Jonas Kahn wrote:
> I guess you have checked that with your rules for getting probability
> distributions out of gammas, the mean of the probability of your move 1
> was that that you observed (about 40 %) ?
If I understand your post, there may be a misunderstanding by my fault.
Here gamma is not a gamma function nor a gamma distribution but a constant.
It is just the same Greek letter. I don't remember if it was in
Crazystone's
description or in some other paper I read to understand what Bradley Terry
models are, I just got used to that notation.
The best thing of BT models (for me) is the extreme simplicity at runtime
(calibration may have more black magic) so:
prob of move i = gamma[i] / SUMj gamma[j]
where gamma[·] is a constant each pattern has. Setting those constants is
the learning process.
The 40% is obtained between move 20 and 119 of over 55K games. That is more
than 5 M competitions. The patterns are learned for other move numbers as
well. It considers the urgency modified by the first time the pattern
appears.
Also ko, but ko is learned to (hopefully) find ko threats, its impact on
guessing is less important. It counts the number of times the first move
was the right move, then the first + second, etc.
The reason why two different ways of measuring the same:
a. Probability expected for each move.
b. Number of guesses of the best move, 2nd best, 3rd best, etc.
don't match is mainly academic, because form a practical point of view, the
important is to have a good move generator and (even more important) to
understand its limitations. It cannot be considered as the only source of
moves, but the first moves in terms of urgency are moves that should be
paid attention.
I admit, that what I call a probability distribution over the legal moves,
is not really balanced I don't understand why, but, nevertheless, in terms
of urgency, better moves get higher urgency. This is all I really need.
Of course, I would welcome an explanation on why the 2 things don't match
or if someone else can verify if his patterns give correct values.
Jacques.
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