Probability and Statistics

Forum Archive : Probability and Statistics

Distribution of points per game

From:   Stig Eide
Date:   12 September 1995
Subject:   1000 Jellyfishgames
Google:   433l0p$

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 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,

Kit Woolsey  writes:

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.

Did you find the information in this article useful?          

Do you have any comments you'd like to add?     


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Distribution of points per game  (Roland Sutter, June 1999) 
Distribution of points per game  (Stig Eide+, Sept 1995)  [Recommended reading]
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How many games to decide who's better?  (Stephen Turner, Mar 1997) 
How often is too often?  (Gary Wong, Oct 1998) 
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Number of games per match  (Jason Lee+, Jan 2005) 
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