Optimal Ranges for Cut-O ff Probabilities of Discrete Distributions - PowerPoint PPT Presentation

Optimal Ranges for Cut-O ff Probabilities of Discrete Distributions Derived from Non-Standard Decks of Cards Project by: Kathryn “Nikki” Bolinger and Jirani Smith https://i.pinimg.com/originals/ae/0a/e6/ae0ae65bacdf7b8ae357b2340e0c2aca.jpg Queen of Hearts http://unocardinfo.victorhomedia.com/graphics/uno_card-blue7.png Blue Uno 7 https://deckmaster.info/images/cards/PRM/-1540-hr.jpg Magic Card https://52f4e29a8321344e30ae-0f55c9129972ac85d6b1f4e703468e6b.ssl.cf2.rackcdn.com/products/pictures/242416.jpg Yu Gi Oh Card http://ullagegroup.com/wp-content/uploads/2010/04/ccg93b.jpg Dutch Blitz Card

Questions We Asked • How many draws does it typically take for all the cards of one suit to be drawn? • What is the shortest interval within which 90% of the time one of the suits will be exhausted? • How would this work with a non- standard deck? • A variation on that deck? • Why does this matter? http://blogs.onlineeducation.touro.edu/wp-content/uploads/2015/07/question-mark-with-laptop.jpg Computer ? https://images.techhive.com/images/article/2014/05/red-question-mark-165419798-100265543-primary.idge.jpg Lots of ? http://www.renegadetribune.com/wp-content/uploads/2016/12/19130-Question-Man-Lightbulb-1.jpg Lightbulb ?

Making and Using the Program • Language: r • Parameters: # of suits, # of cards per suit, # of redundant cards, # of simulations • The simulation measures the number of draws/turns • The simulation’s process

Our “Standard” Deck • Porta’s Game: 4 suits, 5 cards per suit, 12 redundant cards • Constant 1 Million Simulations Related Non-Standard Decks • 4 suits, 5 cards per suit, 20 redundant cards • 4 suits, 5 cards per suit, 5 redundant cards • 4 suits, 10 cards per suit, 12 redundant cards • 4 suits, 2 cards per suit, 12 redundant cards • 6 suits, 5 cards per suit, 12 redundant cards • 2 suits, 5 cards per suit, 12 redundant cards

Interpreting the Data: The Histograms Porta’s Games Average Median Mode Turns Taken

Histograms Cont. Increasing Number of Suits Increasing Cards Per Suit Increasing Redundant Cards Turns Taken Turns Taken Turns Taken Decreased Number of Suits Decreasing Redundant Cards Decreasing Cards Per Suit Turns Taken Turns Taken Turns Taken

Interpreting the Data: Comparing the Data Cont. Box & Whisker Plot

Interpreting the Data: The 90% Ranges for Each Deck • Porta’s Game . . . . . . . . . . . . . . . . . . . 15-28 Turns • Increasing Redundant Cards . . . . . . 18-35 Turns • Decreasing Redundant Cards . . . . . . 12-21 Turns • Increasing Cards Per Suit . . . . . . . . . 36-48 Turns • Decreasing Cards Per Suit . . . . . . . . . 3-14 Turns • Increasing the Number of Suits . . . . 18-34 Turns • Decreasing the Number of Suits . . . 12-21 Turns