# Computer Chess Club Archives

## Messages

### Subject: A new look.

Author: Dan Andersson

Date: 02:41:04 06/20/03

Go up one level in this thread

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
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.

MvH Dan Andersson

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