At 16:20 09/01/2007, you wrote:
i'd like to follow this up by saying that i'm interested
to see if anyone has compared winning percentage
in the following two situations:
i) maximize probability of win
ii) maximize probability of win until p_win > 1-eps, then maximize
total score among all moves that give > 1-eps probability of winning.
if ii) gives a lower percentage of wins than i), it'd be an interesting
result in its own right, and if it doesn't, then there's a simple formula
for getting a lot more resignations out of your opponents (not to
mention, it'll give the impression that your program is incredibly strong
whenever it wins).
To me it seems sensible to maximize a different measure. I would be interested
to know how the following scheme performs.
Choose the starting move which maximizes [sum (s(n)+k*w(n))]/N,
where N is the number of games with this starting move,
n takes the values 1...N: the sum is over these values,
k is a non-negative constant,
s(n)is the net score of the bot (eg the bot's area minus its opponent's
area) in game n, and
w(n) is 1 if the bot wins game n and 0 if it loses.
When k is very large, this scheme should essentially just count the wins, like
traditional monte-carlo. Smaller values of k will encourage the bot to try
to accumulate more points unless that makes a significant difference to the
winning percentage.
A value of k around 300 might be a sensible value. The computer might then
trade
a 30 point group for a 1% chance of winning.
I suspect that this scheme will still reduce the bot's winning percentage,
but that there
might be a value of k that will improve the 'look' of the bot's play while only
making a negligible difference to the winning percentage.
When working out s(n), it makes no difference to the play if komi is taken
into account,
as long as a consistent method of evaluating the score is used.
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