1000 Jellyfishgames
Kit Woolsey
: I asked Jellyfish to play 1000 moneygames at level 5 (both sides,
: using the 'Finnish game' command) and recorded the results.
: This is the distribution of points per game:
: 1 point: 35.4%
: 2 points: 40.7%
: 4 points: 20.3%
: 6 points: 0.6%
: 8 points: 2.5%
: 16 points: 0.5%
: Sum : 100.0% (Average points per game: 2.296)
: (Sample Variance : 8.334)
The most interesting result of this trial to me is that the % of 1 point
games was 35.4%. This means that Jellyfish thinks that with proper play,
64.6% of initial cubes should be taken. I have always believed this --
in fact, I think the proper figure might even be higher. However, in a
survey of over 1000 matches (most of which were played in the 1980's,
most involving at least one world-class player), the percent of initial
doubles taken was only 40%. I only looked at match scores where the
score figured to be irrelevant to initial cube action -- i.e. both
players had several points to go. I wonder who is doing the right thing
-- jellyfish, or these players.
Kit
Stig Eide
using the 'Finnish game' command) and recorded the results.
This is the distribution of points per game:
1 point: 35.4%
2 points: 40.7%
4 points: 20.3%
6 points: 0.6%
8 points: 2.5%
16 points: 0.5%
Sum : 100.0% (Average points per game: 2.296)
(Sample Variance : 8.334)
The Jacoby rule was not in use, but the effect in ppp is small.
(It'll only affect those games where the equity swings from
less than .5 to greater than 1 in one sequence, making the
average ppp smaller).
An example of how this information can be used:
If you've played n games in a chouette with P others, then you
can be 96% sure that your winnings was due to skill, and not luck
if you won more than
5*sqr(nP) points.
(The Central Limit Theorem is used. n should be more than 12).
Thanks for reading.
Stig Eide, stig...@avh.unit.no
Robert D. Johnson
>Stig Eide (stig...@avh.unit.no) wrote:
>: 1 point: 35.4%
>
>The most interesting result of this trial to me is that the % of 1 point
>games was 35.4%. This means that Jellyfish thinks that with proper play,
>64.6% of initial cubes should be taken.
> Kit
Some of the 64.6% could have been due to gammons or backgammons
on a 1 cube rather than the acceptance of a double.
--
Robert D. Johnson MAIL: rjoh...@cvbnet.cv.com FIBS: rjohnson
Darse Billings
>Stig Eide (stig...@avh.unit.no) wrote:
>: I asked Jellyfish to play 1000 moneygames at level 5 (both sides,
>: using the 'Finnish game' command) and recorded the results.
>: This is the distribution of points per game:
>: 1 point: 35.4%
>: 2 points: 40.7%
>: 4 points: 20.3%
>: 6 points: 0.6%
>: 8 points: 2.5%
>: 16 points: 0.5%
>: Sum : 100.0% (Average points per game: 2.296)
>: (Sample Variance : 8.334)
>The most interesting result of this trial to me is that the % of 1 point
>games was 35.4%. This means that Jellyfish thinks that with proper play,
>64.6% of initial cubes should be taken. I have always believed this --
>in fact, I think the proper figure might even be higher. However, in a
>survey of over 1000 matches (most of which were played in the 1980's,
>most involving at least one world-class player), the percent of initial
>doubles taken was only 40%. I only looked at match scores where the
>score figured to be irrelevant to initial cube action -- i.e. both
>players had several points to go. I wonder who is doing the right thing
>-- jellyfish, or these players.
If I read the data correctly 35.4% of the games ended in a simple 1-point
win (no double) or with a double/drop. The 2-point games unfortunately
mix 1-cube gammons and 2-cube wins, so we can't say what the actual drop
rate was.
But for sake of argument, suppose fewer games *were* taken by humans than
Jellyfish, and that the machine is right. Does this mean humans drop too
easily, or that they wait too long before doubling? (or both)?
From my experience in limit poker, I wouldn't be surprised to find out
that even the best human players drop (fold) too often. One reason may be
that the chances for the underdog are often underestimated because of what
I'll call the "bizarro" factor.
When we estimate the chances for the favourite (call this Pf) and the
chances for the underdog (Pu), we usually only consider the "most likely"
follow-ups. But the number of peculiar or "bizarro" outcomes (Pb) that
aren't accounted for in this quick analysis may have some significance.
These bizarro cases tend to work in favour of the underdog more than the
favourite because any 50-50 proposition is a bargain for the dog. As a
result, the player who is behind has a slightly better chance than would
normally be indicated by the first-order analysis.
To look at a concrete example in terms of probabilities, suppose we feel
we are a two-to-one favourite in a given position, but we are only looking
at (the most likely) nine tenths of the follow-ups. Then Pf = 0.60,
Pu = 0.30, and Pb = 0.10. If half of those bizarro outcomes win for each
side, then a more accurate estimate is a 65-35 edge for the favourite,
which represents a difference of -0.033 in game equity. Furthermore, the
bizarro cases *could* heavily favour the underdog, in practice.
In many common Hold'em situations, the underestimate for the underdog can
be on the order of 0.05 (5%), because the drawing hand can "accidentally"
win in ways other than making the obvious draw. Whether or not this same
idea applies to backgammon is pure speculation on my part, since I'm only
an intermediate player, but my guess is that it probably does.
Cheers, - Darse.
--
BlddLDfddFdbfRuuruBuubUF
Albert Steg
> An example of how this information can be used:
>
> If you've played n games in a chouette with P others, then you
> can be 96% sure that your winnings was due to skill, and not luck
> if you won more than
> 5*sqr(nP) points.
> (The Central Limit Theorem is used. n should be more than 12).
I'm not much of a mathematician, but in my experience, the simple net
*result* of 13 games will make you 96% sure of hardly anything in
backgammon.
Albert
Bernhard Kaiser
: idea applies to backgammon is pure speculation on my part, since I'm only
: an intermediate player, but my guess is that it probably does.
: Cheers, - Darse.
: --
Of course it does! Nice explanation, Darse!
But i still think, according to the notations of many expert-matches,
that much more mistakes are made by waiting to long to double than to
pass a takeable cube!
onepointer