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Re: [Bug-gnubg] RE:Why is odd ply equity always lower?

From: Joseph Heled
Subject: Re: [Bug-gnubg] RE:Why is odd ply equity always lower?
Date: Fri, 13 Jun 2003 07:41:53 +1200
User-agent: Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.2) Gecko/20021202

Nis wrote:

--On 12 June 2003 15:42 +0100 Ian Shaw <address@hidden> wrote:

As I understand it, on a 1-ply evaluation of a position, the net is fed
all 21 possible return rolls for the opponent, and the equities of the
best moves are averaged. The equity for the original player is then one
minus this average. If the net tends to overvalue the equity of the side
on roll, then the 1-ply equity will tend to be lower than the 0-ply
equity. We would then expect this trend to continue for even and odd

Yes, this is a true implication. I don't know whether the 0-ply evals ARE too high on average. I would suspect something like that would have caught Joseph's eye

Furthermore, I just realised one possible cause for difference between 0-ply and 1-ply:

If 0-ply is unbiased but imprecise (as in having average error 0) then the value of the best move will be overrated.

Move    True Equity    0-ply equity
A            0.4         0.35
B            0.4         0.45
C            0.5         0.45
D            0.5         0.55  (*BEST MOVE*)

Note that the average error is 0, but the best move is off by 0.05.

Not sure I follow that. The 1 ply is the average of 21 "best 0ply moves" resulting from 21 dice combinations. For the best move, we compare different moves with the same dice. What am I missing?


The result of this should be that 1-ply, which is the average of 21 BestMoves for the opponent, is underrated by some amount. This will be added to the (negated) 0-ply, so if 0-ply is overrated, 1-ply is even more underrated.


In our next issue: Implications + How to repair this ...

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