2010/5/28 Massimiliano Maini
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Hi all,
another criteria to separate usual positions from unusual ones could
be the number of occupied points. In Trice's formula you sum over the
range 0..15 for m:
C(24,m) X D(m+2,15-m) X D(26-m,15)
m being the (regular) points occupied by black.
Now, how frequent is that black holds 15 points ?
Good idea!
According to rough calculations (excel not having big integers),
all the positions where black occupies 10 or less (regular) points are
already less than 2^64.
True!
Do not use Excel because it has limitations like the one you mention, and lot's of others. Use Google Docs Spreadsheet, and you can quite easily extend it with _javascript_ functions. And of course you can share your spreadsheet with others. I've made the Trice calculation in Google Docs here:
https://spreadsheets.google.com/ccc?key=0AiXPuo_wblgydHFVY0stekZkZ1
This can even be refined, as in the total there are positions where
white occupies more than 11 points (and impossible positions, game
over positions etc).
Yes, I believe this is theoretical possible. Thanks for your suggestions.