aaronliftig / chessupperbound

An individually derived expression that computes a strict upper bound of chess positions, and a generalization of part of that expression which finds the total number of piece combinations for an arbitrary number of piece types and counts.

chessUpperBound

upperBound.py

is an expression that computes a strict upper bound of chess positions. The expression includes many illegal positions, and I intend to refine the expression in time.

The current output is: 3.0697566281670323e+63

This is a slightly optimized version of second expression from my paper "Of Games Greater than Ours:..." seen here:

https://docs.google.com/document/d/1UWJC7tDZ8oAECuALFpj7aFKycrjLjSlN7t3B_SGteis/edit?usp=sharing

GeneralTotalPieceCombinations.py

is an expression that counts all of the various unique piece combinations if chess had an arbitrary number of piece types and each piece type had an arbitrary number of duplications.

This algorithm has other applications, but the chess applications was its original inspiration.

This is the first and main expression found in the paper in the link above.