Craps Conditional Probability

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The dice game craps is played as follows: The player throws 2 dice, and if the sum is 7 or 11, he/she wins. If the sum is 2, 3, or 12, he/she loses. If the sum is anything else, then he/she continues throwing until that number appears again, or throws a 7, where the game ends in a loss. What I do know is that P(7) = 6 / 36, P(11) = 2 / 36. Conditional probability is one way to do that, and conditional probability has very nice philosophical interpretations, but it fits into this more general scheme of “decomposing” events and variables into components. The usual way to break up a set into pieces is via a partition. Recall the following set-theoretic definition.

Course Coordinator

Mark Hunacekmhunacek@iastate.edu

Catalog Description

MATH 104. Introduction to Probability(3-0) Cr. 3. F.S.SS. Prereq: Satisfactory performance on placement exam, 2 years of high school algebra, 1 year of high school geometryPermutations, combinations, probability, binomial and multinomial theorems, expected value, and applications. Either MATH 104 or MATH 150 may be counted toward graduation, but not both.

Textbook

Basic Probability

Craps Conditional Probability Rule

AngelISU Custom Edition ISBN: 9781269234993.

Conditional Probability Formula

Syllabus

  1. Basic language and results of probability: sample spaces, events, odds. (Sections 1, 2 and 3)
  2. Expected value. (Section 4)
  3. Roulette probabilities and expectation, a roulette strategy and its flaws. (Supplemental Notes; problems 57 and 58 in section 4)
  4. Tree diagrams, conditional probablitity, compound events. (Sections 5 – 7)
  5. Discussion and mathematical analysis of the dice game Craps. (Supplemental Notes)
  6. Introduction to basic combinatorics (Sections 8- 10)
  7. Using basic combinatorics to help analyze the probabilities associated with poker (Supplemental Notes)
  8. Using basic combinatorics to help analyze the probabilities associated with Lotteries. (Supplemental notes)
  9. Using basic combinatorics to help analyze the probabilities associated with Blackjack (Supplemental Notes)
  10. (Time permitting) Backgammon (Supplemental Notes)

Objectives

Basic Rules of Discrete Probability

  1. Understand the concept of “sample space” and be able to construct sample spaces for simple experiments
  2. Understand the definition of “probability” in the case where all outcomes are equally likely
  3. Understand and be able to apply the basic rules for probability: the union, intersection and complement of an event
  4. Understand the concept of “conditional probability” and be able to compute the conditional probability of simple events
  5. Understand the significance of tree diagrams when computing conditional probability Understand the concept of independent events
  6. To have some exposure to real-life cases (e.g., court decisions) where the concept of independent events was misapplied
  7. To understand the concept of “expected value” and be able to compute the expected value in cases where the outcomes of an experiment, and their probabilities, are known
  8. To have some idea of how “expected value” is applied in certain real-life situations, including insurance policies and other forms of risk-taking

Basic Principles of Combinatorics

  1. To understand the meaning of combinations and permutations, and the difference between these ideas
  2. To know the definition of the binomial coefficients and to be able to compute simple examples of them
  3. To use the concept of combinations and permutations to solve simple counting problems

Applications to Games and Gambling

  1. To understand the basic rules and bets for poker (video, Texas Hold Em, and other variants) and to be able to compute the probabilities of the various hands
  2. To understand the basic rules of the game of Blackjack, to be able to compute simple probabilities associated with the game, and to understand the mathematics behind “card counting”
  3. To understand the basic rules of roulette, to be able to analyze the various bets using the concept of expected value, to understand why there is no such thing as a perfect “system” for winning this and other gambling games, to understand why European roulette (with no 00) is a better bet for the gambler than is American roulette
  4. To understand the rules of some of the various lottery games, including Powerball, and to be able to compute the probability of winning the jackpot, and to be able to appreciate why lottery tickets are such poor bets
  5. To understand the rules of Backgammon and to be able to use probability to determine the best moves in certain situations
  6. To apply conditional probability to analyze and understand the game of craps
  7. To use probability to analyze other games, including, for example, Farkle, Keno or Chuck-a-Luck

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Students With Disabilities

ExamplesIowa State University is committed to assuring that all educational activities are free from discrimination and harassment based on disability status. Students requesting accommodations for a documented disability are required to work directly with staff in Student Accessibility Services (SAS) to establish eligibility and learn about related processes before accommodations will be identified. After eligibility is established, SAS staff will create and issue a Notification Letter for each course listing approved reasonable accommodations. This document will be made available to the student and instructor either electronically or in hard-copy every semester. Students and instructors are encouraged to review contents of the Notification Letters as early in the semester as possible to identify a specific, timely plan to deliver/receive the indicated accommodations. Reasonable accommodations are not retroactive in nature and are not intended to be an unfair advantage. Additional information or assistance is available online at www.sas.dso.iastate.edu, by contacting SAS staff by email at accessibility@iastate.edu, or by calling 515-294-7220. Student Accessibility Services is a unit in the Dean of Students Office located at 1076 Student Services Building.More information about disability resources in the Mathematics Department can be found at https://iastate.app.box.com/s/c17d3ljul83lujr2j1mdeqoqcdqiva1t.