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Dice Rolls as an Example of the Coupon Collector's Problem
This Demonstration shows an example of the "coupon collector's problem": you roll
fair
-sided dice until all possible sums appear.
Using Monte Carlo simulation, the Demonstration estimates
• the expected number of rolls needed to get all possible sums and the number of rolls needed for selected confidence levels (top table).
• the histogram of the number of rolls needed (upper graph).
• the distribution of totals when rolling the specified dice (lower graph).
If you increase the number of iterations, you get more accurate estimates, but this requires more computational effort and time.
Contributed by:
Michail Bozoudis
Suggested by:
Michail Boutsikas
THINGS TO TRY
Slider Zoom
Gamepad Controls
Automatic Animation
SNAPSHOTS
RELATED LINKS
Coupon Collector's Problem
(
Wolfram
MathWorld
)
Coupon Collector Problem
(
Wolfram Demonstrations Project
)
Coverage Probability with the Occupancy Problem
(
Wolfram Demonstrations Project
)
Rolling Multiple Dice
(
Wolfram Demonstrations Project
)
Open Dice Rolls
(
Wolfram Demonstrations Project
)
Multiple Multiply Sided Dice Probability
(
Wolfram Demonstrations Project
)
Two Dice with Histogram
(
Wolfram Demonstrations Project
)
PERMANENT CITATION
Michail Bozoudis
"
Dice Rolls as an Example of the Coupon Collector's Problem
"
http://demonstrations.wolfram.com/DiceRollsAsAnExampleOfTheCouponCollectorsProblem/
Wolfram Demonstrations Project
Published: August 4, 2014
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