Draw Evaluation

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Home * Evaluation * Game Phases * Endgame * Draw Evaluation

It is important for the evaluation function to recognize the endgame positions which are likely drawn, even though one side has a nominal advantage. This page is devoted to listing some of them. More of that kind of knowledge can be found in the KPK section.

Obvious Draws

According to the rules of a dead position, Article 5.2 b, when there is no possibility of checkmate for either side with any series of legal moves, the position is an immediate draw if

  • both sides have a bare king
  • one side has a king and a minor piece against a bare king
  • both sides have a king and a bishop, the bishops being the same color

Simple Heuristics

The bishops of different colors are not counted as an immediate draw, because of the possibility of a helpmate in the corner. Since this is unlikely given even a four ply search, we may introduce another class of drawn positions: those that cannot be claimed, but can be evaluated as draws:

  • two knights against the bare king
  • both sides have a king and a minor piece each
  • the weaker side has a minor piece against two knights
  • two bishops draw against a bishop
  • two minor pieces against one draw, except when the stronger side has a bishop pair

Please note that a knight or even two knights against two bishops are not included here, as it is possible to win this ending.

Implementation note: When a program uses heuristics of that kind, it is of utmost importance to be consistent. For example, if KBN vs KB is scored as a draw, the same must be done with KBN vs KBP. A possible idea is to divide a score by a large constant, such as 16 or 32, when the side nominally ahead has the wrong piece combination.

Complex Heuristics

  • If the stronger side has a pawn and a bishop against the minor piece, the position is almost certainly drawn if the weaker side's king occupies a square on the path of a pawn that is inaccessible to the enemy bishop (the degenerate cases like trapping the minor piece are best left for search).
  • KQKP with rook pawn or bishop pawn on its seventh rank supported by own king threatening stalemate, other king far enough away [1] [2]
  • Wrong Color Bishop and Rook Pawn

One-sided Heuristics

There are some heuristics that tells us only that one of the players cannot win the endgame

  • a single minor piece should not win against any number of pawns (again, there is a special case of a smothered mate in the corner, but it is search issue, not to be taken into account by the evaluation function)

See also

Forum Posts

2000 ...

2010 ...

Re: question on draw evaluation by Robert Houdart, CCC, June 07, 2010

2015 ...

References

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