[computer-go] A new pairing system idea for CGOS

[Don Dailey]

Thanks Christoph,

I'll take a look.

- Don


On Thu, 2006-10-05 at 16:30 -0700, Christoph Birk wrote:
> On Thu, 5 Oct 2006, Don Dailey wrote:
> > Yes, simulations are good.   N may need to change with the number of
> > active players at scheduling time.
> 
> Here are the results. The alorithm works like this:
> 1) take highest ranking (remaining) player
> 2) choose N candidates at random (N depends on #players remaining)
> 3) select highest ranking of the canditates
> 4) if un-paired players remain then goto 1)
> 
> I tried 4 formulas for N: (NP=14, #players currently active).
> The tables show the probability of player at rank XX to be paired
> against player at rank YY, divided by the 'unbiased' probability 1/(N-1)
> 
> N = 1+(NP-npaired-1)/2       (ie. half the players available)
>         2    3    4    5    6    7    8    9   10   11   12   13   14
> 01:  7.0  3.5  1.6  0.6  0.2  0.1  0.0  0.0  0.0  0.0  0.0  0.0  0.0
> 02:       1.4  2.2  1.4  0.7  0.3  0.1  0.0  0.0  0.0  0.0  0.0  0.0
> 03:            3.9  2.1  1.2  0.6  0.2  0.1  0.0  0.0  0.0  0.0  0.0
> 04:                 1.2  2.0  1.3  0.6  0.2  0.0  0.0  0.0  0.0  0.0
> 05:                      3.8  2.0  1.2  0.5  0.2  0.0  0.0  0.0  0.0
> 06:                           1.1  2.0  1.3  0.6  0.2  0.0  0.0  0.0
> 07:                                3.9  2.1  1.1  0.5  0.1  0.0  0.0
> 08:                                     0.9  2.1  1.4  0.5  0.0  0.0
> 09:                                          4.3  2.2  1.1  0.2  0.0
> 10:                                               0.7  2.4  1.6  0.0
> 11:                                                    5.0  2.5  0.4
> 12:                                                         0.0  3.9
> 13:                                                              8.7
> 
> N=1+(NP-npaired-1)/5  i    (ie. 20% of the players available)
>         2    3    4    5    6    7    8    9   10   11   12   13   14
> 01:  3.0  2.5  2.0  1.6  1.3  1.0  0.7  0.5  0.3  0.1  0.0  0.0  0.0
> 02:       2.0  1.9  1.7  1.4  1.1  0.8  0.6  0.4  0.2  0.1  0.0  0.0
> 03:            1.4  1.3  1.2  1.1  1.0  0.8  0.7  0.5  0.3  0.2  0.0
> 04:                 1.1  1.1  1.1  1.1  1.0  0.9  0.7  0.5  0.3  0.0
> 05:                      1.2  1.2  1.1  1.1  1.0  0.8  0.6  0.3  0.0
> 06:                           1.2  1.2  1.2  1.1  1.0  0.7  0.4  0.0
> 07:                                1.2  1.2  1.2  1.1  0.9  0.6  0.2
> 08:                                     1.2  1.2  1.1  1.0  0.8  0.6
> 09:                                          1.1  1.0  1.0  1.1  1.3
> 10:                                               0.8  1.1  1.5  1.9
> 11:                                                    1.4  1.9  2.4
> 12:                                                         2.4  3.0
> 13:                                                              3.6
> 
> N=1+sqrt(NP-npaired-2)
>         2    3    4    5    6    7    8    9   10   11   12   13   14
> 01:  4.0  3.0  2.2  1.5  1.0  0.6  0.4  0.2  0.1  0.0  0.0  0.0  0.0
> 02:       2.2  2.0  1.7  1.3  0.9  0.5  0.3  0.1  0.0  0.0  0.0  0.0
> 03:            1.9  1.6  1.4  1.1  0.8  0.5  0.3  0.1  0.0  0.0  0.0
> 04:                 1.3  1.4  1.3  1.1  0.9  0.5  0.3  0.1  0.0  0.0
> 05:                      1.6  1.5  1.3  1.1  0.8  0.4  0.1  0.0  0.0
> 06:                           1.5  1.6  1.4  1.1  0.6  0.2  0.0  0.0
> 07:                                1.8  1.6  1.4  1.0  0.4  0.0  0.0
> 08:                                     1.5  1.9  1.3  0.7  0.1  0.0
> 09:                                          2.5  1.5  1.1  0.6  0.0
> 10:                                               0.7  2.2  1.4  0.1
> 11:                                                    4.4  2.2  0.5
> 12:                                                         0.0  3.7
> 13:                                                              8.7
> 
> N=1 (fixed, just for verification :-)
>         2    3    4    5    6    7    8    9   10   11   12   13   14
> 01:  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0
> 02:       1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0
> 03:            1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0
> 04:                 1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0
> 05:                      1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0
> 06:                           1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0
> 07:                                1.0  1.0  1.0  1.0  1.0  1.0  1.0
> 08:                                     1.0  1.0  1.0  1.0  1.0  1.0
> 09:                                          1.0  1.0  1.0  1.0  1.0
> 10:                                               1.0  1.0  1.0  1.0
> 11:                                                    1.0  1.0  1.0
> 12:                                                         1.0  1.0
> 13:                                                              1.0
> 
> Don: I appended the (C-) program for your own experiments.
> 
> Christoph