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

[Nis Jorgensen]

--On 13 June 2003 07:41 +1200 Joseph Heled <address@hidden> wrote:

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

For the "best 0ply move" we compare the equities of the positions resulting 
from different moves (listed A, B, C and D above). This is fine. But if a 
move (that is, the resulting position) is overrated, it will more often be 
considered the best than if it is underrated - especially if the decision 
is close or even tied (as above). Therefore, the moves propagating into the 
1-ply evaluation will, on average, be overrated. Therefore if 0-ply is 
unbiased, 1-ply should on average be underrated (since the equities are 
negated).

--
Nis Jorgensen
Amsterdam