A single integer N = a complete chess game

[Maximilian Hasler]

>> over-the-board play do not approach that number of possible moves. I also
>> suspect that there are moves that are much more likely to occur in
>> over-the-board play, making Huffman encoding seem like a possible avenue for
>> shrinking the game description.

I also thought of that, but looking at the first moves (opening), I
realized that there are not so many, and 1/3 of them are quite
probable.
OTOH, in a more advanced position of the game, I think it is difficult
to estimate the "probability" of a move easily in an efficient way.

>   be converted back to a game, then you can simply define a way to order
>   all the possible chess games, and use the index into this list to
>   represent the game.

I'd dare to conjecture that the encoding I proposed is roughly
equivalent to this,
modulo using no pseudo-moves until the end of the game and to use some
reasonable convention for coding the end of the game (when the "remaining"
G[i] is/would be below a small limit)
to ensure that indeed by construction, every integer G corresponds to
exactly one unique sequence of moves and vice versa.

Maximilian