Chrilly Donninger wrote:
I think poker is more difficult than Go and of course chess.
Poker can be analyzed well by (even naif) Monte Carlo methods.
Of course, the fact that you get a better estimate than any
human could dream of, won't necessarily make you win.
This common misconception can be found in many computer go
papers. People who train patterns to predict moves tend to
think the more they predict the better. Some even claim 60%
prediction rates and higher. Of course, we all predict moves
as a play when we watch pro games and feel good when our guess
is right. Two reasons make it easy to have "high" prediction
rate: a. forced moves b. local play is easier to analyze than
the value of all possible tenukis. Usually, you don't do very
wrong answering local and postponing other fights.
My case: I have to give Bradley Terry scores to 1/3 M patterns:
LoadJeitoLibRW_ByName() Importance of database loaded
# of imp = 32 91986 (91986)
# of imp = 31 25466 (117452)
# of imp = 30 20263 (137715)
# of imp = 29 18556 (156271)
# of imp = 28 17592 (173863)
# of imp = 27 17646 (191509)
# of imp = 26 17722 (209231)
# of imp = 25 18575 (227806)
# of imp = 24 19283 (247089)
# of imp = 23 20525 (267614)
# of imp = 22 21695 (289309)
# of imp = 21 23712 (313021)
# of imp = 20 25434 (338455)
Note: The importance of a pattern is the number of disjoint sets
of games where the pattern is found if you divide the whole database
in 32 disjoint sets. E.g. A pattern of importance 28 is a pattern
found in 28 sets of about 1500 games but not found in 4 sets of the
same size. I don't collect data on the number of games in which each
pattern is found.
Note: These are the real untricked patterns. Then, I generate a
crunched version that behaves "mostly" like the big one.
So I have 338455 patterns of importance 32 to 20 I could try to
maximize the probability of a guess, but I don't!
What I really am interested in is _a probability distribution over
the legal moves_. I ask my HSB board to give me the _minimum number
of moves_ that cover a 30%, 50%, 99% probability. (Note: This number
is not an integer. Eg. If it is 3.17 -> If the winning move is in
the 3 first, you add 1, if it is the fourth move you add 0.17 and
else you add 0.) The legal moves are sorted in descending score.
For adjusting my Bradley Terry models I have a loss function and
a very naif method that corrects in small steps. (The good thing
of off-line learning is that you can implement junk because that
does not go into the program. ;-) The program updates a pattern
and finds its score in two digit nanosecond times (< 400 clock
cycles) if it may have changed, and 0 if it may not.)
My loss function evaluates (using a random sample from an independent
test set) if: When I want 50% I really get 50% (and the same for
other values, of course.)
If I want 50%, getting 60% is as bad as getting 40%!! What I need
is a reliable distribution not a "thing that guesses many times".
And also, that this distribution contains the maximum information
(but that is another story).
This explains why when you watch the European Poker Tour on TV
and the journalist identifies half a dozen "legends" including
previous year's world champ, US guest don't-know-what-champion
Las Vegas, and all other "celebrities", none of the legends wins
except by a fluke just like anyone else.
Statistics is not about winning the lottery, its about getting
good estimators. And computer poker programs do better than humans
but that does not make them win.
Jacques.
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