2010/5/28 Massimiliano Maini <[email protected]>

> 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.
I then just have to find the perfect hash function. I guess that can be done
in couple of hours. I'll just get a cup of coffee first. I'll post a follow
up mail when I've found it. :-)


-Øystein
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