Probability and Statistics

 Average luck of each roll

 From: Jørn Thyssen Address: jth@gnubg.org Date: 14 February 2004 Subject: Useless(?) statistics Forum: GammOnLine

```Being a bit bored, I decided to find out if 52 is really a bad roll!
I let gnubg play against itself in a cubeful money session with Jacoby
rule, and calculated the luck for every roll (excluding the opening roll).

I don't know if such statistics has been published before. Anyway, here it
is:

die 0 die 1   #occ   Average luck    95% CI
----- -----   ----   ------------   --------
1     1      783     0.044728     0.016868
2     1     1483    -0.044567     0.009203
2     2      708     0.075278     0.020103
3     1     1482    -0.024314     0.008989
3     2     1463    -0.028514     0.008908
3     3      736     0.090565     0.018224
4     1     1463    -0.034533     0.008335
4     2     1476    -0.021577     0.008230
4     3     1449    -0.010387     0.009062
4     4      760     0.114789     0.022337
5     1     1502    -0.043662     0.008349
5     2     1480    -0.012667     0.009066
5     3     1447    -0.009966     0.009893
5     4     1473    -0.001106     0.010445
5     5      677     0.124630     0.025492
6     1     1450    -0.019983     0.010032
6     2     1494    -0.013842     0.009551
6     3     1484    -0.010234     0.010245
6     4     1573    -0.006179     0.009885
6     5     1467    -0.015088     0.009980
6     6      725     0.114510     0.025760
Sum      26575    -0.001081     0.002546

... and 52 does appear to be an unlucky move on average :-) However, not
as unlucky as 51.

Jørn
```

 Roger Gabrielson  writes: ```This proves what I've always known. I'm unlucky five rolls out of six. ```

### 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)