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Probability and Statistics
Average luck of each roll
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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
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Roger Gabrielson writes:
This proves what I've always known. I'm unlucky five rolls out of six.
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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)
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