Computer Dice

Forum Archive : Computer Dice

 
FIBS: Analysis of 10 million rolls

From:   Stephen Turner
Address:   sret1@cam.ac.uk
Date:   5 April 1997
Subject:   Re: Randomness and FIBS dice (with 10 MILLION ROLLS!!)
Forum:   rec.games.backgammon
Google:   334636DB.6F9B@cam.ac.uk

Executive summary: FIBS dice appear fair on the tests I carried out.
Details follow.

First some background. Patti's sample of 5,530,616 rolls showed 924,319
doubles. If the dice were fair, this many doubles or more would only come
up 1 in 530 times (0.189%), so there was some cause for concern.

Just before Robert-Jan Veldhuizen noticed this, the FIBS command 'matrix'
was also pointed out to me by someone else, and I had started collecting
data from it. Here is my original post:

---------------------------------------------------------------------------
From: Stephen Turner <sret1@statslab.cam.ac.uk>
Subject: Re: 5 million rolls
Date: Tue, 29 Oct 1996 11:31:53 +0000

I too have been carrying out some tests of the FIBS dice in the last couple
of weeks, using the FIBS matrix command. You probably don't know about this
command because it's not on the list of commands, but it produces data not
only on the frequency of rolls, but on the frequency of each of the
possible 1296 possible pairs of consecutive rolls. So seeing whether these
data are fair will test both whether some rolls come up more than others,
and whether some rolls are more likely than others to come up after
specific rolls.

I won't bore you with the details of another statistical test, except to
say for the benefit of statisticians that it's a simple chi squared test on
1295 degrees of freedom, which I approximate by N(1295,2590). All everyone
else needs to know is that it comes out at the end with a number, which we
hope is near 0. A number greater than 2 indicates that the dice are biased
in some way (too many of one roll or of one pair of consecutive rolls at
the expense of another). A number less than -2 indicates that the dice are
too good -- in the sense that it looks as if they're fixed to try and get
the right proportions, and there's actually too little statistical
variation.

I shall continue to collect more rolls until I have reached 10 million.

Overall, I think we can say that the jury is still out. There may be a
deviation from unskewed-ness, but if so, it is slight, and more data are
needed to be sure. I think that it probably wouldn't affect the game,
UNLESS there is some reason why any imperfections are more likely to occur
at certain times, such as during races, doubles after doubles, etc.
---------------------------------------------------------------------------

In the end, the data took me longer to collect than I had hoped because I
didn't log on to FIBS very often. I collected 14 sets of data over nearly
6 months from 11th October to 5th April. This was a total of 10,593,121
rolls, so 10,593,107 pairs of consecutive rolls.

I can supply the data on request, but the chi-squared statistic gave an
answer of -0.355521, showing no evidence of bias. As I said above, this
test will check both whether some rolls come up more than others, and
whether some rolls are more likely than others to come up after specific
rolls. As a check, the number of doubles in the sample was 1763911, or
16.651%, fractionally less than expected, but well within normal
statistical variation (1.32 s.d.s from the mean, in fact).

Of course this doesn't check for every possible bias in the data, but it
checks for the most plausible and most widely suggested ones.

--
Stephen Turner    sret1@cam.ac.uk    http://www.statslab.cam.ac.uk/~sret1/
  Statistical Laboratory,  16 Mill Lane, Cambridge, CB2 1SB, England
       "This store will remain open during modernisation. We apologise
        for any inconvenience this may cause" Topshop, Cambridge
 
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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)  [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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