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Computer Dice
Yes, it's that FIBS dice topic again!
I played quite a lot of FIBS yesterday (29 games or parts thereof) and
I reckoned that the dice were doing something strange. Specifically, I
reckoned that a roll was more likely to be the same as the subsequent
roll for the same player than it should be. I do not know how FIBS
draws its numbers: in particular if it draws from one string of
numbers for all games this sounds an unlikely result. Nevertheless,
this is what I observed.
I set out to test this this morning as follows. I looked back at all
games from yeterday that were still saved. That is only one per
finished match, which in fact was only 7 games. I extracted the rolls
for each player and saw how many times there were consecutive
identical rolls. For simplicity, I counted (e.g.) 4-2 and 2-4 as
distinct. This means that for any roll including doubles, the same
roll should come up again as the next roll a proportion 1/36 of the
time (binomially distributed).
For a proper investigation, I should have done two further things ---
this was only a quick test. The first is that I should have preferred
a larger sample size. There were only 333 pairs of rolls to look at
here. The second is that I should have preferred to think of the
experiment and then analyse subsequent data, rather than test it on
data which I had already observed were suspicious. Much statistics is
carried out in the latter way for logistical reasons (more data is
theoretically impossible or prohibitively expensive to collect) but if
new data is freely available, obviously the classical scientific
method would use that. Nevertheless, as I have already said, it was
only a quick test.
The results were as follows. The expected number of repetitions is
333/36 = 9.25. The actual number was 7.
Comment: it is well known that many beliefs of all sorts are self-
reinforcing. It seems that it is easier to fit everything into our
current framework of belief than to invent a new framework. Once a
belief is adopted, facts which tally with it are noticed and given
greater weight than those which don't. I claim that I noticed when
consecutive rolls for the same player were the same, and each new time
strengthened my (incorrect) belief.
Stephen Turner
Stochastic Networks Group, Statistical Laboratory,
University of Cambridge, CB2 1SB, England
e-mail: S.R.E.Turner@statslab.cam.ac.uk
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Computer Dice
- Dice on backgammon servers (Hank Youngerman, July 2001)
- Does Agushak Backgammon cheat? (Mr Nabutovsky, June 2000)
- Does BG by George cheat? (George Sutty, Nov 1995)
- Does Backgammon NJ cheat? (Greg+, June 2010)
- Does Cybergammon cheat? (Goto Informatique, Aug 1996)
- Does David's Backgammon cheat? (Joseph B. Calderone, June 1998)
- Does GNU Backgammon cheat? (Robert-Jan Veldhuizen, Nov 2002)
- Does Gammontool cheat? (Jim Hurley, Sept 1991)
- Does Hyper-Gammon cheat? (ZZyzx, June 1996)
- Does Jellyfish cheat? (Fredrik Dahl, June 1997)
- Does MVP Backgammon cheat? (Mark Betz, Oct 1996)
- Does MonteCarlo cheat? (Matt Reklaitis, June 1998)
- Does Motif cheat? (Rick Kiesau+, Mar 2004)
- Does Motif cheat? (Billie Patterson, Feb 2003)
- Does Motif cheat? (Robert D. Johnson, Oct 1996)
- Does Snowie cheat? (André Nicoulin, Sept 1998)
- Does TD-Gammon cheat? (Gerry Tesauro, Feb 1997)
- Error rates with computer dice (NoChinDeluxe+, Feb 2011)
- FIBS: Analysis of 10 million rolls (Stephen Turner, Apr 1997)
- FIBS: Are the dice biased? (Kit Woolsey, Oct 1996)
- FIBS: Entering from the bar (Tom Keith+, Apr 1997)
- GamesGrid: Too many jokers? (Gregg Cattanach, Sept 2001)
- GridGammon: Are the dice random? (leobueno+, Sept 2011)
- Jellyfish: How to check the dice (John Goodwin, May 1998)
- Jellyfish: Proof it doesn't cheat (Gary Wong, July 1998)
- MSN Zone: Security flaw (happyjuggler0, June 2004)
- Official complaint form (Gary Wong, June 1998)
- Randomness testing (Brett Meyer+, Dec 2010)
- Safe Harbor Games dice (Michael Petch+, Aug 2011)
- Synopsis of "cheating" postings (Ray Karmo, Feb 2002)
- Testing for bias (Kit Woolsey, Jan 1995)
- The dice sure seem unfair! (Michael Sullivan, Apr 2004)
- Too many repeated rolls? (Stephen Turner, Mar 1994)
- Winning and losing streaks (Daniel Murphy, Mar 1998)
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