Reference bot enhancement
=========================

Here is another possible enhancement to the reference bot which I am
currently testing.  I do not yet have anything conclusive enough to
report, but it looks good so far with a small number of games.  

But even if this idea doesn't pan out, it will produce a much more
natural playing style without weakening the bot. 

Here is how it works.  We will use 1000 playouts for our example:

1. Modify the bot to keep a "futures" table.  At the end of each
   playout, tally the wins for white and black for each point on the
   board.  (I tally -1 for a white win, 1 for a black win to get a
   final score from -1000 to 1000 for each point.)

2. When the 1000 playouts are complete, compute an "uncertainty value"
   for each point, where 1.0 is completely uncertain, and 0.0 is
   completely certain.  A point is completely certain if at the end of
   each playout it was ALWAYS owned by one player or the other.  It's
   completely uncertain if it won 50% of the time for either side.

3. When determining which move to play, apply an uncertainty delta to
   the computed score of each move.  This is simply some fraction of
   the "uncertainty value" and the best value I've tested so far is
   0.025.  So you get a bonus that ranges from 0.0 to 0.025.  

4. Choose the move with the best (sc + uncertainty_delta.)

5. The incentive must be small, large incentives will destroy the
   playing strength.  For instance 0.1 is too high and weakens it.
   The value that is testing the best for me (of the ones I've tried
   so far) is 0.025

6. This may test at some levels better than others.  I'm testing
   at 2000 playouts.

The idea is to gently encourage the bot to avoid playing to points
that are clearly a forgone conclusion (or conversely, encourage it to
play where the "action" is.)

This should make the bot play much less artificially.  Near the end of
the game it will prefer moves to unresolved points.  Earlier in the
game it will avoid moving to areas that are "probably" already won or
lost.

My feeling is that these "incentives" should probably be calculated in
a non-linear way, but what I described is a good starting point.  From
experiments in the past it seems more important to put the focus and
most of the weight on avoiding play to highly certain points.   So I
will try some non-linear formula next.


- Don
   

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