Darren,
this sounds like a good insight, but only if a very large number of
playouts have been performed. By contrast, the original poster writes:
But in the opening, where the scoring
leaves are 300 moves away from the root, surely a putative half point
win doesn't translate to a significant advantage, where as a 100
This I don't buy. If the scoring leaves are 300 moves away, any random
playout is way too unreliable to take the score into account. You might
as well generate a score randomly. It could be a 100 point win on the
first and 100 point loss on the second. In that case, it will be much
safer to use Fuego's approach of slightly modifying the playout score
from [0.0,1.0] to [0.0+s,1.0-s] where s depends on the size of the win
relative to the board size.
It is also worth bearing in mind - again, only if the state space was
only very superficially searched - that winning by large margins can
entail taking large risks. Human players do that only when behind and
otherwise actively seek the safer route.
Christian
On 01/07/2009 04:23, Darren Cook wrote:
It seems to be surprisingly difficult to outperform the step function
when it comes to mc scoring. I know that many surprises await the mc
adventurer, but completely discarding the final margin of victory
just can't be optimal. ...
an mc program, holding on to a half point victory in the endgame, is
a thing of beauty and terror. But in the opening, where the scoring
leaves are 300 moves away from the root, surely a putative half point
win doesn't translate to a significant advantage, where as a 100
point win would.
I had a breakthrough in my understanding of why it is "surprisingly
difficult to outperform the step function" when analyzing some 9x9 games
with Mogo and ManyFaces. Let's see if I can extract that insight into
words...
I observed that in many situations I could map the winning percentage to
the final score. E.g.
50-55%: 0.5pt
55-60%: 1.5pt
60-65%: 2.5pt
etc.
It wasn't as clear cut as that. In fact what I was actually noticing was
if I made a 1pt error the winning percentage for the opponent often
jumped by, say, 5%.
Thinking about why... In a given board position moves can be grouped
into sets: the set of correct moves, the set of 1pt mistakes, 2pt
mistakes, etc. Let's assume each side has roughly the same number of
moves each in each of these groupings.
If black is winning by 0.5pt with perfect play, then mistakes by each
side balance out and we get a winning percentage of just over 50%. If he
is winning by 1.5pt then he has breathing space and can make an extra
mistake. Or in other words, at a certain move he can play any of the
moves in the "correct moves" set, or any of the moves in the "1pt
mistakes" set, and still win. So he wins more of the playouts. Say 55%.
If he is winning by 2.5pts then he can make one 2pt mistakes or two 1pt
mistakes (more than the opponent) and still win, so he wins more
playouts, 60% perhaps. And so on.
My conclusion was that the winning percentage is more than just an
estimate of how likely the player is to win. It is in fact a crude
estimator of the final score.
Going back to your original comment, when choosing between move A that
leads to a 0.5pt win, and move B that leads to a 100pt win, you should
be seeing move B has a higher winning percentage.
Darren
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