Changes

Assuming symmetric [[Evaluation|evaluation]] and [[Negamax|negamaxed]] values, positive scores indicate the [[Side to move|side to move]] is ahead, and negative if behind, which defines the value of zero as a natural [[Draw|draw]] score, no matter whether the draw is caused by a [[Stalemate|stalemate]], [[Repetitions|three-fold repetitions]], [[Fifty-move Rule|fifty-move rule draw]], or [[Draw evaluationEvaluation#immediate|draws]] by [[Material#InsufficientMaterial|insufficient material]].

Other [[Leaf Node|leaf nodes]] than terminal nodes determine a heuristic value of the [[Chess Position|position]] by an [[Evaluation Function|evaluation function]]. The value range of heuristic values has a symmetrical reduced value range far outside the mate scores, dominated by the [[Material|material balance]], with the theoretical maximum of

* [[Draw evaluationEvaluation]]

* [[Mop-up evaluationEvaluation]]

The coarser the grain of eval, the less passes MTD(f) has to make to converge to the minimax value. Some programs have a fine grained evaluation function, where positional knowledge can be worth as little as one hundredth of a pawn. Big score swings can become inefficient for these programs. It may help to dynamically increase the step size: instead of using the previous bound, one can, for example, add an extra few points in the search direction (for failing high, or searching upward, adding the bonus, and for failing low, or searching downward, subtracting the bonus) every two passes or so. ([[Don Dailey]] found that a scheme like this works well in a version of [[CilkchessCilkChess]].) At the end, if you overshoot the minimax value, you have to make a small search in the opposite direction, using the previous search bound without an extra bonus, to make the final convergence. Also, it can be quite instructive to experiment with different evaluation function grain sizes. Sometimes coarse grain functions work better than fine grain, both for [[NegaScout]] and MTD(f).

* [[Pawn Advantage, Win Percentage, and ELOElo]]

* [https://www.stmintz.com/ccc/index.php?id=58 Using too-shallow mate scores from the hash table] by [[David Eppstein]], [[CCC]], July 05, 1998 » [[Transposition Table]], [[Checkmate#MateScore|Mate Score]]

* [http://www.talkchess.com/forum/viewtopic.php?t=41640 Mate score in TT] by [[Marco Costalba]], [[CCC]], December 28, 2011 » [[Transposition Table]], [[Checkmate#MateScore|Mate Score]]

* [http://www.talkchess.com/forum/viewtopic.php?t=63948 Update Best Score and Best Move] by [[Tamás Kuzmics]], [[CCC]], May 10, 2017 » [[Best Move]]* [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=64428 Mate Score] by [[Tamás Kuzmics]], [[CCC]], June 27, 2017 » [[Checkmate#MateScore|Mate Score]]