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

ajm8 at damtp.cam.ac.uk ajm8 at damtp.cam.ac.uk
Wed Jan 2 15:38:33 EST 2019

Thanks a lot Joose - 192 (+8) is presumably maximal then.

On Jan 2 2019, joose norri wrote:

> Olavi Riihimaa published the same position, except a4<>b4, d4<>e4,
> g4<>h4, in the British Chess Magazine November 1954, see also Schach und
> Zahl. He arrived at 192 positions.
>
>
> As to your second question, Olli Heimo constructed a position with I
> believe something like wKe1 Rh1 - bKe8 pe2, where obviously white can
> never castle, even though he hasn't lost the right to do so.
>
>
>Joose
>
>
>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
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>
>