Dice, Cards and Darts Probabilities in Games Finding the Right Representation.
-
Upload
ashlynn-douglas -
Category
Documents
-
view
216 -
download
1
Transcript of Dice, Cards and Darts Probabilities in Games Finding the Right Representation.
Finding a winning strategy – playing the odds
• How do we represent probabilities?– Discuss
• Odds vs. Probabilities
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 patterns
What did we find?
• Is there a pattern?
Excel: Dice patterns
• What would have happened with multiplication?
• What about other dice? – Create your own spreadsheets in
groups.
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?
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?
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?
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.htm– http://www.s-a-g-e.com/blackjack_info/bjinfo.html – Game program: Sage Blackjack (shareware)
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
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?
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?
Hitter Batting Average
Jose 0.260
Brian 0.264