[Retros] A single integer N = a complete chess game

[Thomas Brand]

Some notes:

It's simple to include promotion into "my algorithm": just add two bits 
for the promoted piece to the end of a promotion move; this will keep 
uniqueness unchanged.

Marks and my approach are different: I construct a unique number for a 
single game, while Mark needs such an algorithm to "generate" a subset 
of the natural numbers, which, of course is well ordered, so he can map 
a game to its index: true, that results in "shorter" numbers, but 
requires the array of the presentation of all possible games to do so 
(and in reverse, to map a natural number to a game).

Otto is correct, that Huffman like (context sensitive) encoding will 
theoretically result in shorter (since compressed) numbers than my 
algorithm, but you have to take into account, that these "context 
sensitive information" has to be stored anywhere -- with the number, if 
you want to optimize the compression for any game notation. Or you 
require to optimise the compression for all possible games -- and than 
your approach results in the same problems as Marks: you have to take 
into account all possible games.

Regards, Thomas