Difference between revisions of "Queen versus Pawn"

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(Created page with "'''Home * Evaluation * Game Phases * Endgame * Queen versus Pawn''' The '''Queen versus Pawn Endgame''' (KQKP) is usually won by the queen side, in...")
 
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Even if the pawn is ready to [[Promotions|promote]], supported by its own king, the technique is to come closer with the attacking king, after the defending king was forced to block the [[Promotion Square|promotion square]] due to a queen check.
 
Even if the pawn is ready to [[Promotions|promote]], supported by its own king, the technique is to come closer with the attacking king, after the defending king was forced to block the [[Promotion Square|promotion square]] due to a queen check.
 
However, with rook and bishop pawns on the seventh (second) rank, [[stalemate|stalemate]] is looming with the defending king in the corner.
 
However, with rook and bishop pawns on the seventh (second) rank, [[stalemate|stalemate]] is looming with the defending king in the corner.
There are even some rare cases with center and knight pawns where the attacking king hinders its own queen to give check <ref>[https://en.wikipedia.org/wiki/Queen_versus_pawn_endgame#Central_pawn_or_knight_pawn Queen versus pawn endgame - Central pawn or knight pawn | Wikipedia]</ref>.
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There are even some rare cases with center and knight pawns where the attacking king hinders its own queen to give check <ref>[https://en.wikipedia.org/wiki/Queen_versus_pawn_endgame#Central_pawn_or_knight_pawn Queen versus pawn endgame - Central pawn or knight pawn | Wikipedia]</ref>.
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This endgame with pawn on the 7th rank often occurs after a [[KPKP]] [[Pawn Race|pawn race]] with [[Unstoppable Passer|unstoppable passers]], where the [[Population Count|cardinality]] of their [[Pawn Spans|frontspans]] differs by two with the defending side to move.
 
<span id="RookPawn7"></span>
 
<span id="RookPawn7"></span>
 
=Rook Pawn on 7th=
 
=Rook Pawn on 7th=
 
The [[Draw|draw]] motive is a [[stalemate|stalemate]] threat, after the defending king blocks its own pawn after a queen check on the neighbouring knight file, so that the attacking king can't come closer.
 
The [[Draw|draw]] motive is a [[stalemate|stalemate]] threat, after the defending king blocks its own pawn after a queen check on the neighbouring knight file, so that the attacking king can't come closer.
A [[Distance|Chebyshev Distance]] of at least four to the [[Promotion Square|promotion square]] with a [[Manhattan-Distance|Manhattan distance]] less than eight for the attacking king is necessary to win that game (<span style="background-color: #c0ffc0;">green area below</span>).
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A [[Distance|Chebyshev distance]] of at least four to the [[Promotion Square|promotion square]] with a [[Manhattan-Distance|Manhattan distance]] less than eight for the attacking king is necessary to win that game (<span style="background-color: #c0ffc0;">green area below</span>).
While implementing this pattern inside a [[Interior Node Recognizer|interior node recognizer]], one has to take care that with the king in the corner (i.e. black king on a1), the queen has no mate in one (i.e. on c1).
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However, there are positions where the attacking king may reduce the distance due to [[Discovered Check|discovered check]].
  
<fentt border="double" style="font-size:24pt">...Q..../....K.../......../(....)..../(.....).../(.....).../(pk...).../(kk...)...</fentt>
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{|
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| <fentt border="double" style="font-size:24pt">...Q..../......../......../(....)K.../(.....).../(.....).../(pk...).../([k]k...)...</fentt>
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| <fentt border="double" style="font-size:24pt">.......Q/......../......../(....)K.../(.....).../(.....).../(pk...).../(k....)...</fentt>
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|-
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| Draw, &#172;([[King|&#9818;]][[Squares|a1]] &and; [[Queen|&#9813;]][[Square Control|&#10503;]][[Squares|c1]])
 +
| Win due to [[Discovered Check|discovered check]]
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|}
 
<span id="BishopPawn7"></span>
 
<span id="BishopPawn7"></span>
 
=Bishop Pawn on 7th=  
 
=Bishop Pawn on 7th=  
A similar draw motive occurs here with [[stalemate|stalemate]] after the queen captured the bishop pawn.  
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A similar draw motive occurs here with [[Stalemate|stalemate]] after the queen captured the bishop pawn.  
The winning area of the attacking king requires a bit more calculation.  
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The <span style="background-color: #c0ffc0;">winning area</span> of the attacking king is depending whether the defending king resides on the [[Pawn Spans|lee-side]] or [[Pawn Spans|luff-side]] .  
Critical squares for the [[Distance|Chebyshev Distance]] are the neighbouring square on the same rank on the luff-side (i.e. for black pawn on c2, [[Distance|&#977;(&#9812;,d2)]]),
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<span id="Lee"></span>
and the diagonal neighbouring square on the lee-side one rank back (i.e. for black pawn on c2, [[Distance|&#977;(&#9812;,b3)]]).
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==Lee case==
<ref>[[Interior Node Recognizer]] implemented in [[IsiChess]]</ref>
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The defending king on the [[Pawn Spans|lee-side]] is able to threaten [[Stalemate|stalemate]] in the corner.
* With a <span style="background-color: #c0ffc0;">distance below two</span> to any of these critical squares, the game is won.
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Critical squares are the neighbouring square on the [[Pawn Spans|luff-side]] (i.e. for black pawn on c2, d2),
* A <span style="background-color: #cc80cc;">distance of two</span> to any of these critical squares is required to win the game if the defending king blocks its pawn
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and the diagonal neighbouring square on the lee-side one rank back (i.e. for black pawn on c2, b3).
* Even a distance of two is not sufficient, if the defending king occupies the corner square (i.e. a1), or the 7th/8th (1st/2nd) rank on the neighbouring knight file (i.e. b1, b2).
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Only if the attacking king can reach these squares in one move, it can assist in a [[Checkmate|checkmate]] with the queen - otherwise it is a draw
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- except the rare cases the attacking king may reduce the [[Distance|Chebyshev distance]] accordantly, giving [[Discovered Check|discovered check]] <ref>Lee-case implemented as [[Interior Node Recognizer]] in [[IsiChess]]</ref>.
  
<fentt border="double" style="font-size:24pt">...Q..../....K.../......../{....}..../(...){...}../(.+...){.}../(.kp+.){.}../kk{k}(..){.}..</fentt>
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{|
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<fentt border="double" style="font-size:24pt">...Q..../......../......../......../(...)K..../(.+...).../(.kp+.).../[k]k(...)...</fentt>
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|  <fentt border="double" style="font-size:24pt">.......Q/......../......../......../(...)K..../(.+...).../(.kp+.).../k.(...)...</fentt>
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|-
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| Draw, &#172;([[King|&#9818;]][[Squares|a1]] &and; [[Queen|&#9813;]][[Square Control|&#10503;]][[Squares|c1]])
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| Win due to [[Discovered Check|discovered check]]
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|}
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==Luff case==
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When the defending king supports its pawn from the "wrong" [[Pawn Spans|luff-side]], including occupying its [[Promotion Square|promotion square]], 
 +
the <span style="background-color: #c0ffc0;">winning area</span> for the attacking king is enlarged by at least one move, in luff-direction even two moves.
 +
The critical luff-side square is now one file farther away (i.e. for black pawn on c2, e2), and one critical square needs to be reached in two moves now,
 +
to either transpose to a winning [[#Lee|lee-side case]], or to assist in a checkmate on the luff-side.
 +
 
 +
{|
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|  <fentt border="double" style="font-size:24pt">......../......../..Q...../(....)..K./(.......)./(.+.....)./(..pk+..)./(..kk...).</fentt>
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|  <fentt border="double" style="font-size:24pt">......../......../.......Q/(....)..K./(.......)./(.+.....)./(..pk+..)./(.......).</fentt>
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|  <fentt border="double" style="font-size:24pt">......../......../.......Q/(....)..K./(.......)./(.+.....)./(..p.+..)./(..k....).</fentt>
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|-
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| Draw
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| Win due to [[Discovered Check|discovered check]]
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| Draw since check parried by [[#Lee|Kb1/b2]]
 +
|}
  
 
=See also=
 
=See also=
 
* [[Draw Evaluation]]
 
* [[Draw Evaluation]]
 
* [[Interior Node Recognizer]]
 
* [[Interior Node Recognizer]]
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* [[KPKP]]
  
 
=Publications=
 
=Publications=
 
* [https://en.wikipedia.org/wiki/Reuben_Fine Reuben Fine] ('''1941'''). ''[https://archive.org/details/basicchessending00reub Basic Chess Endings]''. [https://en.wikipedia.org/wiki/George_Bell_%26_Sons Bell & Sons]
 
* [https://en.wikipedia.org/wiki/Reuben_Fine Reuben Fine] ('''1941'''). ''[https://archive.org/details/basicchessending00reub Basic Chess Endings]''. [https://en.wikipedia.org/wiki/George_Bell_%26_Sons Bell & Sons]
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* [https://en.wikipedia.org/wiki/Yuri_Averbakh Yuri Averbakh], Victor Henkin, [https://en.wikipedia.org/wiki/Vitaly_Chekhover Vitaly Chekhover] ('''1986'''). ''Comprehensive Chess Endings 3: Queen Endings''. [https://en.wikipedia.org/wiki/Pergamon_Press Pergamon Press]
 
* [[Karsten Müller]], [https://en.wikipedia.org/wiki/Frank_Lamprecht Frank Lamprecht] ('''2001'''). ''[http://www.gambitbooks.com/books/Fundamental_Chess_Endings.html Fundamental Chess Endings]''. [https://en.wikipedia.org/wiki/Gambit_Publications Gambit Publications]
 
* [[Karsten Müller]], [https://en.wikipedia.org/wiki/Frank_Lamprecht Frank Lamprecht] ('''2001'''). ''[http://www.gambitbooks.com/books/Fundamental_Chess_Endings.html Fundamental Chess Endings]''. [https://en.wikipedia.org/wiki/Gambit_Publications Gambit Publications]
 
* [https://en.wikipedia.org/wiki/Reuben_Fine Reuben Fine], [https://en.wikipedia.org/wiki/Pal_Benko Pal Benko] ('''2003'''). ''[https://en.wikipedia.org/wiki/Basic_Chess_Endings Basic Chess Endings]''. [https://en.wikipedia.org/wiki/David_McKay_Publications McKay]
 
* [https://en.wikipedia.org/wiki/Reuben_Fine Reuben Fine], [https://en.wikipedia.org/wiki/Pal_Benko Pal Benko] ('''2003'''). ''[https://en.wikipedia.org/wiki/Basic_Chess_Endings Basic Chess Endings]''. [https://en.wikipedia.org/wiki/David_McKay_Publications McKay]

Revision as of 10:50, 26 July 2020

Home * Evaluation * Game Phases * Endgame * Queen versus Pawn

The Queen versus Pawn Endgame (KQKP) is usually won by the queen side, in particular if the queen can occupy the pawn's frontspan. Even if the pawn is ready to promote, supported by its own king, the technique is to come closer with the attacking king, after the defending king was forced to block the promotion square due to a queen check. However, with rook and bishop pawns on the seventh (second) rank, stalemate is looming with the defending king in the corner. There are even some rare cases with center and knight pawns where the attacking king hinders its own queen to give check [1]. This endgame with pawn on the 7th rank often occurs after a KPKP pawn race with unstoppable passers, where the cardinality of their frontspans differs by two with the defending side to move.

Rook Pawn on 7th

The draw motive is a stalemate threat, after the defending king blocks its own pawn after a queen check on the neighbouring knight file, so that the attacking king can't come closer. A Chebyshev distance of at least four to the promotion square with a Manhattan distance less than eight for the attacking king is necessary to win that game (green area below). However, there are positions where the attacking king may reduce the distance due to discovered check.

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       
        
        
       
        
        
      
      
   ♕    
        
        
    ♔   
        
        
♟♚      
♚♚      
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       
        
        
       
        
        
      
       
       ♕
        
        
    ♔   
        
        
♟♚      
♚       
Draw, ¬(a1c1) Win due to discovered check

Bishop Pawn on 7th

A similar draw motive occurs here with stalemate after the queen captured the bishop pawn. The winning area of the attacking king is depending whether the defending king resides on the lee-side or luff-side .

Lee case

The defending king on the lee-side is able to threaten stalemate in the corner. Critical squares are the neighbouring square on the luff-side (i.e. for black pawn on c2, d2), and the diagonal neighbouring square on the lee-side one rank back (i.e. for black pawn on c2, b3). Only if the attacking king can reach these squares in one move, it can assist in a checkmate with the queen - otherwise it is a draw - except the rare cases the attacking king may reduce the Chebyshev distance accordantly, giving discovered check [2].

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       
        
        
        
       
        
      
      
   ♕    
        
        
        
   ♔    
 •      
 ♚♟•    
♚♚      
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       
        
        
        
       
        
      
       
       ♕
        
        
        
   ♔    
 •      
 ♚♟•    
♚       
Draw, ¬(a1c1) Win due to discovered check

Luff case

When the defending king supports its pawn from the "wrong" luff-side, including occupying its promotion square, the winning area for the attacking king is enlarged by at least one move, in luff-direction even two moves. The critical luff-side square is now one file farther away (i.e. for black pawn on c2, e2), and one critical square needs to be reached in two moves now, to either transpose to a winning lee-side case, or to assist in a checkmate on the luff-side.

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       
       
        
        
      
      
        
        
  ♕     
      ♔ 
        
 •      
  ♟♚•   
  ♚♚    
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    
        
        
       
       
        
        
      
        
        
        
       ♕
      ♔ 
        
 •      
  ♟♚•   
        
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       
       
        
        
       
       
        
        
       ♕
      ♔ 
        
 •      
  ♟ •   
  ♚     
Draw Win due to discovered check Draw since check parried by Kb1/b2

See also

Publications

Forum Posts

External Links

References

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