We are dealing with a quantity (the score difference) which can be positive or negative, so neither square root nor log are very natural functions to use.
If you want diminishing returns, here's a better way to do it: Give each player 1/(1+exp(-K*score)) points. As K goes to infinity this converges to the usual loss=0, draw=1/2, win=1. As K goes to 0 it becomes linear. Also the sum of points awarded to both players is 1, which is kind of a nice property to maintain. However, it is unclear what exactly they are trying to achieve, so I can't really suggest a particular function to use. On Thu, Jul 12, 2012 at 9:41 AM, Don Dailey <dailey....@gmail.com> wrote: > Like you I agree that they should not not use this at all. However, > given that this is what they want to do I would argue that using using the > square root function (or something like it) is really what they want. If > they believe 150 is no better than 50, but that it's suddenly linear below > 50, what sense does that make? It goes from being linear to being > nothing. So using the log of the score, or the square root, anything > like that, is a huge win and gives them the basic behavior they really want > without having an arbitrary cap. > > And by the way, the square root is not just as arbitrary as capping - > unless you define arbitrary as anything you might do (which in a sense it > is.) So maybe arbitrary is not the right word here. What we are looking > for is something that is a more logical means to an ends - and the cap is > not nearly as good as the log or the square root. > > Don > > > > On Thu, Jul 12, 2012 at 9:25 AM, Álvaro Begué <alvaro.be...@gmail.com> > wrote: >> >> The square root is just as arbitrary as capping at 50. The only >> function I really like is capping at 0.5. >> >> Álvaro. >> >> >> On Thu, Jul 12, 2012 at 9:16 AM, Don Dailey <dailey....@gmail.com> wrote: >> > Truncating to [-50 .. 50] seems rather arbitrary to me too. There >> > should >> > either be no truncation at all, or if the concept is to not "over >> > reward" >> > big wins it should be replaced by a function such as the square root of >> > the >> > score. In this way you get progressively less credit for bigger and >> > bigger wins. >> > >> > Don >> > >> > >> > On Thu, Jul 12, 2012 at 5:48 AM, Rémi Coulom <remi.cou...@free.fr> >> > wrote: >> >> >> >> Why truncate to [-50..50] ? >> >> >> >> On 10 juil. 2012, at 22:20, Łukasz Lew wrote: >> >> >> >> > Fellow Go enthusiasts, >> >> > I would like you invite you to: >> >> > >> >> > Kaś Cup - a peculiar computer Go tournament. >> >> > >> >> > There will be prize pool of total 100$, yay! >> >> > It will take place on 5th of August on KGS. >> >> > >> >> > The peculiarity will come from the scoring method. >> >> > While this will be a Round Robin, the score for each game won't be >> >> > +-1 >> >> > point, >> >> > but the exact result of the game truncated to the [-50 .. 50] >> >> > interval. >> >> > >> >> > One last rule is that participants may not use more than 4 cores of >> >> > CPU >> >> > power. >> >> > >> >> > Nick kindly agreed to organize and look after the tournament for >> >> > which >> >> > I am grateful. >> >> > Also he is in charge of choosing a ruleset and time settings. >> >> > >> >> > Thank you and let us know if you will participate. >> >> > Łukasz >> >> > _______________________________________________ >> >> > Computer-go mailing list >> >> > Computer-go@dvandva.org >> >> > http://dvandva.org/cgi-bin/mailman/listinfo/computer-go >> >> >> >> _______________________________________________ >> >> Computer-go mailing list >> >> Computer-go@dvandva.org >> >> http://dvandva.org/cgi-bin/mailman/listinfo/computer-go >> > >> > >> > >> > _______________________________________________ >> > Computer-go mailing list >> > Computer-go@dvandva.org >> > http://dvandva.org/cgi-bin/mailman/listinfo/computer-go >> _______________________________________________ >> Computer-go mailing list >> Computer-go@dvandva.org >> http://dvandva.org/cgi-bin/mailman/listinfo/computer-go > > > > _______________________________________________ > Computer-go mailing list > Computer-go@dvandva.org > http://dvandva.org/cgi-bin/mailman/listinfo/computer-go _______________________________________________ Computer-go mailing list Computer-go@dvandva.org http://dvandva.org/cgi-bin/mailman/listinfo/computer-go
