You example is perfect for explaining the strengths of Monte Carlo.

And I think your analysis is wrong.   A Monte Carlo program will choose
the group that maximizes it win expectancies.   If it see's all groups
as 85%  then it would clearly go for the biggest group since that has a
bearing on the probability of winning.

The beauty of it is that if you have a complicated situation such as
yours,  but imagine each group has different odds of survival and there
are many of them of different sizes.   A human will probably take the
naive approach of immediately defending the largest group because that
is often the right choice.     Or he will intuitively choose the move
that is ON AVERAGE going to win the most stones.   

But the monte carlo engine takes a more measured and intelligent
approach.  It does a pragmatic calculation to determine which exact move
gives it the best chances of winning the game.    What less are you
asking for? 

And it's not STUPID about this.   Usually the biggest group is the one
you want and it's not like the monte carlo programs purposely will go
after the little group - they are not trying to minimize their score as
some people seem to believe. 

They are doing what every player should be doing - maximize your winning
chances.   It's irrelevant whether they are good at this or not or if
they make mistakes that cause them to lose games - the point is that
they are focused on the only goal of winning to the best of their
ability.  It's just plain silly to focus on a less relevant goal and I
don't understand the compulsion to make them play for less worthy
goals.   If it made them play stronger - then sure - go for it.  But it
doesn't work that way.

I rather like this style of play.    When the game is over and you have
lost,  I think it makes you look like a chump to fight as if you still
believe you are winning.     And even more I think trying to win big
makes you look like  a fool - at least it makes you look arrogant.     I
remember as immature children we would get upset if our opponents
resigned (at chess.)   We wanted the thrill of victory.    And it wasn't
good enough to just checkmate them,  we had to wipe out every piece and
pawn and then proceeded to checkmate them.     As an adult you want to
move on to the next game - this one is played out and no longer
interesting.   Monte Carlo programs are like this - the game is no
longer interested and they don't pretend it is.

With the greedy approach you recommend,  it's possible that you could
convert some losses to wins - but you have to program the machine first
to win less!   There is little point in that.
 

- Don



Dave Dyer wrote:
> Here's a more likely scenario: Approaching endgame, there
> are 10 "resolved" fights that remain to be played out.  The
> program estimates is won 5 of them and lost 5 of them,
> each with 85% confidence.  The sizes of the groups is
> such that any single switch from won to lost will swing
> the game.  The probability of one such flip is pretty high.
>
> If one of the groups is much larger, you should go for the big
> group, because if it switches, the game is flipped irrevocably,
> whereas if one of the small groups flips, it might be corrected
> by switching status of another group. 
>
> That's why you should play for the big win, or to avoid the
> big loss.  It swamps all the other uncertainties.
>
> Of course, current programs don't see the situation with
> anything approaching this level of analysis, but given
> a choice or a big win or a small win with slightly higher
> probability, I suspect that detailed analysis would be
> similar to the above.
>
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