ChessPositionRanking VS syzygy-tables.info

3. There's extra nuanced things you might want to handle in the coding, like that pawns can't be on their own back row. That is significantly harder.

It looks to me like https://github.com/tromp/ChessPositionRanking has resolved these sorts of issues, but I haven't dug into exactly how.

Multinomial rankings can be combined with a dozen others to rank a subset of all chess positions including all legal ones. This allows one to sample millions of random such positions, determine how many are legal, and thus obtain an accurate estimate of 4.8&10^44 legal chess positions [2].

[1] https://github.com/tromp/ChessPositionRanking/blob/main/src/...

[2] https://github.com/tromp/ChessPositionRanking

The key words being "without promotion". Both bounds, this one and Steinerberger's, only consider positions reachable without promotion. Allowing promotions, one estimate suggests that the number is close to 4.82 × 10^44.

source

This one as well as Shannon number wiki seem to say that possible sensible moves are about 10^40 while and 10^120 while taking any moves (maybe including some illogical / illegal ones) .

Shannon's estimate was based on very primitive methods; by generating random positions and using fairly advanced methods to see whether they are legal or not (ie., can you construct a proof game for it, or prove that it could never happen), you will get much closer. A group of people have been working on this, and their current best estimate is (4.822 +- 0.028) * 10^44, or a bit over 148 bits. (Amazingly enough, Shannon wasn't all that far off on this account! His estimated number of legal games seems much more dodgy, though.)

http://talkchess.com/forum3/viewtopic.php?f=7&t=77685&sid=e3...

Practically speaking, https://github.com/tromp/ChessPositionRanking gives a number between 0 and approx. 8.7 * 10^45 for any legal position, so it's only a couple of bits away from optimality.

The number of chess positions has now been estimated with 2 digits of accuracy as ~ 4.8 x 10^44: https://github.com/tromp/ChessPositionRanking

If both sides play correctly, yes this is a draw. Chess is solved with fewer than 7 pieces on the board. At this website, you can check any such position and see what the result will be, assuming perfect play from both sides

There is some truth to this.

In theory, chess is a game of perfect information.

But in practice, this is only true for ~6-piece endgames: every outcome has been / can be computed. But for any middle- or early-game position, the amount of finite information greatly exceeds any person's or computer's capacity, practically speaking.

In concrete terms, the tablebase for 6-piece endgames is ~150 GiB. For 7-piece, it's 16 TiB.

[1] https://syzygy-tables.info/

Syzygy-Tables https://www.chessprogramming.org/Syzygy_Bases

Alternatively, if you're playing an endgame with seven or fewer pieces, I suggest you use the Syzygy 7-piece tablebase to get the objectively best response on every move.

I suppose you mean the syzgy 7 man tablebases? Yes, they do take 50MR into account because they use DTZ metric (fastest way to checkmate, capture or pawn move).

I'd assume that Stockfish just hasn't found the M9. Tablebases already know the quickest mates in a given position, you can check the tablebase here