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Subject: Re: Number of reachable positions

Author: Robert Pope

Date: 06:44:39 08/31/00

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On August 31, 2000 at 04:27:38, Andreas Stabel wrote:

>Here is what I have calculated:
>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               |        |
>
>I started calculating ply 8 and it ran for 2-3 weeks before I had to stop it.
>Sadly this program is not restartable, so all was lost - it needed approx. a
>week more to finish. But it seemed that the expected approx. 10^9 unique nodes
>on ply 8 was what it was approaching when I terminated it. The problem with
>this calculation is that I need a fast machine with at least 11 giga byte
>free space to run for nearly a month to finish, so if anybody want to try
>tell me !
>
>Best regards
>Andreas Stabel
Thanks!  Just to make sure I am reading this correctly: These are total # of
nodes traversed, not total # of ending positions?  So to get total ply n
positions, I would do Nodes(n)-Nodes(n-1).  E.g. Positions reachable in two
plies = 421-21=400.



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