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Pathology in game-trees is a counterintuitive phenomenon where a deeper minimax search results in worse play. It was discovered by Don Beal [1], who constructed a simple mathematical model to analyze the minimax algorithm. To his surprise, the analysis of the model showed that the backed-up values were actually somewhat less trustworthy than the heuristic values themselves.
Micrograph of membranous nephropathy [2]

Decision vs Evaluation

Independently, pathology in game trees was coined by Dana Nau, who discovered pathology to exist in a large class of games [3] under the assumption of independence of sibling values of trees with low branching factor (i.e. binary trees) with game theoretic leaf values of win and loss {1, -1}. In a simulation, Nau introduced strong dependencies between sibling nodes and discovered that this can cause search-depth pathology to disappear. While Nau was primarily concerned with decision accuracy, Beal [4], as well as Bratko and Gams [5] were concerned with evaluation accuracy.

Random Evaluations

Quite contrary to pathology in chess, Beal and others demonstrated [6], that deeper search with random leaf values yields to better play. As a quintessence, Dana Nau et al. suggested an Error minimizing minimax search in their recent paper [7] .

See also



  • Dana Nau (1979). Quality of Decision Versus Depth of Search on Game Trees. Ph.D. dissertation, Duke University
  • Dana Nau (1979). Preliminary results regarding quality of play versus depth of search in game playing. First Internat. Symposium on Policy Analysis and Information Systems, pp. 210–217, pdf

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External Links


  1. ^ Don Beal (1980). An analysis of minimax. Advances in Computer Chess 2
  2. ^ Very high magnification micrograph of membranous nephropathy, abbreviated MN. MN may also be referred to as membranous glomerulonephritis, abbreviated MGN. Kidney biopsy. Jones stain, Pathology from Wikipedia
  3. ^ Dana Nau (1982). An Investigation of the Causes of Pathology in Games. Artificial Intelligence, Vol. 19, 257–278, University of Maryland, College Park, Recommended by Judea Pearl, pdf
  4. ^ Don Beal (1982). Benefits of minimax search. Advances in Computer Chess 3
  5. ^ Ivan Bratko, Matjaž Gams (1982). Error Analysis of the Minimax Principle. Advances in Computer Chess 3
  6. ^ Don Beal, Martin C. Smith (1994). Random Evaluations in Chess. ICCA Journal, Vol. 17, No. 1
  7. ^ Brandon Wilson, Austin Parker, Dana Nau (2009). Error Minimizing Minimax: Avoiding Search Pathology in Game Trees. pdf

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