the number of unique positions that chess pieces can have since they would be reducing in number? An upper bound on positions before applying any elimination rules would be the sum of (64 C 32 + 64 C 32 ... + 64 C 2). This is less than 10^20. With elimination rules, they should be significantly lower.
Any ideas on how elimination rules are written for chess pieces?
Upper bounds on the number of allowable positions are discussed on the Shannon number  Wikipedia page.
There is an accepted upper bound of 5×10^52 by Vicor Allis, and a less verified upper bound of 2^155 (approx 10^46.7) by John Tromp.
By comparison, the number of atoms on earth is about 10^50.