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Full-Text Articles in Discrete Mathematics and Combinatorics
Blackjack: The Math Behind The Cards, Hanna Blanchard
Blackjack: The Math Behind The Cards, Hanna Blanchard
Mathematics Senior Capstone Papers
In this paper the reader will learn about the math behind the cards in the game of Blackjack. Blackjack or “21” has been played around the world with various rules and regulations in both professional and informal environments. The ultimate objective of the game is to receive a total card value of 21, or as close to 21 as possible without exceeding it, from the cards in a player’s hand in order to beat the dealer’s total. The goal of this project is to calculate the probabilities of various hands to determine the best strategies to win 21. The probabilities …
Runs Of Identical Outcomes In A Sequence Of Bernoulli Trials, Matthew Riggle
Runs Of Identical Outcomes In A Sequence Of Bernoulli Trials, Matthew Riggle
Masters Theses & Specialist Projects
The Bernoulli distribution is a basic, well-studied distribution in probability. In this thesis, we will consider repeated Bernoulli trials in order to study runs of identical outcomes. More formally, for t ∈ N, we let Xt ∼ Bernoulli(p), where p is the probability of success, q = 1 − p is the probability of failure, and all Xt are independent. Then Xt gives the outcome of the tth trial, which is 1 for success or 0 for failure. For n, m ∈ N, we define Tn to be the number of trials needed to first observe n …
Educational Magic Tricks Based On Error-Detection Schemes, Ronald I. Greenberg
Educational Magic Tricks Based On Error-Detection Schemes, Ronald I. Greenberg
Computer Science: Faculty Publications and Other Works
Magic tricks based on computer science concepts help grab student attention and can motivate them to delve more deeply. Error detection ideas long used by computer scientists provide a rich basis for working magic; probably the most well known trick of this type is one included in the CS Unplugged activities. This paper shows that much more powerful variations of the trick can be performed, some in an unplugged environment and some with computer assistance. Some of the tricks also show off additional concepts in computer science and discrete mathematics.
Recounting The Odds Of An Even Derangement, Arthur T. Benjamin, Curtis D. Bennet, Florence Newberger
Recounting The Odds Of An Even Derangement, Arthur T. Benjamin, Curtis D. Bennet, Florence Newberger
All HMC Faculty Publications and Research
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