Hi Jacques

>
> No. for a reason I don't understand, I get something like:
>
> Distribution fit expected 0.1 found 0.153164
> Distribution fit expected 0.2 found 0.298602
> Distribution fit expected 0.3 found 0.433074
> Distribution fit expected 0.4 found 0.551575
> Distribution fit expected 0.5 found 0.651135
> Distribution fit expected 0.6 found 0.727419
> Distribution fit expected 0.7 found 0.776876
> Distribution fit expected 0.8 found 0.804008
> Distribution fit expected 0.9 found 0.823292
>
> So my distribution is distorted, when I try to get 30% of
> the "guessing chance" I get 43.3%, but when I try to get
> 90% I get 82.3%. I don't know why.

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 %) ? And the same for the following
ones ?
For the tails (many moves), I guess that a proportion of available moves
is a better reference.

In fact, doing that for the following moves too would be a way to
calibrate your function (gamma_1, gamma_2) -> Prob(gamma_1);
All the logits and so on are somewhat arbitrary and can be wrong
especially in the tails.

For a distribution fit of .1, I guess you merely always keep the first
one (except very special case). Then, if you had a homogeneous 40%
probability that first choiceis the right one, and you decide it's half
the time 30%,  half the time 50%, you see that you get (.1/.3 + .1/.5) /
2 > .1/.4.
Hence if your fluctuations in the estimation of the first choice are not
adapte, you shall get bigger fit.

On the other hand, when you are not in the first moves, shape is not a
factor for really deciding the move.
Suppose that for 50% of moves, shape counts and the right move is one of
the first 5 candidates, and that for 50% it does not count, and the good
move is chosen uniformly at random with respect to your patterns
criterion;
Then achieving .9 fit merely asks for always taking 80% of the possible
moves (including of course the 'good pattern' ones).
If you have wrong estimation of your tail probabilities, you can easily
select much less moves.

Jonas
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