Author: Owen Lyne
Date: 08:29:28 09/17/99
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On September 17, 1999 at 00:16:19, Will Singleton wrote: >Thorsten, > >I'm a bit confused (as usual). How it is that cstal beats hiarcs in your games, >yet plays about on the same level as my program on ICC on equal hardware? > >Will It's called (mathematically) a lack of 'transitivity'. A relation is transitive if A > B and B > C implies that A > C. Seems logical doesn't it? BUT there are many situations, mathematically or in real life that this property does not hold. In chess terms, 3 players of very different styles, A causes B fits for style rather than strength reasons, B is simply better than C, but C is better than A. In truth perhaps A is the weakest, but his style beats B. So in a 3-way tourney its very close, but bring in some more players who are like like C and then A will score very little. B will beat all the C's, lose once to A, but still win the tourney comfortably. The ELO system relies on this effect averaging out over a set of rated games - if you play lots of different opponents once each you should get a decently reflective rating (reflective of your chess ability). But a sequence of games between 2 individuals can be very, very different. So perhaps ICC is the 'truth' (at least, versus humans), but comp-comp games don't have to bear much relation to ICC. So, in the Hiarcs - CSTal case, one could suggest that CSTal is A, Hiarcs is B, and at ICC we have lots of C, or any such situation. I mean to imply nothing about actual strentgh of any of the programs, just that performance against different opponents doesn't always follow the simple rules you might expect. A different example - in the late '80s the American Football team I follow (the New York Giants) always seem to lose to the Philadelpha Eagles (Randall Cunnigha,m came up with some amazing big plays against us), the Washington Redskins would beat the Eagles, yet the Giants would beat the Redskins. So what determined the relative positions of the 3 teams at the end of the season was not the games between them, they evenly shared them, but the games against all the rest. In purer maths it is possible to write down 4 six-sided dice, number not 1-6 but with specially chosen numbers from 1-24 (so that all 24 numbers appear exactly once on the set of dice) with the property that A rolls higher than B with probability 2/3, lower with probability 1/3. Similarly B beats C 2/3rd of time, C beats D, and the punchline, yes D beats A.... It's a classic con trick, I make you pick a die first, then I can always chose one that beats you 2 times out of 3! There are many more where that came from too... Owen
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