# [Retros] Fwd: FW: How many different positions?

ajm8 at damtp.cam.ac.uk ajm8 at damtp.cam.ac.uk
Wed Jan 2 06:22:30 EST 2019

```---------- Forwarded message ----------
From: "Mestel, Jonathan" <j.mestel at imperial.ac.uk>
To: Jonathan Mestel <ajm8 at maths.cam.ac.uk>
Subject: FW: How many different positions?
Date: Wed, 2 Jan 2019 11:21:20 +0000

From: Mestel, Jonathan
Sent: 02 January 2019 11:20
To: The Retrograde Analysis Mailing List <retros at janko.at>
Subject: How many different positions?

Happy New Year All.

Someone must have done this before. How many different positions can look
the same? We define two positions which are identical in appearance as
different if a sequence of moves could occur in one but not the other, so
that castling or en passant rights may lead to different positions. For
example, the attached position 3k2r/8/8/pPppPppP/pPPpPPpP/8/8/R3K2R I think
could represent 200 different positions:

192 = 4 * 4 * 6 * 2 = (White castling)*(Black castling)*(en passant)*(whose
move)

Then change a1 to h8  and add 2*4 = (whose move)*(en passant)

Giving a nice round total of 200. Is this maximal?

And a related question. According to the current 3fold repetition rules of
Fide, in the game

1 e4 d6 2 Bc4 f6 3 Bf7 Kd7 4 Bd5 Ke8 5 Bf7 Kd7 6 Bb3 Ke8 can White claim a
draw on the grounds he intends to play 7 Bf7 ? The 3 positions are not
identical in the sense that in the first Black could castle, and yet
obviously no legal continuation would enable him to castle. So the
positions are logically the same.

Best wishes,

Jonathan

-----------------------------------------
Jonathan Mestel
Professor of Applied Mathematics
Imperial College London SW7 2AZ
Huxley Building 746
0207-594-8513
http://www.ma.ic.ac.uk/~ajm8
j.mestel at ic.ac.uk<mailto:j.mestel at ic.ac.uk>

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