Probability and Statistics

 Distribution of points per game

 From: Stig Eide Address: stig.eide@avh.unit.no Date: 12 September 1995 Subject: 1000 Jellyfishgames Forum: rec.games.backgammon Google: 433l0p\$r27@due.unit.no

```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).

Stig Eide, stig.eide@avh.unit.no
```

 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. Kit ```

### Probability and Statistics

Average game and match length  (JP White, Dec 2000)
Average luck of each roll  (Timothy Chow+, Mar 2013)
Average luck of each roll  (Jørn Thyssen+, Feb 2004)
Calculating winning chances  (Douglas Zare, June 2000)
Chance of rolling x doubles in y rolls  (Raccoon+, July 2007)
Chance of rolling x or more pips in y rolls  (Tom Keith, Feb 2004)
Clumping of random numbers  (Gary Wong, Sept 1998)
Counting shots  (Koyunbaba+, June 2007)
Counting shots  (John Little+, Mar 2007)
Distribution of points per game  (Roland Sutter, June 1999)
Distribution of points per game  (Stig Eide+, Sept 1995)
Expected variation in points after a series of games  (Achim Müller+, Feb 1999)
How many games to decide who's better?  (Stephen Turner, Mar 1997)
How often is too often?  (Gary Wong, Oct 1998)
Losing after bearing off 14 checkers  (Daniel Murphy, July 1999)
Number of games per match  (Jason Lee+, Jan 2005)
Number of rolls to enter x checkers from bar  (Michael Depreli+, Mar 2011)
Visualizing odds  (Daithi, Mar 2011)