# [Retros] Little less than a million positions leading to the first one!? Yefim 10/09/2004

Francois Labelle flab at EECS.Berkeley.EDU
Sun Oct 10 02:16:35 EDT 2004

Yefim Treger wrote:

> From how many positions can we pass (not necessarily directly) to the

> Original one?

I can't resist questions that I can answer with my chess engine. :)

Let dist = ply distance to the original position (mod 4).

This value is equivalent to whether for each player the knights are on the
same square colors or different.

My computer counts:

73984 positions with dist = 0 (wDiff, bDiff)
69887 positions with dist = 1 (wDiff, bSame)
66609 positions with dist = 2 (wSame, bSame)
69887 positions with dist = 3 (wSame, bDiff)

total: 280367 positions

I found one very special position along the way:

r1bqkbNr/pppppppp/7N/5n2/6n1/8/PPPPPPPP/R1BQKB1R b KQkq -

The position can lead to the starting position, but cannot be reached from
the starting position! So the position is illegal (cannot retract White's
move), and I didn't count it.

The mirror version has the piece colors reversed but it's still Black's
turn, so the situation is reversed: the position can be reached from the
starting position, but cannot lead to the starting position.

Francois