🚀 go-pugleaf

-> >>till now it is absolutely impossible to count the
-> >>possible positions in chess. I heard once that there
-> >>are more posibilities than particles in space.

Until now, I've never considered this question.  I wouldn't say its
impossible though, however lots of conditional probabilities.

For a simple approximation,

There are always at least 32 blank squares. (64! / 32! arrangements)
There are always at least 2 pieces (if youdon't count king capture as
mate)
Each remaining square (exeptions for 8th and 1st rank) can have one of
13 piece values (including empty).

Only one king for each side is allowed.  Up to 8 pawns, and 9
Queens, Rooks,... Here are some calculations:

After the 32 squares with possible pieces are determined, White King can
be in any one of 32, black king in 1 of 31.

Each remaining square can have 1 of 11 values on it.  You can handle the
fact that pawns can't be on certain rows probabilistically.  1 quarter
of the squares have this restriction. 1/4 of the time 9 pieces are
allowed, 3/4 11 pieces.  Therefore use 10.5 possible values per
remaining square.

Again, probabilistic reduction is required to deal with the maximum
piece count restriction.  Of the remaining 30 squares to be optionally
filled, think of it as first filling slots that will then be placed on
the board.

The best way to do this to take the 8 pawns (and their promoted
versions) and 7 pieces for each side as unique, and then adjust for
transposition.  So instead of 10.5 (11) possible values for each
square, use 30 and then divide the end result by

8 * 8 (black and white pawns) *
2 ^3 = 8 (black and white R,B, and N)

= 8* 64

So finally,

64! / 32! *
32 * 31
* (30 ^ 30) / (8*64)

All of this * 30! because each piece can be blank