Difference between revisions of "Queen versus Pawn"

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A similar draw motive occurs here with [[stalemate|stalemate]] after the queen captured the bishop pawn.  
 
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.  
 
The winning area of the attacking king requires a bit more calculation.  
Critical squares for the [[Distance|Chebyshev Distance]] are on the same rank on the luff-side two squares apart (i.e. for black pawn on c2, [[Distance|ϑ(♔,e2)]]),
+
Critical squares for the [[Distance|Chebyshev Distance]] are on the same rank on the [[Pawn Spans|luff-side]] two squares apart (i.e. for black pawn on c2, [[Distance|ϑ(♔,e2)]]),
and the diagonal neighbouring square on the lee-side one rank back (i.e. for black pawn on c2, [[Distance|ϑ(♔,b3)]]).  
+
and the diagonal neighbouring square on the [[Pawn Spans|lee-side]] one rank back (i.e. for black pawn on c2, [[Distance|ϑ(♔,b3)]]).  
 
<ref>[[Interior Node Recognizer]] implemented in [[IsiChess]]</ref>
 
<ref>[[Interior Node Recognizer]] implemented in [[IsiChess]]</ref>
 
* Attacking king may reduce distance by [[Discovered Check|discovered check]]
 
* Attacking king may reduce distance by [[Discovered Check|discovered check]]
 
* With a <span style="background-color: #c0ffc0;">distance below two</span> to any of these critical squares, the game is won.  
 
* With a <span style="background-color: #c0ffc0;">distance below two</span> to any of these critical squares, the game is won.  
* A <span style="background-color: #cc80cc;">distance of two</span> to any of these critical squares 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).
+
* <span id="rule3"></span>A <span style="background-color: #cc80cc;">distance of two</span> to any of these critical squares is not sufficient, if the defending king is on the [[Pawn Spans|lee-side]], corner square (i.e. a1), or the 7th/8th (1st/2nd) rank on the knight file (i.e. b1, b2).
 
* Exception: attacking king can immediately capture pawn  
 
* Exception: attacking king can immediately capture pawn  
* A distance of two is required to win the game otherwise
 
 
{|
 
{|
 
|  <fentt border="double" style="font-size:24pt">...Q..../......../......../{....}..../(...){K...}./(.+....){.}./(.kp.+.){.}./{kk.}(...){.}.</fentt>
 
|  <fentt border="double" style="font-size:24pt">...Q..../......../......../{....}..../(...){K...}./(.+....){.}./(.kp.+.){.}./{kk.}(...){.}.</fentt>
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| Win due to [[Discovered Check|discovered check]]
 
| Win due to [[Discovered Check|discovered check]]
 
|}
 
|}
 +
* A <span style="background-color: #cc80cc;">distance of two</span> is required to win the game otherwise
 +
{|
 +
|  <fentt border="double" style="font-size:24pt">......../......../..Q...../{....}..K./(...){....}./(.+....){.}./(..pk+.){.}./{..k}(k..){.}.</fentt>
 +
|  <fentt border="double" style="font-size:24pt">......../......../.......Q/{....}..K./(...){....}./(.+....){.}./(..pk+.){.}./{...}(...){.}.</fentt>
 +
|  <fentt border="double" style="font-size:24pt">......../......../.......Q/{....}..K./(...){....}./(.+....){.}./(..p.+.){.}./{..k}(...){.}.</fentt>
 +
|-
 +
| Draw
 +
| Win due to [[Discovered Check|discovered check]]
 +
| Draw since check parried by [[#rule3|Kb1/b2]]
 +
|}
 +
 
=See also=
 
=See also=
 
* [[Draw Evaluation]]
 
* [[Draw Evaluation]]

Revision as of 21:10, 25 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 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 requires a bit more calculation. Critical squares for the Chebyshev Distance are on the same rank on the luff-side two squares apart (i.e. for black pawn on c2, ϑ(♔,e2)), and the diagonal neighbouring square on the lee-side one rank back (i.e. for black pawn on c2, ϑ(♔,b3)). [2]

  • Attacking king may reduce distance by discovered check
  • With a distance below two to any of these critical squares, the game is won.
  • A distance of two to any of these critical squares is not sufficient, if the defending king is on the lee-side, corner square (i.e. a1), or the 7th/8th (1st/2nd) rank on the knight file (i.e. b1, b2).
  • Exception: attacking king can immediately capture pawn
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    
       
        
        
        
       
        
      
      
   ♕    
        
        
        
   ♔    
 •      
 ♚♟ •   
♚♚      
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    
       
        
        
        
       
        
      
       
       ♕
        
        
        
   ♔    
 •      
 ♚♟ •   
♚       
Draw Win due to discovered check
  • A distance of two is required to win the game otherwise
    
    
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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

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