Author: Dan Homan
Date: 09:37:37 02/03/00
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On February 03, 2000 at 12:32:30, Dan Homan wrote: >On February 03, 2000 at 10:46:25, Lin Harper wrote: > >> I notice the celebrated 'Ferret' is having a bad run so far. > >An interesting question is: what are the chances that a top program will >have 2 points after only 4 rounds? I think the chances are excellent. This should read: "have only 2 points after 4 rounds" > >There are at least 5, generally regarded, 'top' programs in this >tourney. 3 of them have had the misfourtune of playing 2 of their >peers in the first 4 rounds. Lets make some simple assumptions: > >1) The chances of losing or drawing a 'lesser' program are zero. This >is a gross assumption that will very much reduce the chances of scoring >only two points in four rounds > >2) The chances of losing to a 'peer' program are 1/3. > >3) The interaction between top programs (meaning which program plays >which for a win/loss/draw) is not important. This is also a gross >assumption that will *increase* the chances of scoring only two >points in four rounds, but I think this assumption is more than offset >by assumption 1) > >Under this way of thinking, the two 'top' programs who played only one >of their peer group, have 0 chance of scoring only 2 points, so those >programs are out of consideration. > >For the remaining 3 programs, the chance of not losing their two games >against their peers is 1 - (1/3)*(1/3) = 8/9 > >But there are 3 programs in this situation, so (using assumption 3) the >chances that one of them will lose both games is 1-(8/9)*(8/9)*(8/9) = 30% > >So the chances of a 'top' program having only 2 points after only 4 >rounds is something like 30% - in my estimation, assumption 1 is so bad >that the chances are probably significantly better than 30%. > > - Dan
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