Re: [Bug-gnubg] Even, odd and half plies (WAS: New Contact Net Error Rates)

[David Montgomery]

From: "Nis" <address@hidden>
> 1) Average between 12 rolls at 1-ply and 24 times the static 0-ply eval.
> 2) Average between 12 rolls at 2-ply and 24 at 1-ply.
> 
> Perhaps we can implement both - using 1) for reduced 1-ply, and 2) for 
> higher plies.

Yes.  But to me, these are the same thing. 

Well, I guess I'm still not sure I understand. Let me try again.
For 2-ply, of course, there are 1296 terminal nodes (looking at just
the selected lines of play). So my guess for the best way to
do 2) is:

2A) Do a weighted average of 432 2-ply nodes selected by striated 
    sampling with the result of a full 1-ply evaluation, using 
    empirically derived weights.

It appears to me you are suggesting

2B) Evaluate 12 of the 1-ply continuations at 2-ply, and 24 at 1-ply.
    Add these up and dived by 36.

2A) is taking the current implementation (as I understand it)
and creating a weighted average with the 1-ply evaluation.

2B) requires a different implementation, because you select the
nodes for deeper evaluation at the first ply, rather than spreading
the sampling evenly over the leafs.

Both 2A) and 2B) evaluate 432 nodes at the deepest level.  2A)
evaluates 12 nodes for each of the 36 1-ply rolls, so you get
2-ply information for every 1-ply continuation.  2B) evaluates
36 nodes for each of 12 1-ply rolls, and 0 nodes for the other
24.

In fact, 2A) is exactly the 1-ply lookahead version of 

> 1) Average between 12 rolls at 1-ply and 24 times the static 0-ply eval.

averaging 36 of these evaluations.  

2B) is not.  It's a mixture of

Average between 36 rolls at 1-ply and  0 times the static 0-ply eval.
Average between  0 rolls at 1-ply and 36 times the static 0-ply eval.

David