Author: Dann Corbit
Date: 10:39:08 10/02/01
Go up one level in this thread
On October 02, 2001 at 06:04:38, Andreas Stabel wrote: >On October 01, 2001 at 18:21:09, Dann Corbit wrote: > >>On October 01, 2001 at 18:11:10, robert flesher wrote: >> >>>It has been calculated that the four opening moves can be made in 197,299 ways, >>>leading to some 72,000 different positions. The approximate numbers of different >>>games possible is 25x10 to the power of 116. a number astronomically higher that >>>the number of atmos in the observable universe. This Quote was directly taken >>>from Guiness book of world records 1976 edition. WOW and this is why chess is so >>>damn hard. :) >> >>Unfortunately, they don't know what they are talking about. >>There are 197,281 different ways to make the 4 opening moves. >>There are 99,270 distinct positions at ply 4 (including e.p vulnerability). >>The other numbers are equally suspect. >>This has some interesting information: >>http://www.clark.net/pub/pribut/chessfaq.html >>Though the actual length of the longest possible game may be open to a bit of >>debate. I have seen slightly different figures given elsewhere. > >My program has generated the following table - which does not seem to match >your numbers very well. > >Table from opening position: > | | Unique nodes | Unique nodes II Unique nodes | Factor | >Ply| Total # nodes | ep = pawn two | ep = oppositeII ep = Only if | prev. | > | | | pawn can hit II ep is legal | row | >---+---------------+---------------+--------------II---------------+--------| > 0 | 1 | 1 | 1 II 1 | | > 1 | 21 | 21 | 21 II 21 | 21.00 | > 2 | 421 | 421 | 421 II 421 | 20.05 | > 3 | 9323 | 8023 | 5783 II 5783 | 13.74 | > 4 | 206604 | 109262 | 77796 II 77796 | 13.45 | > 5 | 5072213 | 1351950 | 898812 II 898812 | 11.55 | > 6 | 124132537 | 15334851 | 10281864 II 10281862 | 11.44 | > 7 | 3320034397 | 160373323 | 106193912 II 106193643 | 10.33 | > 8 | 88319013353 | | II | | > 9 | 2527849247520 | | II | | It appears that the only thing that does not match is the unique positions. Here is my list of uniqe epd positions after 4 ply: ftp://cap.connx.com/pub/chess-engines/new-approach/r4.unq.bz2 Perhaps you could be so kind as to compare with what you generate and tell me where I went off. Be advised that some of the positions have "useless" e.p. markers, but that is demanded by the PGN standard.
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