My first try was 1h4 g5 ... I remember a book 1Sc3 2Tb1 was the Title omitting the move for black ' . There was a Variation where the knight goes to f3 d4 b3 & a1 ! Hehehe'
I think I found all the initial novelties. Find the study called Opening Analogy. The link can be found in my profile page. When I get an RTX 40 series, I'll try to continue to analysis those 400 lines.
Novelty in the master database can be found in 2 plies. Looks at example The.a3.turn 1. a3 ...
The chapter names show the N for master database novelty and the second N for lichess novelty. The number after the N is the ply number when there was an initial novelty. Some novelties can later transpose into known positions.
Novelty in the master database can be found in 2 plies. Looks at example The.a3.turn 1. a3 ...
The chapter names show the N for master database novelty and the second N for lichess novelty. The number after the N is the ply number when there was an initial novelty. Some novelties can later transpose into known positions.
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@Brian-E said in #8:
> It's such a hard problem! Of course dividing by 5! or 4! was nonsense because the order the moves are played in does require White and Black to play on their turns!
>
> I give up. :-)
A general solution is indeed very difficult, but brute forcing it I was able to come up with 6482 unique positions after the first three half moves, and 94564 positions after the first four. If we include transpositions, those numbers become 8902 and 197281 respectively.
> It's such a hard problem! Of course dividing by 5! or 4! was nonsense because the order the moves are played in does require White and Black to play on their turns!
>
> I give up. :-)
A general solution is indeed very difficult, but brute forcing it I was able to come up with 6482 unique positions after the first three half moves, and 94564 positions after the first four. If we include transpositions, those numbers become 8902 and 197281 respectively.
@AsDaGo said in #14:
> A general solution is indeed very difficult
However, we could find an upper bound very easily. Note that a pawn always has at most 4 moves, a knight at most 8, a bishop at most 13, a rook at most 14, a queen at most 27, and a king at most 8 (note that if it is legal to castle (on either or both sides), the number of "regular" moves the king has is 5 plus the 2 castling moves, which is 7 which is less than 8, so this holds regardless of castling rights). Adding up 2*8 + 2*13 + 2*14 + 9*27 + 1*8 = 321 gives us an upper bound on the number of legal moves. Of course this is a very loose upper bound since the pieces will get in the way of each other, and you can't have all 9 queens in the center of the board, for example. But in any case, this gives us 321^n as a (very very loose) upper bound on the number of positions that can be reached after n half moves.
> A general solution is indeed very difficult
However, we could find an upper bound very easily. Note that a pawn always has at most 4 moves, a knight at most 8, a bishop at most 13, a rook at most 14, a queen at most 27, and a king at most 8 (note that if it is legal to castle (on either or both sides), the number of "regular" moves the king has is 5 plus the 2 castling moves, which is 7 which is less than 8, so this holds regardless of castling rights). Adding up 2*8 + 2*13 + 2*14 + 9*27 + 1*8 = 321 gives us an upper bound on the number of legal moves. Of course this is a very loose upper bound since the pieces will get in the way of each other, and you can't have all 9 queens in the center of the board, for example. But in any case, this gives us 321^n as a (very very loose) upper bound on the number of positions that can be reached after n half moves.
1. a3 Na6 2. Ra2 f6
1. a3 a6 2. Ra2 e5 3. f4