166:... 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. (
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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 900, which is 1.478...×10, for which 10 is a poor approximation. If 900 is indeed the Shannon Number, then that doesn't really belong in this
667:
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
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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
299:
Yes, it's wrong, and I'll change it. While it is unclear exactly what the
Shannon number is, whether it's 900^40 or some more accurate estimate, this article does not state that 10^120 is the Shannon number, so its title is misplaced. In general, you should trust the more specialized Knowledge
190:
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.
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I think that
Shannon knew that some games might last 41 moves, which gives 900=1.3x10 so he just rounded it off to 10. However it is true that for him to say that 900 "will be 10 variations" is pretty sloppy mathematics. Was he using a slide rule at the time?
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It only seems pretty close because the exponents are pretty close, but really it is larger than the
Shannon Number by a factor of about 67...saying that this is pretty close would be like saying that pi is pretty close to 200 (3.14...×10 vs. 2×10).
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Approximating 118 with 120 is hardly the same as approximating 0 with 2. A better picture is pi to 10 (10 vs 10) More importantly; when dealing with that large numbers approximating the exponent is usual, and frequently
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I restored the number 10^120, with a quote from the paper. Sure, it's an approximation, but it's
Shannon's number so we should use Shannon's approximation, not Ardric47's approximation!
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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
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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.
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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
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site when mentioning the lower bound of an estimate of all the atoms in the universe. However, the following calculation on that page is incorrect:
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article, it says "The
Shannon number is a rough estimate of the number of possible chess games, and is more than a googol: 10120". Is it wrong?
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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.
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I've changed where it claimed that it was the
Shannon number. While it might not be the Shannon number, it's pretty close in size to it.
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Do you know offhand if there was ever anything about 10 (and not the Shannon number) that might need to be moved to its own article?
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article. Also, for the number of atoms in the universe: can that figure really be estimated with so much precision?
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If this other Shannon number were important it should have its own article. The reference doesn't belong here.
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64! / 32! = 482219923991114978843459072919892677776312893440000000, but that's not what Shannon's number is.
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Hmmm... well, it occured to me that the total number of posible board positions couldn't be more than
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on Knowledge. If you would like to participate, please visit the project page, where you can join
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368:. I'm actually now inclined to leave the redirect and this page as they are. As long as
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Due to confusing redirects, this page has been mirrored (and then added to by me...) at
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Just in case it's not clear, the program above (allegedly) computes an
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1621:-- multiplier, edge kings, fixed white rooks, fixed black rooks
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estimates that there are 10 unique games of chess possible.
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is now (as of 21:46, 8 April 2006 (UTC)) a redirect to
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2047:-- 45193640626062205213735739171550309047984050718
1618:-- 22124621884617108585387385940828998876019391612
665:2006 posting to newsgroup rec.games.chess.computer
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614:literally, the claim is of course quite false.)
487:{\displaystyle 1*10^{57}*4*10^{11}=5*10^{68}}
8:
2116:Start-Class chess articles of Mid-importance
300:article above other articles mentioning it.
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715:-- max number of pawns and initial rooks
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95:This article is within the scope of
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605:Page 70 in “The Immortal Game” by
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415:Calculation error in refered page
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389:I'm sure the creator meant well
383:The root of the problem is the
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331:Actually, as I type this, the
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182:16:01, 26 September 2005 (UTC)
1:
2111:Mid-importance chess articles
2074:bound on the number of chess
109:and see a list of open tasks.
638:15:27, 2 February 2010 (UTC)
586:{\displaystyle 3.2*10^{79}}
171:08:36, 17 August 2005 (UTC)
115:Knowledge:WikiProject Chess
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2106:Start-Class chess articles
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339:on top of Shannon number.
141:project's importance scale
118:Template:WikiProject Chess
653:18:10, 26 July 2010 (UTC)
553:{\displaystyle 5*10^{68}}
520:{\displaystyle 4*10^{68}}
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396:21:52, 8 April 2006 (UTC)
377:21:53, 8 April 2006 (UTC)
361:21:46, 8 April 2006 (UTC)
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333:page history is at 10^120
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158:Number of Board Positions
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2114:
2112:
2109:
2107:
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2085:
2081:
2077:
2073:
2069:
2068:
2067:
2064:
2063:
2059:
2055:
676:Control.Monad
669:
666:
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642:
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385:first version
382:
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375:
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354:Large numbers
351:
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1732:-- Positions
662:
630:Practicality
627:
612:
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292:64.194.43.49
271:
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247:
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187:
163:
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136:
96:
90:Chess portal
40:WikiProjects
1591:-- Diagrams
659:Upper bound
624:Other uses?
607:David Shenk
30:Start-class
2100:Categories
2084:variations
366:Not really
240:necesarry.
2076:positions
1030:listArray
193:The Swami
168:The Swami
402:Melchoir
393:Ardric47
374:Melchoir
358:Ardric47
341:Melchoir
323:Ardric47
302:Melchoir
278:Melchoir
232:Ardric47
212:Ardric47
1771:countep
1624:countep
1000:Integer
688:getArgs
400:Right.
286:In the
164:64!/32!
139:on the
1615:count0
1537:count0
1450:pspace
1432:pspace
1420:return
1357:bproms
1336:wproms
1264:bproms
1222:armies
1207:bproms
1186:wproms
1144:armies
1129:wproms
1075:pspace
997:-: -->
901:return
700:armies
694:import
682:System
679:import
673:import
668:info.
645:Lubrom
527:, not
288:googol
36:scale.
2080:lower
2072:upper
2054:Tromp
1741:print
1702:count
1666:count
1600:print
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1564:count
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1375:space
1360:<=
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1339:<=
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1024:fac64
1021:where
1012:fac64
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898:<-
889:<=
886:proms
880:guard
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847:proms
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337:moved
268:Move?
112:Chess
103:Chess
59:Chess
2058:talk
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817:max
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568:3.2
250:Gdr
179:Soo
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