MatPlus.Net

 Website founded by
Milan Velimirović
in 2006

3:19 UTC
 
  Forum*
 
 
 
 

Username:

Password:

Remember me

 
Forgot your
password?
Click here!
SIGN IN
to create your account if you don't already have one.
CHESS
SOLVING

Tournaments
Rating lists
1-Oct-2019

B P C F





 
 
MatPlus.Net Forum General Percentage of legal positions with legal material
 
You can only view this page!
(1) Posted by Hauke Reddmann [Saturday, Aug 3, 2013 19:15]

Percentage of legal positions with legal material


Foreign thread needs retro buffs!

http://mathoverflow.net/questions/138133/what-proportion-of-chess-positions-that-one-can-set-up-on-the-board-using-a-leg/138365#138365

Hauke
 
(Read Only)pid=10697
(2) Posted by seetharaman kalyan [Wednesday, Aug 7, 2013 08:37]

The book 'A guide to Fairy chess' by ASM Dickens had an estimate of the legal positions possible in a game of chess, but I cant locate my copy.
 
 
(Read Only)pid=10707
(3) Posted by Eugene Rosner [Thursday, Aug 8, 2013 17:00]

according to the Dickins book(p.28) all 32 men regardless of legality can stand~4.6x10^42. it does not give an estimate of legal positions, as mentioned before, far less.
 
   
(Read Only)pid=10711
(4) Posted by seetharaman kalyan [Friday, Aug 9, 2013 10:17]

Oh.... my memory was not right :). That was a different estimate.
 
   
(Read Only)pid=10716
(5) Posted by Diyan Kostadinov [Saturday, Aug 10, 2013 07:28]

Ram, I upload the book here, so you can download:
http://dox.bg/files/dw?a=b0dfd631e1

The link will be active till 24.08.2013
 
   
(Read Only)pid=10727
(6) Posted by Hauke Reddmann [Sunday, Aug 11, 2013 16:47]

Unfortunately, the estimate helps nil for the asked question.
As you can see in the MathOverflow thread, the percentage of
legal positions with 32 pieces is only an almost vanishing part
of the possible ones. And the problem is that the ratio
(Positions with n pieces)/(Positions with n-1 pieces) is of
order 1, where (Legal percentage of Positions with n pieces)/
(Legal percentage of Positions with n-1 pieces) skyrockets
with falling n, and you have almost no idea where the one
effect outdoes the other.
Or does it? At how many pieces "almost any" pawn structures
become legal?

Hauke
 
 
(Read Only)pid=10743

No more posts


MatPlus.Net Forum General Percentage of legal positions with legal material