Author: Jeremiah Penery
Date: 05:01:59 10/16/99
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On October 16, 1999 at 03:54:35, Ratko V Tomic wrote: <snipped attribution, Bob Hyatt wrote:> >> yes, 3 is pretty typical, although it steadily drops as material >> comes off. >I tried Crafty 16.6 within Fritz UI (default engine settings, 64Mb hash) in a >middle game position with 38 avaliable moves. The depths tested were 10, 11 and >12 plies. The effective branching factor (calculated from the total nodes N it >displayed at the end of search as: B=ln(N)/ln(D)) ranged from 4.5 to 4.7. Of course, the effective branching factor will vary with the position. For some positions it will simply be fairly low. Others, higher. Or it can be low for many ply, and then suddenly be high at certain depths in the search. The best way to really test this is to try it on many positions, from all phases of the game, and all types of positions (open, closed, tactical, 'positional', endgame, etc.) Also, it must be measured over many different depths (although this part isn't as important as measuring many positions). Only an average from all these kinds of positions can give the true effective branching factor (EBF). :) I have an example: I've been letting my modified Crafty search from the end of Kasparov/DB game 2 for a couple of days. Here are the numbers for branching factor at each ply (after 10): 10->11 = 11.46 (3.74 to 42.89 seconds) 11->12 = 1.51 (42.89 seconds to 65 seconds) 12->13 = 5.30 (1:05 to 5:45) 13->14 = 3.85 (5:45 to 22:10) 14->15 = 1.78 (22:10 to 39:36) 15->16 = 1.92 (39:36 to 76:06) 16->17 = 2.40 (76:06 to 182:42) 17->18 = 2.88 (182:42 to 525:47) 18->19 = At 2176 minutes now, still searching. Average: 3.89 (not counting the last iteration). Without 10->11, the average is only 2.8. The branching factor for each ply under 10 was very near two, most being less. If these were counted, the average would be probably less than 3, counting ALL ply up to 18. Jeremiah
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