Author: Dan Andersson
Date: 13:04:27 04/03/04
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On April 02, 2004 at 20:39:38, Dann Corbit wrote: >On March 31, 2004 at 21:43:09, Dan Andersson wrote: > >>Averaged results over 1000 runs per depth: >>value depth nodes relative minimax relative a-b >>2 2 3.463 0.86575 1.1543333333333 >>10 4 10.399 0.6499375 1.4855714285714 >>42 6 28.148 0.4398125 1.8765333333333 >>170 8 74.578 0.2913203125 2.4057419354839 >>682 10 185.363 0.1810185546875 2.9422698412698 >>2730 12 459.625 0.11221313476563 3.619094488189 >>10922 14 1106.041 0.067507385253906 4.3374156862745 >>43690 16 2691.694 0.041071990966797 5.2675029354207 >>174762 18 6280.954 0.023959938049316 6.1397399804497 >>699050 20 14867.996 0.014179225921631 7.2633102100635 >>2796202 22 34813.976 0.0083002986907959 8.5015814407814 >>11184810 24 80965.644 0.0048259284496307 9.8847080942498 >>44739242 26 185048.509 0.0027574376612902 11.295154062138 > >I am guessing this is what the table means: >value = the number of nodes in the full tree >depth = search depth >nodes = nodes examined by alphabeta (but then the depth=2 makes no sense) >relative minimax = ratio of nodes examined compared to minimax > >relative a-b I do not understand. > >Can you explain to greater detail what this represents? The program is a representation of A-B search of a simple game where the two players alternate in appending a trailing digit to a binary number to an even depth. Trivial but essentially representing the minimal game. And Nodes is the number of leaf-nodes searched by an algorithm with a random move ordering in that tree. Value is the result of the search. It will never vary under the current distribution function (It's easy to create a pseudo-random sequence) as it is the fixed sequence 0..2^d-1. Where the value of a leaf-node is the binary representation of the sequence of moves through the tree. And its value is the value of a binary string '10' repeated d/2 times. Depth is searched depth. Nodes should really be leaf-nodes. Relative minimax is the quotient of the value Nodes to the number of leaf-nodes searched by minimax. Relative A-B is the quotient of the value Nodes to the number of leaf-nodes searched by a perfect alpha-beta search. MvH Dan Andersson
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