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

[Joseph Heled]

Ingenious. If true, this is a general argument that applies to all bots.

I would like to repeat my personal view that bots play well not because 
they get the absolute equity right, but despite it. A bot chooses well 
between several positions. This applies both to play and doubling. Takes 
is the only case where this does not apply, and is the greatest source 
of bot mistakes.

-Joseph

Nis Jorgensen wrote:
> --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).