© Clark Creative Education Casino Royale

Total Page:16

File Type:pdf, Size:1020Kb

© Clark Creative Education Casino Royale © Clark Creative Education Casino Royale Dice, Playing Cards, Ideal Unit: Probability & Expected Value Time Range: 3-4 Days Supplies: Pencil & Paper Topics of Focus: - Expected Value - Probability & Compound Probability Driving Question “How does expected value influence carnival and casino games?” Culminating Experience Design your own game Common Core Alignment: o Understand that two events A and B are independent if the probability of A and B occurring S-CP.2 together is the product of their probabilities, and use this characterization to determine if they are independent. Construct and interpret two-way frequency tables of data when two categories are associated S-CP.4 with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. Calculate the expected value of a random variable; interpret it as the mean of the probability S-MD.2 distribution. Develop a probability distribution for a random variable defined for a sample space in which S-MD.4 probabilities are assigned empirically; find the expected value. Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding S-MD.5 expected values. S-MD.5a Find the expected payoff for a game of chance. S-MD.5b Evaluate and compare strategies on the basis of expected values. Use probabilities to make fair decisions (e.g., drawing by lots, using a random number S-MD.6 generator). Analyze decisions and strategies using probability concepts (e.g., product testing, medical S-MD.7 testing, pulling a hockey goalie at the end of a game). © Clark Creative Education Procedures: A.) In “Expectations”, students encounter five different situations that involve expected value. The purpose of this is to build this skill prior to the project. B.) In "The Inexpensive and Odd Game Room" (p. 8-12), students work with five different odd games that include a mix of conditional probability and regular probability. Students will then complete the reflection to analyze their results and make decisions. C.) In "Casino Royale", students are tasked with being intelligent Game Makers and Game Players. First, students will complete “Welcome to Casino Royale” (p. 13-14). This is a proposal for their own game. They will need to plan all aspects of the game and design all of the outcomes so that they make sense. All games will be played with “Swagg Cash” and each person will be given 125 Swagg Dollars. I suggest having students complete this activity and then the next day having the “Game Day”. Students will need to create a sign advertising their game for the next day. The sign should briefly describe how the game is played. Each outcome should be defined with an assigned value. Students will need to bring everything they will need for their game the next day. They will need to be reminded! D.) Suggested Logistics for Game Day. The students need to be split into two groups. “Game Makers” and “Game Players”. The Game Makers will host their game at a table or desk. The Game Players will go around to calculate expected values and play the games. Print 2 pages of (p. 15) for each student. They will have one page to use as a Game Maker and one page to use as a Game Player. All students will need a packet to record their Game Day participation (p 16-20). Make sure the Players are recording in the Player section and the Makers are recording in the Maker Section. The object of the game is to end with the most Swagg Cash. I suggest setting a timer and having the groups switch roles Makers-Players at the halfway point or making the activity a two day event where each group plays their role for an entire period. Students will need 5-10 minutes at the end of the period to collect all of their Swagg and complete the reflection questions. E.) After the games are finished, students will finish their reflections and determine who has the most overall swagg. They will add their Game Maker Swagg to their Game Player Swagg. The winner will be the Master of Swagg. * Aspects of the project can be completed independently. The entire project does not need to be completed to have a great learning experience, though it is suggested because it will best scaffold the skills and context. © Clark Creative Education Expectations Name ___________________________ Date ________________ How do you make decisions? Some will opt for a random strategy, some will trust their gut and others will try to make decisions that make the most sense. One such mathematical strategy to analyze these types of decisions is expected value. Expected value is the most likely value that would occur if the situation happened infinitely many times. By understanding expected value, people can make stronger decisions and make numerical sense of a variety of problems. In each of the following problems, create probability distribution tables, calculate the expected value and make a decision based on the data. -Raffle Time- Raffles are a popular way to raise money for different causes. Often a reward is given to attract people to buy the tickets. Two different raffles are going on. Which one gives a buyer the best chance to win? The Raffle Queen Snappy Raffle 1000 raffle tickets are sold for $3.00 each. There is 250 raffle tickets are sold for $1.00 each. There is one grand prize for $750 and two consolation prizes one grand prize for $150 and three consolation of $200 each that will be awarded. What is the prizes of $25 each that will be awarded. What is the expected value of one ticket? expected value of one ticket? Outcome Outcome Probability Probability Which raffle has the higher expected value? If you are going to buy a ticket for one of the raffles, which one would you pick? © Clark Creative Education -Hack a Dwight?- During the early 2000’s a strategy to defend NBA legend Shaquille O’Neal was to intentionally foul him as soon as he got the basketball. Teams felt that O’Neal, a historically bad foul shooter, would score less points if he took foul shots than if he took a regular shot in the game. This strategy became known as “Hack a Shaq”. In the early 2010’s a similar strategy has at times been used against star center Dwight Howard. Is this a good strategy? How does Howard’s expected values compare to O’Neal’s? Shaquille O’Neal Dwight Howard In his career O’Neal made 58.2% of his field goal In his career Howard has made 57.7% of his field attempts during the game and 52.7% of his free goal attempts during the game and 57.6% of his throws. free throws. Field Goal Attempts (taking a shot) Field Goal Attempts (taking a shot) Outcome 2 0 Probability Shooting 2 Free Throws Shooting 2 Free Throws Outcome 2 1 0 Probability Is “Hack-a-Shaq” an effective strategy for either O’Neal or Howard? Why or why not? If a team debates whether they should intentionally foul Dwight Howard, what would you suggest? © Clark Creative Education -SAT Time- On some standardized tests like the SAT, there is a penalty for getting a question wrong. On the SAT, a test taker earns 1 point for every correct answer and subtracts ¼ for each incorrect answer. A test taker has a question blank and less than ten seconds to go in the test. The question has 5 multiple choice options, should the test taker guess or not? Outcome 1 -1/4 Probability .2 .8 If the test taker can eliminate an answer choice, how much does it improve their odds? Outcome 1 -1/4 Probability .25 .75 -Health Insurance Premiums- In most businesses, companies are given health insurance premiums (how much it costs for each employee) from insurance companies based on the amount of usage from that business for the previous year. In this example, determine the appropriate insurance premium for this company. An insurance agency has compiled data for a company into the following chart. How much should they charge as an annual premium for each employee in order to cover the costs? Amount of Annual Claims Probability Last year the company paid a $525 monthly premium for their employees. They cannot afford any health insurance cost increases <4000 .35 and will need to pass along any additional costs to its employees. How much will the employees need to pay? 6000 .28 8000 .15 10000 .12 >12000 .10 © Clark Creative Education .
Recommended publications
  • 1.3 Algebraic Expressions
    1.3 Algebraic Expressions Modeling words with an Algebraic Expression: Example 1: Multiple Choice Which algebraic expression models the phrase "seven fewer than a number t"? A) -7t B) 7 - t C) t - 7 D) 7 + t Example 2: Multiple Choice Which algebraic expression models the phrase "two times the sum of a and b"? F) a + b G) 2a + b H) 2(a + b) I) a + 2b Modeling a Situation: Example 3: You start with $20 and save $6 each week. What algebraic expression models the total amount you save? Example 4: You had $150, but you are spending $2 each day. What algebraic expression models this situation? 1 Evaluating Algebraic Expressions: Example 5: What is the value of the expression for the given values of the variables? a. 7(a + 4) + 3b - 8 for a = -4 and b = 5 b. c. 2 Writing and Evaluating Algebraic Expressions: Example 6: In football, a touchdown (TD) is worth six points, and extra-point kick (EPK) one point, and a field goal (FG) three points. a. What algebraic expression models the total number of points that a football team scores in a game, assuming each scoring play is one of the three given types? Let t = the number of touchdowns Let k = the number of extra-point kicks Let f = the number of field goals b. Suppose a football team scores 3 touchdowns, 2 extra-point kicks, and 4 field goals. How many points did the team score? 3 Example 7: In basketball, teams can score by making two-point shots, three-point shots, and one-point free throws.
    [Show full text]
  • The Value Point System
    THE VALUE POINT SYSTEM This system, which incorporates several key statistics like points, rebounds, assists, and recoveries, is based on a formula that assesses player and team performance with a more well-rounded approach than other common forms of evaluation. With THE VALUE POINT SYSTEM, a playerʼs and/or teamʼs overall performance and make recommendations on where improvement should be made on the systemʼs formula and scale. Along with its many other benefits, THE VALUE POINT SYSTEM also encouraging the aspect of “team play”. Often, players that are excellent one-on-one players are not very good team players; a problem that creates a lot of trouble when trying to develop an effective team strategy. By emphasizing statistics like assists, charges and turnovers, players are trained to focus on working as a team, and therefore boost their abilities and become better basketball players on a better basketball TEAM. THE VALUE POINT SYSTEM Formula and Scale THE VALUE POINT SYSTEM is based upon a carefully calculated formula. The system utilizes the most pertinent player and/or team statistics to provide a more accurate evaluation of the player or teamʼs performance. Statistics Needed to Calculate Value Points When calculating THE VALUE POINTS of your players or team, the following statistics are necessary. Total Points: A player or teamʼs total points, including free throws. Rebounds: A player or teamʼs total rebounds, both offensive and defensive. Assists: A player or teamʼs total number of passes that directly led to a basket. Steals: The total number of times a player or team takes the ball from an opposing team.
    [Show full text]
  • Instructions to and Duties of the Scorer for Basketball Games Rules Coverage: 7
    2019 Scorers & Timers Sheets_2004 Basketball Scorers & timers.qxd 7/10/2019 10:07 AM Page 1 INSTRUCTIONS TO AND DUTIES OF THE SCORER FOR BASKETBALL GAMES RULES COVERAGE: 7. First of one-and-one: First made, bonus awarded: Rule 1-17: The scorer’s location at the scorer’s and timer’s table must be Bonus free throw made: clearly marked with an “x.” 8. Record the number of charged time-outs (who/when) for each team. Rule 2-1-3: It is recommended that the official scorer and timer be seated 9. Check the scoreboard often and have the progressive team totals next to each other. available at all times. Points scored in the wrong basket are never Rule 2-4-3: The referee designates the official scorebook and the official credited to a player, but are credited to the team in a footnote. Points scorer. awarded for basket interference or goaltending by the defense are Rule 2-11: The duties and responsibilities of the official scorer are indicat - credited to the shooter. When a live ball goes in the basket, the last ed. In case of doubt, signal the floor official as soon as conditions permit player who touched the ball causes it to go there. to verify the official’s decision. Rule 2-11-12: The official scorer is required to wear a black-and-white ver - tically striped garment. NOTIFY THE NEARER OFFICIAL WHEN: 1. The bonus penalty is in effect for the seventh, eighth and ninth team RESPONSIBILITY: foul in each half. The bonus display indicates a second free throw is awarded for all common fouls (other than player-control) if the first The scorer’s responsibility is so great that floor officials must establish the free throw is successful.
    [Show full text]
  • Rules of the Game January 2015
    3x3 Official Rules of the Game January 2015 The Official FIBA Basketball Rules of the Game are valid for all game situations not specifically mentioned in the 3x3 Rules of the Game herein. Art. 1 Court and Ball The game will be played on a 3x3 basketball court with 1 basket. A regular 3x3 court playing surface is 15m (width) x 11m (length). The court shall have a regular basketball playing court sized zone, including a free throw line (5.80m), a two point line (6.75m) and a “no-charge semi-circle” area underneath the one basket. Half a traditional basketball court may be used. The official 3x3 ball shall be used in all categories. Note: at grassroots level, 3x3 can be played anywhere; court markings – if any are used – shall be adapted to the available space Art. 2 Teams Each team shall consist of 4 players (3 players on the court and 1 substitute). Art. 3 Game Officials The game officials shall consist of 1 or 2 referees and time/score keepers. Art. 4 Beginning of the Game 4.1. Both teams shall warm-up simultaneously prior to the game. 4.2. A coin flip shall determine which team gets the first possession. The team that wins the coin flip can either choose to benefit from the ball possession at the beginning of the game or at the beginning of a potential overtime. 4.3. The game must start with three players on the court. Note: articles 4.3 and 6.4 apply to FIBA 3x3 Official Competitions* only (not mandatory for grassroots events).
    [Show full text]
  • Analysis of Different Types of Turnovers Between Winning and Losing Performances in Men’S NCAA Basketball
    한국컴퓨터정보학회논문지 Journal of The Korea Society of Computer and Information Vol. 25 No. 7, pp. 135-142, July 2020 JKSCI https://doi.org/10.9708/jksci.2020.25.07.135 Analysis of different types of turnovers between winning and losing performances in men’s NCAA basketball 1)Doryung Han*, Mark Hawkins**, HyongJun Choi*** *Honorary principal professor, Major of Security secretary Studies Continuing Education Center, Kyonggi University, Seoul, Korea **Head coach, Performance Analysis of Sport, University of Wales, UK ***Associate Professor, Dept. of Physical Education (Performance Analysis in Sport), Dankook University, Yongin, Korea [Abstract] Basketball is a highly complex sport, analyses offensive and defensive rebounds, free throw percentages, minutes played and an efficiency rating. These statistics can have a large bearing and provide a lot of pressure on players as their every move can be analysed. Performance analysis in sport is a vital way of being able to track a team or individuals performance and more commonly used resource for player and team development. Discovering information such as this proves the importance of these types of analysis as with post competition video analysis a coach can reach a far more accurate analysis of the game leading to the ability to coach and correct the exact requirements of the team instead of their perceptions. A significant difference was found between winning and losing performances for different types of turnovers supporting current research that states that turnovers are not a valid predictor of match outcomes and that there is no specific type of turnover which can predict the outcome of a match as briefly mentioned in Curz and Tavares (1998).
    [Show full text]
  • The Unseen Play the Game to Win 03/22/2017
    The Unseen Play the Game to Win 03/22/2017 Play the Game to Win What Rick Barry and the Atlanta Falcons can teach us about risk management “Something about the crowd transforms the way you think” – Malcolm Gladwell - Revisionist History With 4:45 remaining in Super Bowl LI, Matt Ryan, the Atlanta Falcons quarterback, threw a pass to Julio Jones who made an amazing catch. The play did not stand out because of the way the ball was thrown or the agility that Jones employed to make the catch, but due to the fact that the catch eas- ily put the Falcons in field goal range very late in the game. That reception should have been the play of the game, but it was not. Instead, Tom Brady walked off the field with the MVP trophy and the Patriots celebrated yet another Super Bowl victory. NBA basketball hall of famer Rick Barry shot close to 90% from the free throw line. What made him memorable was not just his free throw percentage or his hard fought play, but the way he shot the ball underhanded, “granny-style”, when taking free throws. Every basketball player, coach and fan clearly understands that the goal of a basketball game is to score the most points and win. Rick Bar- ry, however, was one of the very few that understood it does not matter how you win but most im- portantly if you win. The Atlanta Falcons crucial mistake and Rick Barry’s “granny” shooting style offer stark illustrations about how human beings guard their egos and at times do imprudent things in order to be viewed favorably by their peers and the public.
    [Show full text]
  • Sheryl Howard Always Wanted a House Filled with Chil
    Celebrity Midday Soirée will have live entertainment (Khicks urban ball- In Walk Like You Have Somewhere to Go, Lucille Join Felicia Young on the sidelines as she reviews room dance group, DJ Party-Man), food, giveaways, and a silent auction. O’Neal takes you on a 40-year journey from “mental the tapes of her past and shares how God changed Kyle Moore (Buffalo Bills defensive end) and several teammates will at- welfare to mental wealth.” You will laugh, you may her game plan. tend. Felicia Young, mother of Vince Young (Philadelphia Eagles quar- cry, and in the process you will be encouraged, en- In the fi rst quarter, get in the huddle with Young as terback), will sign copies of her book, Touchdown From Heaven. Lucille lightened, and empowered. she explicity recalls the trying times of motherhood, O’Neal, mother of Shaquille O’Neal (retired NBA star) will be onhand to marriage, and the bondage of addiction. She reveals sign copies of her book, Walk Like You Have Somewhere To Go, for the fi rst As the mother of one of the greatest athletes of all the choices she made and the company she kept led 50 purchasers of VIP tickets! Other NFL and NBA players, members of the time, her journey is exceptional; but her story reveals her down a path of destruction. Professional Football Players Mothers Association, and members of Moth- that she is more than just Shaquille O’Neal’s mom. O’Neal is a woman you know, a woman you under- ers of Professional Basketball Players Association are also slated to attend! In the second quarter, observe play by play how she stand.
    [Show full text]
  • DISCUSSION GUIDE Based on the Novel by E.B
    DISCUSSION GUIDE Based on the novel by E.B. Vickers PRE-READING QUESTIONS: 1. Under what circumstances should a person reveal someone else’s secret? Under what circumstances should a person keep another’s secret? 2. There are times when we make assumptions about someone’s life. What assumptions might people make about you? What things might they get wrong? Are assumptions helpful? Why do we make them? 3. What comes to mind when you hear the word addiction? If you don’t know about addiction through people you know personally, where have you gathered ideas of what addiction looks like? READING ACTIVITIES: • Have students read Stephanie Ericsson’s “The Ways We Lie,” summarizing each of the ten kinds of lies she outlines. As students are reading Fadeaway, have them note an example of characters telling each kind of lie, and why they think the character told that kind of lie. (See chart at the end of this guide.) • When Kolt starts telling his part of the story, he says he and Jake “were from the same part of town – the wrong part” (7). What might he have meant by this? Based on what you have read so far, what do you think the wrong part of this town is? What kinds of assumptions do people make upon hearing a statement like this? • At the start of the book, there are several characters who give statements to the police. Re-read Kolt’s (5), Daphne’s (16), Luke’s (52), Sabrina’s (70) and then Kolt’s second statement (84).
    [Show full text]
  • The 25 Most Misunderstood Rules in High School Basketball
    THE 25 MOST MISUNDERSTOOD RULES IN HIGH SCHOOL BASKETBALL 1. There is no 3‐second count between the release of a shot and the control of a rebound, at which time a new count starts. 2. A player who is not a dribbler in control can keep (tap) a ball inbounds, go out of bounds, and return inbounds and play the ball. 3. There is no such thing as “over the back”. There must be contact resulting in advantage/disadvantage. Do not put a tall player at a disadvantage merely for being tall! 4. “Reaching” is not a foul. There must be contact and the player with the ball must have been placed at a disadvantage. 5. A player may always recover his/her fumbled ball; a fumble is not a dribble, and any steps taken during recovery are not traveling, regardless of progress made and /or advantage gained. Running while fumbling is not traveling! 6. It is not possible for a player to travel while dribbling. 7. A high dribble is always legal provided the dribbler’s hand stays on top of the ball, and the ball does not come to rest in the dribbler’s hand. 8. A “kicked” ball must be ruled intentional to be ruled a violation. 9. It is legal for a player to rebound/catch his/her own air ball, provided the official deems the shot a legitimate try. 10. It is a jump ball (AP Arrow) when the ball lodges on or in the basket support. If it happens during a throw‐in or free throw, violation.
    [Show full text]
  • Dwight Howard / Orlando Magic
    Dwight Howard / Orlando Magic When he was 14-years-old, Dwight Howard made a goal —be selected as the no. 1 pick in the NBA draft. In the 2004, Dwight accomplished this goal when he was drafted no. 1 overall by the Orlando Magic, beginning his road to superstardom in the National Basketball Association. After becoming the youngest player ever to average a double-double in his rookie season, he’s been a five-time NBA All-Star, three- time NBA Defensive Player of the Year, four-time All-NBA and All-Defensive team member and the 2008 NBA Slam Dunk Contest winner. Widely considered the best big man in the game, he is consistently among league leaders in rebounds, blocks, field goal percentage and scoring. His play has helped lead the Magic to a franchise record five straight postseason appearances, three division titles and their first NBA Finals appearance in more than 10 years. Howard gained national recognition while attending Southwest Atlanta Christian Academy in his hometown of Atlanta, Georgia. Over his four-year high school career, he averaged 16.6 points, 13.4 rebounds and 6.3 blocks and lead his team to a state title. He was bestowed with all major high school awards that year including McDonald’s National High School Player of the Year, Gatorade National Player of the Year, Morgan Wootten High School Player of the Year and the Naismith Prep Player of the Year. Raised as a devout Christian by parents Dwight Sr. and Sheryl Howard, Dwight Jr. views his basketball career as much more than an opportunity for money and fame.
    [Show full text]
  • Illegal Defense: the Irrational Economics of Banning High School Players from the NBA Draft
    University of New Hampshire University of New Hampshire Scholars' Repository University of New Hampshire – Franklin Pierce Law Faculty Scholarship School of Law 1-1-2004 Illegal Defense: The Irrational Economics of Banning High School Players from the NBA Draft Michael McCann University of New Hampshire School of Law Follow this and additional works at: https://scholars.unh.edu/law_facpub Part of the Antitrust and Trade Regulation Commons, Collective Bargaining Commons, Entertainment, Arts, and Sports Law Commons, Labor and Employment Law Commons, Sports Management Commons, Sports Studies Commons, Strategic Management Policy Commons, and the Unions Commons Recommended Citation Michael McCann, "Illegal Defense: The Irrational Economics of Banning High School Players from the NBA Draft," 3 VA. SPORTS & ENT. L. J.113 (2004). This Article is brought to you for free and open access by the University of New Hampshire – Franklin Pierce School of Law at University of New Hampshire Scholars' Repository. It has been accepted for inclusion in Law Faculty Scholarship by an authorized administrator of University of New Hampshire Scholars' Repository. For more information, please contact [email protected]. +(,121/,1( Citation: 3 Va. Sports & Ent. L.J. 113 2003-2004 Content downloaded/printed from HeinOnline (http://heinonline.org) Mon Aug 10 13:54:45 2015 -- Your use of this HeinOnline PDF indicates your acceptance of HeinOnline's Terms and Conditions of the license agreement available at http://heinonline.org/HOL/License -- The search text of this PDF is generated from uncorrected OCR text. -- To obtain permission to use this article beyond the scope of your HeinOnline license, please use: https://www.copyright.com/ccc/basicSearch.do? &operation=go&searchType=0 &lastSearch=simple&all=on&titleOrStdNo=1556-9799 Article Illegal Defense: The Irrational Economics of Banning High School Players from the NBA Draft Michael A.
    [Show full text]
  • Opinions Vary on Fouling Late in Games
    NEWSLETTER #15 - 2005-06 TO FOUL OR NOT TO FOUL "Team A is up 3 with 15 seconds remaining. Team B has the ball. Both teams in bonus. If you are team A do you foul, and send them to the line?" The question to foul or not to foul at the end of the game has been posed several times this year. Most recently, a head varsity coach from Strasburg, Illinois posed the question after he was taken to OT in 3 of his last 4 games on late shots. Xavier has also had bad luck in the same situation over the past 2 years. Most unforgetable was last year at the University of Miami (FL). Miami in bounded the ball with 13.8 left on the clock. With 8 seconds to go, Robert Hite hit a 3 with to tie the game and send it to overtime. Fortinuatly for us, we outscored the Canes 18-5 in OT and escaped Florida with a big win. Recently, Jay Bilas from ESPN.com did a great piece on this endless dilema on his online blog. Opinions vary on fouling late in games http://insider.espn.go.com/ncb/insider/columns/story?columnist=bilas_jay&id=2324605&univLogin02=stateChanged The strategy of fouling in late-game situations, when one team is ahead by three points and its opponent has the ball with a chance to tie, has long been debated. Some say, without reservation, that it is a no-brainer to foul when up three points … but many are not as certain as to when the "cut line" is on the clock.
    [Show full text]