1. Dice, Cards and Darts Probabilities in Games Finding the Right Representation

2. Finding a winning strategy – playing the odds How do we represent probabilities? –Discuss Odds vs. Probabilities

3. Simple dice games Many dice games use throws of two, or more, dice and the sum of the scores. What are the most likely scores? –Experiment in class –Collect data Can we explain it? Can we represent what is going on? Excel: Dice patternsDice patterns

4. What about nonstandard dice? Let’s play!!

5. What did we find? Is there a pattern? Excel: Dice patternsDice patterns What would have happened with multiplication? What about other dice? –Create your own spreadsheets in groups.

6. Variations to consider Suppose one conventional die and one with values 0, 1, 2 with probabilities 1/3, 1/2, 1/6 What are values and probabilities of possible sums? Products? Can we modify our tables for this or other variations?

7. Cards – blackjack “score” Deal two cards from a standard deck Add values with the following rules: →Ace counts 1 or 11 at player’s option →2 – 10 count for face value →Jack, Queen, King all count 10 What are the possible scores? What is a good way of representing/showing this?

8. Cards – blackjack “score” Deal two cards from a standard deck Add values with the following rules: →Ace counts 1 or 11 at player’s option →2 – 10 count for face value →Jack, Queen, King all count 10 Over 21 is “bust” so … When should you stand? What if you can see one of the dealers cards?

9. Technology? Excel spreadsheet can help compute odds –Scoring chart spreadsheet – exercise –Use experiment to verify/validate model –Test your strategy in actual play Download a program to play/deal/check your odds? –http://www.qfit.com/CVDPC.htmhttp://www.qfit.com/CVDPC.htm –http://www.s-a-g-e.com/blackjack_info/bjinfo.htmlhttp://www.s-a-g-e.com/blackjack_info/bjinfo.html –Game program: Sage Blackjack (shareware)Sage Blackjack

10. Darts? Strategy for maximum score –Ignore doubles, triples, bulls What about best chance to get a fixed score? –This is typically the way a game finishes Strategy depends on skill level –Conditional probabilities

11. Darts Why is a dart board arranged the way it is? Could it be designed better? What is your expected score if you aim at 20 each time? –How does this change for different target locations on the board?

12. Who is the better hitter? Two baseball hitters, Jose and Brian have the batting averages 0.260 and 0.264 respectively. –Which is the better batter? HitterBatting Average Jose0.260 Brian0.264

13. Who is the better hitter? These two hitters have the batting averages shown when facing left or right-handed pitchers. –Which is the better batter? –Are these statistics consistent? HitterAverage v. lefties Average v. righties Jose0.3000.250 Brian0.2700.240