Consider this legal chess position which can never be reached from the normal starting position.
[FEN "6kb/6p1/6K1/8/8/8/8/8 w - - 0 1"]
The Black bishop is placed on h8, but with the Black pawn on g7, there is no way the bishop could have actually reached h8. How many such positions exist in chess which are legal but unreachable? Is there any research on reachable/non-reachable positions?
I found that endgame tablebases don't necessarily take this into consideration, but if the number of non-reachable positions is significantly large, it might possibly help minimize the size of endgame tablebases.
Here's a screenshot from the online Nalimov tablebases.
Now, in this unreachable position, I can add another piece like a knight on almost every square.
I can add an additional piece, like a rook.
This can go on and on and I can keep adding more pieces, but all those positions would be unreachable. We thus end up storing unnecessary positions in the tablebase and increasing its size.
Of course, it's a good thing for tablebases to have these positions if we want to use them for chess variants like Chess960, but they are not necessary for the standard version of chess. It would be quite interesting to know how many such unreachable positions exist.
(Addition of more relevant tags suggested)