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'''[[Main Page|Home]] * [[Chess]] * Transposition'''
A '''transposition''' in chess is a sequence of [[Moves|moves]] that results in a [[Chess Position|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|tempo]], more or less forced but often plausible transpositions with different number of moves may occur. A common example is this position from the [https://en.wikipedia.org/wiki/Sicilian_Defence#Sveshnikov_Variation:_4...Nf6_5.Nc3_e5 Sveshnikov Variation] in the Sicilian, which regularly appears after seven or eight moves:
<fentt border="double" style="font-size:24pt">r1bqkb1r/pp3ppp/2np1n2/1N2p1B1/4P3/2N5/PPP2PPP/R2QKB1R</fentt>
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|opening]], there are zillions of possibilities to transpose into [[Color Flipping|color flipped positions]] from known opening lines, often by the prosaic loss of a [[Tempo|tempo]] by performing a move, i.e. a [[Pawn Push#DoublePush|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|opening book]] early, but also by programs, like in the [[WMCCC 1988]] the [[WMCCC 1988#Pandix-Y!|Pandix-Y!88]] game. Therefor, books indexed by positions or [[Zobrist Hashing|hash keys]] may be re-probed with a color flipped position to cover those kinds of transpositions as well:
{|
|-
| <fentt border="double" style="font-size:24pt">r1bqkb1r/pp3ppp/2n1pn2/2pp4/4P3/2NP1NP1/PPP2P1P/R1BQKB1R</fentt>
| <fentt border="double" style="font-size:24pt">r1bqkb1r/ppp2p1p/2np1np1/4p3/2PP4/2N1PN2/PP3PPP/R1BQKB1R</fentt>
|-
| 1. e4 c5 2. Nc3 Nc6 3. Nf3 e6 <br/>4. g3 Nf6 5. d3 d5
| 1. c4 e5 2. Nc3 Nc6 3. Nf3 d6 <br/>4. d3 Nf6 5. e3 g6 6. d4
|}
<span id="RetrogradeAnalysis"></span>
=Retrograde Analysis=
In analyzing book lines, [[Retrograde Analysis]] from an opening or early [[Middlegame|middlegame]] position backwards reaching the [[Initial Position|initial position]] might be applied to traverse a "reverse" tree of [[Unmake Move|unmade moves]] of variations with all its transpositions. However, one has to distinguish possible variations, where for instance pieces were put [[En prise|en prise]] but not captured, from plausible ones.
=See also=
* [[Boris Baczynskyj#CrayBlitzFidelity|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=
* [http://www.talkchess.com/forum/viewtopic.php?t=22274&postdays=0&postorder=asc&topic_view=flat&start=14 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]], [http://www2.denizyuret.com/ref/schijf/schijf93proofnumber.pdf pdf]
* [[Martin Schijf]], [[Victor Allis]], [[Jos Uiterwijk]] ('''1994'''). ''Proof-Number Search and Transpositions''. [[ICGA Journal#17_2|ICCA Journal, Vol. 17, No. 2]] » [[Proof-Number Search]]
* [[Bernard Helmstetter]], [[Tristan Cazenave]] ('''2004'''). ''[http://link.springer.com/chapter/10.1007/11674399_15 Incremental Transpositions]''. [[CG 2004]], [http://www.ai.univ-paris8.fr/~bh/articles/it.pdf pdf]
* [https://en.wikipedia.org/wiki/Andrew_Soltis Andrew Soltis] ('''2007'''). ''Transpo Tricks in Chess''. [https://en.wikipedia.org/wiki/Anova_Books Batsford], [http://www.amazon.com/Transpo-Tricks-Chess-Batsford-Books/dp/0713490519 amazon.com] <ref>[http://www.chessville.com/reviews/TranspoTricks.htm Chessville Reviews - Transpo Tricks in Chess: Finesse Your Chess Moves and Win - by GM Andrew Soltis - Batsford, 2007 - Reviewed by Rick Kennedy]</ref>
=External Links=
* [https://en.wikipedia.org/wiki/Transposition_(chess) Transposition (chess) from Wikipedia]
* [https://en.wikipedia.org/wiki/Transposition_(mathematics) Transposition (mathematics) from Wikipedia]
* [https://en.wikipedia.org/wiki/Transpose Matrix Transpose from Wikipedia]
* [http://www.cut-the-knot.org/do_you_know/pgroups.shtml Transpositions] from [http://www.cut-the-knot.org/ Interactive Mathematics Miscellany and Puzzles] by [http://www.informatik.uni-trier.de/~ley/db/indices/a-tree/b/Bogomolny:A=.html A. Bogomolny]
* [https://en.wikipedia.org/wiki/Transposition_(music) Transposition (music) from Wikipedia]
* [https://en.wikipedia.org/wiki/Transposon Transposon from Wikipedia]
* [https://en.wikipedia.org/wiki/Transposition_of_the_great_vessels Transposition of the great vessels from Wikipedia]
* [https://en.wikipedia.org/wiki/Transposition_cipher Transposition cipher from Wikipedia]
* [https://en.wikipedia.org/wiki/Directed_graph Directed graph from Wikipedia]
* [https://en.wikipedia.org/wiki/Directed_acyclic_graph Directed acyclic graph from Wikipedia]
* [[Videos#HiromiUehara|Hiromi Uehara]] - Sicilian Blue, [http://fr.wikipedia.org/wiki/Jazz_in_Marciac Jazz in Marciac], August 4, 2010, [https://en.wikipedia.org/wiki/YouTube YouTube] Video
: {{#evu:https://www.youtube.com/watch?v=G7xAbT4jzD8|alignment=left|valignment=top}}
=References=
<references />
'''[[Chess|Up one Level]]'''
A '''transposition''' in chess is a sequence of [[Moves|moves]] that results in a [[Chess Position|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|tempo]], more or less forced but often plausible transpositions with different number of moves may occur. A common example is this position from the [https://en.wikipedia.org/wiki/Sicilian_Defence#Sveshnikov_Variation:_4...Nf6_5.Nc3_e5 Sveshnikov Variation] in the Sicilian, which regularly appears after seven or eight moves:
<fentt border="double" style="font-size:24pt">r1bqkb1r/pp3ppp/2np1n2/1N2p1B1/4P3/2N5/PPP2PPP/R2QKB1R</fentt>
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|opening]], there are zillions of possibilities to transpose into [[Color Flipping|color flipped positions]] from known opening lines, often by the prosaic loss of a [[Tempo|tempo]] by performing a move, i.e. a [[Pawn Push#DoublePush|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|opening book]] early, but also by programs, like in the [[WMCCC 1988]] the [[WMCCC 1988#Pandix-Y!|Pandix-Y!88]] game. Therefor, books indexed by positions or [[Zobrist Hashing|hash keys]] may be re-probed with a color flipped position to cover those kinds of transpositions as well:
{|
|-
| <fentt border="double" style="font-size:24pt">r1bqkb1r/pp3ppp/2n1pn2/2pp4/4P3/2NP1NP1/PPP2P1P/R1BQKB1R</fentt>
| <fentt border="double" style="font-size:24pt">r1bqkb1r/ppp2p1p/2np1np1/4p3/2PP4/2N1PN2/PP3PPP/R1BQKB1R</fentt>
|-
| 1. e4 c5 2. Nc3 Nc6 3. Nf3 e6 <br/>4. g3 Nf6 5. d3 d5
| 1. c4 e5 2. Nc3 Nc6 3. Nf3 d6 <br/>4. d3 Nf6 5. e3 g6 6. d4
|}
<span id="RetrogradeAnalysis"></span>
=Retrograde Analysis=
In analyzing book lines, [[Retrograde Analysis]] from an opening or early [[Middlegame|middlegame]] position backwards reaching the [[Initial Position|initial position]] might be applied to traverse a "reverse" tree of [[Unmake Move|unmade moves]] of variations with all its transpositions. However, one has to distinguish possible variations, where for instance pieces were put [[En prise|en prise]] but not captured, from plausible ones.
=See also=
* [[Boris Baczynskyj#CrayBlitzFidelity|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=
* [http://www.talkchess.com/forum/viewtopic.php?t=22274&postdays=0&postorder=asc&topic_view=flat&start=14 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]], [http://www2.denizyuret.com/ref/schijf/schijf93proofnumber.pdf pdf]
* [[Martin Schijf]], [[Victor Allis]], [[Jos Uiterwijk]] ('''1994'''). ''Proof-Number Search and Transpositions''. [[ICGA Journal#17_2|ICCA Journal, Vol. 17, No. 2]] » [[Proof-Number Search]]
* [[Bernard Helmstetter]], [[Tristan Cazenave]] ('''2004'''). ''[http://link.springer.com/chapter/10.1007/11674399_15 Incremental Transpositions]''. [[CG 2004]], [http://www.ai.univ-paris8.fr/~bh/articles/it.pdf pdf]
* [https://en.wikipedia.org/wiki/Andrew_Soltis Andrew Soltis] ('''2007'''). ''Transpo Tricks in Chess''. [https://en.wikipedia.org/wiki/Anova_Books Batsford], [http://www.amazon.com/Transpo-Tricks-Chess-Batsford-Books/dp/0713490519 amazon.com] <ref>[http://www.chessville.com/reviews/TranspoTricks.htm Chessville Reviews - Transpo Tricks in Chess: Finesse Your Chess Moves and Win - by GM Andrew Soltis - Batsford, 2007 - Reviewed by Rick Kennedy]</ref>
=External Links=
* [https://en.wikipedia.org/wiki/Transposition_(chess) Transposition (chess) from Wikipedia]
* [https://en.wikipedia.org/wiki/Transposition_(mathematics) Transposition (mathematics) from Wikipedia]
* [https://en.wikipedia.org/wiki/Transpose Matrix Transpose from Wikipedia]
* [http://www.cut-the-knot.org/do_you_know/pgroups.shtml Transpositions] from [http://www.cut-the-knot.org/ Interactive Mathematics Miscellany and Puzzles] by [http://www.informatik.uni-trier.de/~ley/db/indices/a-tree/b/Bogomolny:A=.html A. Bogomolny]
* [https://en.wikipedia.org/wiki/Transposition_(music) Transposition (music) from Wikipedia]
* [https://en.wikipedia.org/wiki/Transposon Transposon from Wikipedia]
* [https://en.wikipedia.org/wiki/Transposition_of_the_great_vessels Transposition of the great vessels from Wikipedia]
* [https://en.wikipedia.org/wiki/Transposition_cipher Transposition cipher from Wikipedia]
* [https://en.wikipedia.org/wiki/Directed_graph Directed graph from Wikipedia]
* [https://en.wikipedia.org/wiki/Directed_acyclic_graph Directed acyclic graph from Wikipedia]
* [[Videos#HiromiUehara|Hiromi Uehara]] - Sicilian Blue, [http://fr.wikipedia.org/wiki/Jazz_in_Marciac Jazz in Marciac], August 4, 2010, [https://en.wikipedia.org/wiki/YouTube YouTube] Video
: {{#evu:https://www.youtube.com/watch?v=G7xAbT4jzD8|alignment=left|valignment=top}}
=References=
<references />
'''[[Chess|Up one Level]]'''
