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Subject: Re: Number of reachable positions

Author: Andreas Stabel

Date: 01:27:38 08/31/00

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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



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