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 the neighbouring square on the same rank on the luff-side (i.e. for black pawn on c2, [[Distance|ϑ(♔,d2)]]),
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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)]]),
 
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 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>
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* A distance of two is required to win the game otherwise
 
* A distance of two is required to win the game otherwise
  
 
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<fentt border="double" style="font-size:24pt">...Q..../....K.../......../{....}..../(...){....}./(.+....){.}./(.kp.+.){.}./{kk.}(...){.}.</fentt>
<fentt border="double" style="font-size:24pt">...Q..../....K.../......../{....}..../(...){...}../(.+...){.}../(.kp+.){.}../kk(...){.}..</fentt>
 
  
 
=See also=
 
=See also=

Revision as of 16:19, 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). While implementing this pattern inside a 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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       
       
        
        
        
        
      
      
   ♕    
    ♔   
        
        
        
        
♟♚      
♚♚      

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]

  • 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 occupies the corner square (i.e. a1), or the 7th/8th (1st/2nd) rank on the neighbouring knight file (i.e. b1, b2).
  • A distance of two is required to win the game otherwise
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       
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      
      
   ♕    
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 •      
 ♚♟ •   
♚♚      

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