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

 From: Nis Subject: RE: [Bug-gnubg] RE:Why is odd ply equity always lower? Date: Thu, 12 Jun 2003 19:46:33 +0200

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--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
plies.
```
```
```
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:
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```
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.

```
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.
```
QED

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

--
Nis Jorgensen
Greenpeace
Amsterdam

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