Re: [Bug-gnubg] quasi-random dice for the Initial Position

[Joern Thyssen]

On Mon, Jul 07, 2003 at 08:50:39AM +0200, Jim Segrave wrote
[snip]
> 
> The dice sequence doesn't know how man trials it will be asked for, it
> simply generates sequences such that every 30/36 games you get all
> possible 1st rolls, every 1080/1296 games get every possible first 2
> rolls, every 38880/46656 games you get full sets of 3 rolls, etc.

Hmm, are you sure? 

For example, for a 1080 trial rollout you remove 216 sequences from the
quasi-random dice array. Can you be sure that the sequences you remove
have a uniform distribution on the second roll?

I did a 1080 trial rollout (RAIP, trunc. after 6 plies) and stored the
dice. Here is 12:

Roll 12 11 16 16 51 63 (iGame 1022)
Roll 12 14 12 52 45 51 (iGame 902)
Roll 12 14 25 33 52 62 (iGame 662)
Roll 12 15 25 32 11 34 (iGame  62)
Roll 12 15 51 23 21 61 (iGame  32)
Roll 12 21 22 26 43 54 (iGame 512)
Roll 12 22 43 14 16 25 (iGame 272)
Roll 12 23 36 62 51 24 (iGame 452)
Roll 12 24 11 64 63 51 (iGame 962)
Roll 12 24 16 46 34 61 (iGame 332)
Roll 12 24 26 31 61 16 (iGame 932)
Roll 12 26 64 16 16 34 (iGame   2)
Roll 12 26 66 43 22 61 (iGame 632)
Roll 12 32 45 32 51 65 (iGame 182)
Roll 12 32 64 23 65 54 (iGame 812)
Roll 12 33 22 11 21 44 (iGame 602)
Roll 12 33 32 44 41 11 (iGame 572)
Roll 12 35 35 54 16 22 (iGame 842)
Roll 12 42 16 35 14 12 (iGame 422)
Roll 12 42 62 26 63 41 (iGame 392)
Roll 12 43 23 52 33 45 (iGame 782)
Roll 12 43 35 23 56 24 (iGame 152)
Roll 12 43 44 21 46 64 (iGame 752)
Roll 12 45 23 44 31 41 (iGame 692)
Roll 12 55 14 51 22 12 (iGame 362)
Roll 12 55 45 46 42 41 (iGame 992)
Roll 12 55 54 15 41 46 (iGame 122)
Roll 12 56 11 21 32 11 (iGame 872)
Roll 12 61 61 55 52 51 (iGame  92)
Roll 12 62 24 31 55 64 (iGame 1052)
Roll 12 64 34 41 46 26 (iGame 302)
Roll 12 64 46 35 65 44 (iGame 542)
Roll 12 65 31 45 61 23 (iGame 482)
Roll 12 65 41 11 42 45 (iGame 722)
Roll 12 66 35 51 23 65 (iGame 242)
Roll 12 66 65 46 33 54 (iGame 212)

There is 36 trials starting with 12 as expected, but the distribution of
the second roll is clearly not uniform....

I've attached a file with all 1080 games. Run "gzip -cd log.gz | sort"
to get a list like mine above.

Jørn

log.gz
Description: application/gunzip