Total number of reasonable moves per turn.


How many of those legal chess positions are impossible to reach by any set of legal moves?



A legal chess position is by definition
a position that can be reached from the initial position by a sequence of legal moves.


It depends on how you define it.

You could define an illegal position as something like pawns on the back rank, White in check on Black's move, multiple queens without a missing pawn, etc.

These positions will never show up even in variants such as Crazyhouse. They are illegal.

But there are also positions where no individual piece or combination of pieces is in an illegal position but it is not possible to reach that position via any set of legal moves. For example, the starting position but with rooks and knights swapped could happen via a legal set of moves, but the starting position with rooks and bishops swapped could not happen via a legal set of moves.

Identifying and finding some of these might be difficult to do when trying to count the total number of "legal" positions that could actually be reached in a legal game.