Talk:Shannon number

message: Hmmm... well, it occured to me that the total number of posible board positions couldn't be more than 64!/32!... that is, the total number of ways of arranging 32 distinguishable pieces on a board of 64 spaces. But I didn't consider the affect of promoting pawns, and all the various choices that might be available in that case, and the extra board positions that this would create... still though, if promoting pawns was disallowed, it would limit the positions to 64!/32! (as well as noticably changing the dynamics of the game)... just a curious thought. (The Swami 08:36, 17 August 2005 (UTC)
replies: text: 64! / 32! = 482219923991114978843459072919892677776312893440000000, but that's not what Shannon's number is. Soo 16:01, 26 September 2005 (UTC)
replies: text: I know it's not, I was just posting some musings on the derivation of said number... but here's a few more while I'm thinking of it... I think the total number of board positions could not excede 64!/32! ^ 6^32; this would be the total thirty two pieces maximum on the board, each of which can be one of six types. The game-tree complexity may be larger than this, I'm just saying that the total number of board positions could not (I believe) excede this. (The Swami 02:53, 28 September 2005 (UTC)
thread_title: Number of Board Positions

message: There are several possible problems with this page. First, "One novemtriginillion is known as the Shannon number." It seems like the Shannon Number is actually 90040, which is 1.478...×10118, for which 10120 is a poor approximation. If 90040 is indeed the Shannon Number, then that doesn't really belong in this article. Also, for the number of atoms in the universe: can that figure really be estimated with so much precision? Ardric47 05:18, 6 April 2006 (UTC)
thread_title:  Shannon Number 

message: This article is about the Shannon number. Now that it has been decided that the Shannon number is not 10^120, shouldn't the article be moved back to Shannon number? Melchoir 01:49, 8 April 2006 (UTC)
thread_title:  Move? 

message: Due to confusing redirects, this page has been mirrored (and then added to by me...) at Talk:10^120 (number). Ardric47 21:14, 8 April 2006 (UTC)
replies: text: Actually, as I type this, the page history is at 10^120. The redirect at 10^120 should be reverted and then moved on top of Shannon number. Melchoir 21:41, 8 April 2006 (UTC)
replies: text: Do you know offhand if there was ever anything about 10120 (and not the Shannon number) that might need to be moved to its own article? 10^120 (number) is now (as of 21:46, 8 April 2006 (UTC)
replies: text: Not really. I'm actually now inclined to leave the redirect and this page as they are. As long as 10^120 (number) isn't deleted, it will retain a record of this page's early history, which includes so many moves that it might be best forgotten anyway. Melchoir 21:53, 8 April 2006 (UTC)

text: The root of the problem is the first version, in which 10120 is equated with the so-called "Shannon number". Let me add though, that I'm sure the creator meant well. Ardric47 21:52, 8 April 2006 (UTC)
replies: text: Right. Melchoir 21:53, 8 April 2006 (UTC)
thread_title:  Confusing redirects 

message: I cut this text from the article:
:Page 70 in “The Immortal Game” by David Shenk estimates that there are 10120 unique games of chess possible.
because it appears (considered very charitably) merely to be a restatement of Shannon's estimate from the first sentence of the article, adding nothing to the article, which is not a general article on combinatorial estimates relating to chess. (Considered uncharitably, with "unique games" taken literally, the claim is of course quite false.) Gdr 10:31, 25 September 2008 (UTC)
thread_title:  Cut restatement 

message: How in the world can a large number about chess variants be an analog to a joking reference about how close you are to a mathematician? I don't understand. Practicality (talk) 15:27, 2 February 2010 (UTC)
replies: text: If this other Shannon number were important it should have its own article. The reference doesn't belong here. Lubrom (talk) 18:10, 26 July 2010 (UTC)
thread_title:  Other uses? 

message: In a 2006 posting to newsgroup rec.games.chess.computer
Will Entriken proved an upper bound of 23937533792747905898433845980097921846050276105440 on the number
of chess diagrams (roughly 2^164).
The following Haskell program, if correct, improves this to just under 2^155 for the number of positions,
which includes side-to-move, castling, and en-passant info.
import Control.Monad
import System(getArgs)
import Array
armies np ir = do -- max number of pawns and initial rooks
  q <- [0..1+np]
  let prom1 =         max (q-1) 0
  r <- [0..ir+np-prom1]
  let prom2 = prom1 + max (r-ir) 0
  b <- [0..2+np-prom2]
  let prom3 = prom2 + max (b-2) 0
  n <- [0..2+np-prom3]
  let proms = prom3 + max (n-2) 0
  guard $ proms <= np
  p <- [0..np-proms]
  return (q+r+b+n, p, proms, fac q*fac r*fac b*fac n*fac p)
fac :: Int -> Integer
fac n = fac64!n where fac64 = listArray (0,64) (scanl (*) 1 [1..64])
count fixp pspace fixwr fixbr = sum $ do
  let np = 8-fixp
  (wpcs,wp,wproms,wprod) <- armies np (2-fixwr)
  let wpx = np-wp-wproms                 -- white p captured
  (bpcs,bp,bproms,bprod) <- armies np (2-fixbr)
  let bpx = np-bp-bproms                 -- black p captured
  let caps = 30-2*fixp-fixwr-fixbr-wp-bp-wpcs-bpcs
  guard $ wproms <= bpx + caps
  guard $ bproms <= wpx + caps
  let space = 62-4*fixp-fixwr-fixbr-wp-bp
  return $ (fac pspace `div` fac (pspace-wp-bp)) *
           (fac space `div` fac (space-wpcs-bpcs)) `div` (wprod * bprod)
count0 (mul,ek) = mul * count 0 (46+ek) 0 0
-- Diagrams
main0 = print . sum $ map count0 [(212,2),(1448,1),(1952,0)]
-- 22124621884617108585387385940828998876019391612
-- multiplier, edge kings, fixed white rooks, fixed black rooks
countep (mul,ek,fwr,fbr) = mul *
  (count 0 (46+ek) fwr fbr + 14 * count 1 (42+ek) fwr fbr)
-- Positions
main = print . (* 2) . sum $ map countep
  [(1,2,2,2),(4,2,1,2),(4,2,1,1),
   (2*9,2,0,2),(2*43,1,0,2),(4*11,2,0,1),(4*44,1,0,1),
   (212,2,0,0),(1448,1,0,0),(1952,0,0,0)]
-- 45193640626062205213735739171550309047984050718
--Tromp (talk) 17:32, 5 May 2010 (UTC)
replies: text: Just in case it's not clear, the program above (allegedly) computes an upper bound on the number of chess positions, whereas Shannon was estimating a simple lower bound on the number of variations needed to calculate the game-theoretic value of the initial position. Gdr 00:24, 4 August 2010 (UTC)
thread_title:  Upper bound