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

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

Jan 16, 2023 142 likes •243 views

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

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SLIDE 1

Optimal Ranges for Cut-Off 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
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SLIDE 2

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 ?
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SLIDE 3

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
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SLIDE 4

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
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SLIDE 5

Porta’s Games Turns Taken

Interpreting the Data: The Histograms

Average Median Mode

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SLIDE 6

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

Histograms Cont.

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SLIDE 7

Comparing the Data Cont.

Interpreting the Data: Box & Whisker Plot

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SLIDE 8

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