NAME: Video Lottery Terminal Data
TYPE: Random Sample
SIZE: 345 observations, 5 variables
DESCRIPTIVE ABSTRACT:
The video lottery terminal dataset contains observations on the three
windows of an electronic slot machine for 345 plays together with the
prize paid out for each play. The prize payout distribution is so
badly skewed that confidence intervals for expected payout based on the
central limit theorem are not accurate. The dataset can be used at the
graduate or upper undergraduate level to illustrate parametric
bootstrapping. The dataset can also be used in a graduate course to
illustrate tests of independence for two and three-way contingency
tables involving random zeroes, or these tables may be collapsed and
used as examples in an introductory course.
SOURCE:
The data were collected in Manitoba by the author on two different
nights in the winter of 1993.
VARIABLE DESCRIPTIONS:
The first three columns of the dataset record the objects observed in
the three windows. The fourth column records the prize awarded, and
the fifth column indicates the night the sample was obtained. Values
are delimited by blanks; note that columns are not aligned.
Coding for variables 1, 2, 3:
CODE OBJECT
0 BLANK (0)
1 SINGLE BAR (B)
2 DOUBLE BAR (BB)
3 TRIPLE BAR (BBB)
5 DOUBLE DIAMOND (DD)
6 CHERRIES (C)
7 SEVEN (7)
Coding for variable 5:
CODE INDICATES
1 SAMPLE TAKEN ON FIRST NIGHT
2 SAMPLE TAKEN ON SECOND NIGHT
SPECIAL NOTES:
The payout table is needed to estimate the expected payout properly:
COMBINATION PRIZE PAYOUT
DD DD DD 800
7 7 7 80
BBB BBB BBB 40
BB BB BB 25
B B B 10
C C C 10
AB AB AB 5
C C 0 5
C 0 C 5
0 C C 5
C 0 0 2
0 C 0 2
0 0 C 2
A double diamond doubles any winning combination, while two double
diamonds quadruple any winning combination. Cherries result in a
payout regardless of what appears with them.
AB = ANY BAR (i.e., a single, double or triple bar).
STORY BEHIND THE DATA:
Video lottery terminals are electronic slot machines with several
line-up style games, including one called Double Diamond. This game
consists of three windows in which one of seven objects may appear
(after the gambler has inserted a quarter). If the objects in the
three windows match one of several possible combinations, the gambler
is awarded a prize (in quarters). Otherwise, nothing is awarded.
The data were collected to test whether the advertised payout of 92%
was exaggerated. The Canadian Broadcasting Corporation (CBC) asked the
author to conduct the investigation, since a CBC reporter suspected a
payout of closer to 40%.
The author took an initial sample of 138 plays in which the actual
payout was around 38%, appearing to confirm the reporter's claims. A
more careful analysis (which is greatly simplified by using the
parametric bootstrap) gives an estimate of the expected payout that is
considerably higher, together with more sensible standard error
estimates. Along the way, it was necessary to confirm the
manufacturer's claim that the objects appear in the three windows
independently of each other. The resulting three-way contingency table
is riddled with zeroes so that care must be taken when computing the
degrees of freedom for the chi-square test. The author has found it
much quicker to use the bootstrap to test for independence. An
additional sample of 207 plays was taken later to confirm the results
obtained from the smaller sample.
PEDAGOGICAL NOTES:
These data have been used with graduate students and upper level
undergraduates to illustrate the power of bootstrapping. They have
also been used in introductory courses for examples of goodness-of-fit
and independence tests. They lend themselves to interesting
probability questions, such as "What is an estimate of the probability
of winning the largest prize?"
Additional information about these data can be found in the "Datasets
and Stories" article "An Illustration of Bootstrapping Using Video
Lottery Terminal Data" in the _Journal of Statistics Education_ (Braun
1995).
SUBMITTED BY:
W. John Braun
Department of Mathematics and Statistics
University of Winnipeg
515 Portage Ave.
Winnipeg, Manitoba R3B 2E9
CANADA
braun@uwpg02.uwinnipeg.ca