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Subject: Unique nodes from the start position

Author: Andreas Stabel

Date: 05:16:25 06/29/00


I have made a program that calculates this and here is the result to ply 7.

   |               | Unique nodes  | Unique nodes | Unique nodes  | Factor |
Ply| Total # nodes | ep = pawn two | ep = opposite| ep = Only if  | prev.  |
   |               |               | pawn can hit | ep is legal   | row    |
---+---------------+---------------+--------------+---------------+--------|
 0 |             1 |             1 |            1 |             1 |        |
 1 |            21 |            21 |           21 |            21 |  21.00 |
 2 |           421 |           421 |          421 |           421 |  20.05 |
 3 |          9323 |          8023 |         5783 |          5783 |  13.74 |
 4 |        206604 |        109262 |        77796 |         77796 |  13.45 |
 5 |       5072213 |       1351950 |       898812 |        898812 |  11.55 |
 6 |     124132537 |      15334851 |     10281864 |      10281862 |  11.44 |
 7 |    3320034397 |     160373323 |    106193912 |     106193643 |  10.33 |
 8 |   88319013353 |               |              |               |        |
 9 | 2527849247520 |               |              |               |        |

It is interesting to note how great the reduction is just by not
setting the E.P. target square if there is not pawn to hit. This simple
test reduses the number of unique positions by a third !

It is also interresting to note how the "branching factor" of unique nodes
gets smaller - from 21 to nearly 10 from ply 6 to ply 7. One wonders if
it continues to grow smaller. I've calculated that the average branching
factor (average number of legal moves in all positions) in a game is 31.

My program can calculate even greater plys, but I need a machine with
more than 10Gb of disc space and it will have to run for 2-3 weeks, so
don't know when I will be able to do this. It would be interesting to
check my numbers with others if anybody have calculated this.

Regards
Andreas Stabel



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