# full_deck_simulation

full_deck_simulation, a MATLAB code which simulates a process in which a random card is drawn from a deck of 52, and then replaced, continuing until every card has been seen at least once.

A New York artist carried out an equivalent project by wandering the streets and picking up single playing cards that had been thrown away. Once a full, though motley, deck had been collected, it was displayed in a gallery. (Of course, many of the collected cards were duplicates, and thus didn't make the show!)

This is a version of a well-known problem in probability known as "the coupon collector's problem".

### Languages:

full_deck_simulation is available in a MATLAB version.

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### Reference:

1. John D Cook,
Sampling with replacement until you've seen everything,
https://www.johndcook.com/blog/2022/05/14/exhaustive-sampling/
14 May 2022.
2. Herbert Wilf,
Some New Aspects of the Coupon Collector's Problem,
SIAM Review,
Volume 48, Number 3, September 2006, pages 549-565.

### Source Code:

• full_deck_expected.m, computes the exact expected value for the number of cards that must be viewed in order to have seen every card at least once.
• full_deck_stats.m, returns the minimum, average, and maximum number of cards in a full deck process, over N trials.
• full_deck_try.m, returns the number of times each card was viewed in a single full deck process.

Last revised on 21 May 2022.