# Computer Chess Club Archives

## Messages

### Subject: Re: A new look.

Date: 03:05:38 06/20/03

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```On June 20, 2003 at 05:41:04, Dan Andersson wrote:

> I tried to look at it in a new way. Reflect upon this:
> d(t) is the depth reached by the perfectly ordered tree were t is nodes or
>time.
> dm(t) is the depth of the minimax tree.
> dm(t)=2*d(t)
> di(t,k) is a tree in the middle.
> di(t,k)=(1+k)*d(t) k is in [0, 1]
> di(t,k1)<di(t,k2) iff k1<k2
di(t,k1)<di(t,k2) iff k2<k1
> what properties does di have?
> The gain is linear to search depth. A doubling in search depth gives a doubling
>in gained depth. 2*di(t,k2)-2*di(t,k1)=2(1+k2)*d(t)-2*(1+k1)*d(t)=2*(k2-k1)*d(t)
> The gain is constant to time. A doubling in time gives a constant addition in
>gained depth. (k2-k1)*(d(2*t)-d(t))=(k2-k1)*constant since d is a logarithic
>function of t.
> This might also be horribly wrong. Feel free to comment.
Very tired right now :)
Only problem with this analysis is that k is not defined properly. But if move
ordering is close to perfect this won't matter for reasonable search depths.
Then k will be close to zero anyway. Maybe I'll lok into that after some sleep.
>