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Subject: Re: A New Self-Play Experiment -- Diminishing Returns Shown with 95% Conf.

Author: Ernst A. Heinz

Date: 15:03:06 05/24/00

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Hi Dann,

>In these experiments, you varied the depth from 5 to 12 plies, but in the "goes
>deep" experiments, it was deeper, if I recall correctly.

Yes, right -- but so what?

The "go deep" experiments and the new self-play experiment are not
really related to one another, or are they?!

>In the earlier experiments, it seemed to level out.

In _which_ experiments did _what_ seem to level out?

>I would like to see control matches where the plies are equal.
>IOW, 5:5, 6:6 up to 12:12.

As an answer please see the paragraph about "Engine Calibration"
on page 9.

`` [...] Scaling the engine calibration to other fixed depths
   requires additional calibration matches at these depths. We did
   not deem the according effort worthwhile because it is quite
   unlikely that the Black/White behaviour of "Fritz 6" at other
   fixed depths differs substantially from the one at 8 plies. ''

>In that way, you will know what the gain of the extra ply is.
>I don't think you
>can tell clearly strictly from the data given.

The confidence intervals from Table 6 put bounds on the
_differences_ in real winning probabilities between versions
of "Fritz 6" searching to fixed depths "X+1 <=> X".

This very difference exactly quantifies the gain in playing
strength from depth "X" to "X+1".

>For example, in your 12 <==> 11 experiment, you show 35.71% wins, 52.38% draws,
>and 11.9% losses.  What would the result be for 12:12?

Does not really matter -- but please see above regarding
"Engine Calibration".

Which reasons do you have to doubt that "Fritz 6" against
itself at any same depth "X <=> X" exhibits significantly
different behaviour than at depth "8 <=> 8"?

>That is the real value of the ply (I think).

???

=Ernst=



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