Transposition

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A transposition in chess is a sequence of moves that results in a position which may also be reached by another sequence of moves. For instance 1. d4 e6 2. e4 versus 1. e4 e6 2. d4, or {6. cxd4 exd4 7. exd4} versus {6. exd4 exd4 7. cxd4}. At least two moves (three plies) are necessary to transpose by exchanging moves, the more plies, the more possible sequences with transpositions are possible.

=Different Number of Moves= Due to both sides may lose tempo, more or less forced but often plausible transpositions with different number of moves may occur. A common example is this position from the Sveshnikov Variation in the Sicilian, which regularly appears after seven or eight moves:

r1bqkb1r/pp3ppp/2np1n2/1N2p1B1/4P3/2N5/PPP2PPP/R2QKB1R 1. e4 c5 2. Nf3 d6 3. d4 cxd 4. Nxd4 Nf6 5. Nc3 Nc6 6. Bg5 e5 7. Ndb5 1. e4 c5 2. Nc3 e6 3. Nf3 Nc6 4. d4 cxd 5. Nxd4 Nf6 6. Ndb5 d6 7. Bf4 e5 8. Bg5

=Color Flip= Further, during the opening, there are zillions of possibilities to transpose into color flipped positions from known opening lines, often by the prosaic loss of a tempo by performing a move, i.e. a double pawn push in two steps, for instance 1. d3 d5 2. d4 to play "Black" with the White pieces, as often tried by humans to throw a program out of its opening book early, but also by programs, like in the WMCCC 1988 the Pandix-Y!88 game. Therefor, books indexed by positions or hash keys may be re-probed with a color flipped position to cover those kinds of transpositions as well:

=Retrograde Analysis= In analyzing book lines, Retrograde Analysis from an opening or early middlegame position backwards reaching the initial position might be applied to traverse a "reverse" tree of unmade moves of variations with all its transpositions. However, one has to distinguish possible variations, where for instance pieces were put en prise but not captured, from plausible ones.

=See also=
 * Book Issues in Cray Blitz vs. Fidelity X @ ACM 1984
 * Enhanced Transposition Cutoff
 * Graph History Interaction (GHI)
 * Path-Dependency
 * Persistent Hash Table
 * Repetitions
 * Transposition Table
 * Triangulation

=Forum Posts=
 * Re: Is 64 bits enough as a hash length (on symmetrical hash keys) by Gerd Isenberg, CCC, Juli 11, 2008

=Publications=
 * Martin Schijf (1993). Proof-number Search and Transpositions. M.Sc. thesis, Leiden University, pdf
 * Martin Schijf, Victor Allis, Jos Uiterwijk (1994). Proof-Number Search and Transpositions. ICCA Journal, Vol. 17, No. 2 » Proof-Number Search
 * Bernard Helmstetter, Tristan Cazenave (2004). Incremental Transpositions. CG 2004, pdf
 * Andrew Soltis (2007). Transpo Tricks in Chess. Batsford, amazon.com

=External Links=
 * Transposition (chess) from Wikipedia
 * Transposition (mathematics) from Wikipedia
 * Matrix Transpose from Wikipedia
 * Transpositions from Interactive Mathematics Miscellany and Puzzles by A. Bogomolny
 * Transposition (music) from Wikipedia
 * Transposon from Wikipedia
 * Transposition of the great vessels from Wikipedia
 * Transposition cipher from Wikipedia
 * Directed graph from Wikipedia
 * Directed acyclic graph from Wikipedia
 * Hiromi Uehara - Sicilian Blue, Jazz in Marciac, August 4, 2010, YouTube Video

=References=

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