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

[Nis]

Quoting myself:

> 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 ...

Some items for consideration:

How does this affect higher plies?

One would think that the same mechanism would lead to 2-ply overestimating 
the best 1-ply play, and thus cancel out some of the error of the 1-ply 
calculation. This is not necessarily so, however, since the best play is 
selected on 0-ply, and only evaluated at 1-ply. Only if the errors of 1-ply 
and 0-ply correlate, will some of the effect be cancelled out at 2-ply.

Even if the correlation is there, the effect will be dampened by the 
imperfect correlation as well as the assumed smaller relative error on 
1-ply compared to 0-ply.

If we ASSUME that the effect only appears at 1-ply, we find that the error 
propagates through the plies, being negative for odd plies and positive for 
even plies.

Thus an "obvious" fix would be to implement my previously suggested 
half-plies - averages between n- and (n+1)-ply

I have written the code to do so, and it compiles and works (as in doesn't 
play obviously bad)

I can send a patch to someone with an account.

For those interested, what I do is

Please note that my code removes the ability of gnubg to do reduced 1-ply 
evaluations. I can reimplement it if people see a need.

---

Only relevant for cube decisions?

The wrong estimations of equity is mainly a problem of absolute equities. 
As Joseph has pointed out, chequerplay relies almost solely on the relative 
equities of positions.

Thus a fix should only "need" to be applied for cube decisions (and cubeful 
chequerplay? Someone help me here)

So we might want to start using reduced evaluation settings for cube 
decisions

---

Training

Another question is: Does this have any impact on the training of the nets? 
Anything that could be done better, or implications for how we want to 
train.

---

Measuring

I am really interested in how this affects playing strength. Joseph has 
already measured the strength difference between 0, 0.5 and 1-ply (0.5-ply 
calculated as the average of the other two). However, I think the really 
interesting question will be how 1.5-ply relate to 1- and 2-ply - 
especially for cube decisions.

--
Nis Jorgensen
Greenpeace
Amsterdam