Am 28.01.2011 12:15, schrieb Nick Wedd:
That sounds crazy, because it has such a gambling feel to it, but its
true.
Its because even a mediocre player can muddle his way through the
roll of the dice, but only a strong player can judge well what his
current chances are.
The basic idea is that you need a 25% chance to win to be able to
accept the double.
Because at 25% the expected value of accepting((2 - 3*2)/4) is the
same as of declining(-1).
This calculation is mistaken (you are forgetting that if he accepts
the cube then he will have it and you won't). The correct value,
assuming that each move makes only a small difference to the winning
chances, is 80%.
Nice. Because you have a 1 in 4 chance to go from 20% to 80% yourself.
And 80% has the same utility as 100%.
So the "real" value is somewhere between 20% and 25% because your
chances might jump past the 80% mark, lowering the utility of the
doubling utensil.
Back to the game of go: instead of the backgammon mechanism, you could
allow each side to double with every move, but for a progressive komi
penalty of 10,20,40 points ect.
Something like that might work. The question remains, would it would
mean to win 8x :-)
It seems to make sense only in the context of gambling.
Stefan
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