FIBS dice
Stephen Turner
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....@statslab.cam.ac.uk
dduff on BIX
Did oyu happen to check the dicetest command that Marvin
installed?
Willis Elias
was saying:
>Did oyu happen to check the dicetest command that Marvin
>installed?
I just checked the dicetest command out. There were 1533 rolls in the
sample since the last restart, so wouldn't you expect between 42-43
occurrences for each possible ordered pair of die rolls (assuming uniform
probability of 1/36 for each possible outcome). Some "outliers", assuming
1533 is large enough of a sample, follow:
1-1 27
5-1 28
6-1 29
4-3 51
6-3 51
5-4 52
5-5 61 !!
2-6 31
I do not know how to interpret the other results of dicetest, but these
frequency results suggest, at least to me, that the "dice" on FIBS are not
entirely uniform. Any _real_ statisticians/math-heads out there, who would
like to comment on my conclusion?.. it is way too possible that I am in
error in my interpretation. Also:
o does anyone have any comments on the other results generated by
dicetest on FIBS?
o does anyone know what kind of random number generator (ie. algorithm) is
being used on FIBS?
I comment on this simply because I have had a suspicion that the FIBS
"dice" are non-uniform just from the short time I've been playing on FIBS
(hmm.. mebbe only 18 experience ..) - I've had quite a few repeat die rolls
in groups of two anyway..
Hope this sparks some conversation re: FIBS and its dice.
BTW: I was checking to see if dicetest operates on ALL rolls since last
restart.. it appears that it does. Here is the latest dicetest output:
*** running dice test:
*** Rolled 2020 times with 2 dice
1-1 43 1-2 50 1-3 52 1-4 57 1-5 64 1-6 53
2-1 61 2-2 55 2-3 56 2-4 55 2-5 57 2-6 42
3-1 47 3-2 54 3-3 57 3-4 57 3-5 61 3-6 61
4-1 61 4-2 56 4-3 67 4-4 55 4-5 49 4-6 56
5-1 38 5-2 60 5-3 62 5-4 70 5-5 76 5-6 64
6-1 40 6-2 57 6-3 65 6-4 51 6-5 58 6-6 53
It appears I've wrongly assumed ~1000 trials is a large enough sample to
test uniformity.. 5-5 seems to still have an inordinately high frequency
with this larger sample, the other, previously listed, "outliers" are more
in line.
'nuff rambling.
- avernesse
=======================================================================
Willis Elias | "Oh Joy of Joys!
The Aerospace Corporation, | What a bee-ootiful day!"
El Segundo, CA | .-------
310-336-8653 | |
wi...@bigsky.aero.org | V
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Fortune:
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