Random evaluation was first examined for the game of chess by Don Beal[2] and Martin C. Smith at the Advances in Computer Chess 7 conference at University of Limburg, July 1993, published in the ICCA Journal and conference proceedings [3], and further analyzed by Mark Levene and Trevor Fenner in 1995 [4] and 2001 [5]. Although using random numbers as "evaluation" results in random play with a one plysearch (root-random), it was found that the strength of play rises rapidly with increased depth (lookahead-random) using a full-width minimax search. While a natural assumption is that lookahead on random numbers would also result in a random choice at the root as well, random evaluation would create a statistical preference for positions with large mobilty, and thus likely strong material[6].
Setup
To demonstrate this so called Beal Effect it is neccessary to consider awareness of terminal nodes where mate scores would favour deeper lookahead. Therefor root-random is replaced by lookahead-zero, performing a lookahead with the same search depth as lookahead-random, but non terminal leaves evaluated as zero, only tie-breaking at the root by a random number. Still a very weak player, a five ply search was already sufficient to win all of 100 games versus a random player.
Beal and Smith used following setup to automatically play the games: Draws by stalemate and four cases of insufficient material were recognized (KK, KNK, KBK, KNNK), but 50-move rule or threefold repetition discarded. Therefor games were limited to 200 moves and then WDL adjudicated by +=- material balance (which happend rarely) [7].
Further Experiments
Beal and Smith further applied random evaluations to components rather than the whole evaluation. They used material balance as dominating term plus a random number below one pawn unit. While a five ply search with random component only gained 63% over zero component, quiescing the material balance by exploring a capture tree in order to obtain the chess specific part of the evaluation, the random component gained 97% within the same search depth of five plies.
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The Beal Effect
Random evaluation was first examined for the game of chess by Don Beal [2] and Martin C. Smith at the Advances in Computer Chess 7 conference at University of Limburg, July 1993, published in the ICCA Journal and conference proceedings [3], and further analyzed by Mark Levene and Trevor Fenner in 1995 [4] and 2001 [5]. Although using random numbers as "evaluation" results in random play with a one ply search (root-random), it was found that the strength of play rises rapidly with increased depth (lookahead-random) using a full-width minimax search. While a natural assumption is that lookahead on random numbers would also result in a random choice at the root as well, random evaluation would create a statistical preference for positions with large mobilty, and thus likely strong material [6].Setup
To demonstrate this so called Beal Effect it is neccessary to consider awareness of terminal nodes where mate scores would favour deeper lookahead. Therefor root-random is replaced by lookahead-zero, performing a lookahead with the same search depth as lookahead-random, but non terminal leaves evaluated as zero, only tie-breaking at the root by a random number. Still a very weak player, a five ply search was already sufficient to win all of 100 games versus a random player.Beal and Smith used following setup to automatically play the games: Draws by stalemate and four cases of insufficient material were recognized (KK, KNK, KBK, KNNK), but 50-move rule or threefold repetition discarded. Therefor games were limited to 200 moves and then WDL adjudicated by +=- material balance (which happend rarely) [7].
Further Experiments
Beal and Smith further applied random evaluations to components rather than the whole evaluation. They used material balance as dominating term plus a random number below one pawn unit. While a five ply search with random component only gained 63% over zero component, quiescing the material balance by exploring a capture tree in order to obtain the chess specific part of the evaluation, the random component gained 97% within the same search depth of five plies.See also
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