Computer Dice

Forum Archive : Computer Dice

Too many repeated rolls?

From:   Stephen Turner
Date:   18 March 1994
Subject:   FIBS dice
Google:   2mc56o$

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
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Computer Dice

Dice on backgammon servers  (Hank Youngerman, July 2001) 
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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)  [Long message]
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)  [Recommended reading]
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)  [Recommended reading]
Jellyfish: Proof it doesn't cheat  (Gary Wong, July 1998) 
MSN Zone: Security flaw  (happyjuggler0, June 2004) 
Official complaint form  (Gary Wong, June 1998)  [Recommended reading]
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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