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Subject: Re: Ply Depth in relation to Elo again...

Author: Dann Corbit

Date: 22:05:11 05/23/00

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On May 24, 2000 at 00:51:01, Peter Kappler wrote:
[snip]
>True, though some of that was due to eval improvements.  To be clear, I totally
>accept the fact that extra plies give increased strength, I just find it
>impossible to believe that this effect doesn't gradually diminish as you get
>deeper and deeper.

The question is (obviously) "How deep is 'deep enough'?"

At some point, you will see all the way to checkmate.  But if it is 50 plies
away on a crowded board, you would like all 50 of those plies.  If one move
leads to sure mate in 50 and none of the others do, then that search will
clearly yield great value.

In the endgame, once you get to the tablebase files, deeper is fairly
meaningless.

So depth primarily applies from opening through early endgame.

In a way, it is astonishing that an additional ply only gives you a 10-15%
better guess at the best move.  You have a multiple of the information you had
at the previous ply.  If (for instance) you have 3 times as many nodes from the
current ply to the next, and you benefit only about 10%, then the value of those
extra nodes is rapidly diminishing.  After all, you spent three times as much
work for such a tiny ray of light.  Let's look at the cost for an approximate
branching factor of 3 to get a coin toss worth of improvement, assuming a 10%
yield in additional plies.  It's easier to consider the odds that the move is
not improved each pass (.9 probablity), as this simplifies the calculation quite
a bit.

.9*.9 = .81 *.9 = .721 *.9 = .6561 *.9 = .59049 * .9 = .531441 *.9 = .4782969
So we now got better than 50% probability of benefit after 7 additional plies.
That's 2187 times as many nodes examined to increase the odds of making a better
choice by about 50%.

When you look at it that way, it's remarkable that the benefit is not higher.




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