[Report] Adjusted Legitimate Go Game Space

[Mousheng Xu <xu@xxxxxxxxxx>]

Dear All,
	
	Below please see the adjusted go game space using the equation I derived.
For a 19 x 19 board, when illegal states are removed, the total number of
states is 9.5 * 10^165 instead of 1.74 * 10^172 (3^361), which is a 6-7
order save in magnitude.
	Given the total number of atoms in the universe is ~10^80, a 13 x 13 board
will have just as many states. Even after we consider symetry (divide by
16), a 14 x 14 board will have as many states as the number of atoms in a
zillion (10^9) universes. Hey, go for it. :)
	Given 10^9 be our complexity upper limit (n <= 4), considering legitimacy
won't save us more than 65%.
	Thanks a lot.

-- Mousheng Xu
____________________________________________________________________
n	adjusted_#_states	#_states	adjusted_#_states/#_states	
2    	45.332001597787645	81.0    	0.5596543407134277
3    	8965.407474819256	19683.0    	0.45548988847326405
4    1.5127702528627643E7    4.3046721E7    0.35142519981086695
5    2.0616194883363025E11    8.47288609443E11    0.24331962749878022
6    2.5072209886542644E16    1.50094635296999136E17    0.16704267835376735
7    2.4453290811817118E22    2.3929932923061753E23    0.10218704285732032
8    2.030078877485961E29    3.4336838202925124E30    0.05912247556075272
9    1.4171462425467587E37    4.434264882430377E38    0.03195898937300369
10    8.088099911584528E45    5.153775207320113E47    0.01569354421996651
11    3.961028920891788E55    5.3910308997432935E57    0.00734744243643716
12    1.5377616086616173E66    5.075287860564156E68    0.0030299002754312415
13    4.969722958049185E77    4.300233593900342E80    0.0011556867434128412
14    1.3074910107845457E90    3.279185047850306E93    3.98724375631586E-4
15    2.8411160849986555E103    2.250517072832484E107    1.262428141201723E-4
16    5.184013219476009E117    1.3900845237714473E122    3.729279141538264E-5
17    7.6035750806965E132    7.727564060276966E137    9.839549722767329E-6
18    9.256164610817395E148    3.8662196978715634E154    2.3941124235420743E-6
19    9.461634664181484E165    1.740896506590319E172    5.434920817155771E-7
Mousheng Xu

Associate Computational Scientist
Chiroscience R & D
1725 220th SE
Bothell, WA 98021
Phone:	(425)489-8034
Fax: 	(425)415-8250