Batch 2 - Class 321 - Game of Pig (Probability)
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Preclass Exercise:
- (536Dudeney - 319) The fly at point A below take a minute to crawl an edge of the cube. How long will it take it to reach point B?
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- Answer: 2.236 minutes along the diagonal
Attendance: Anika, Aditya, Dhriti, Vansh, Kabir, Adyant, Ekagra, Savya, Aneesh, Ayush, Siddharth, Rhea, Advay, Nikhil
Class Notes: (repeat of class 178)
Game of Pig: A game works as follows - The first person to score 100 points wins. In each turn, a player can roll two dice as many times as they want. The total on those dice add to their score. However, if at any point, one dice turns up "6", then the score for that chance goes to zero. If both dice turn "6", then their entire score goes to zero. Think about a strategy to win the game. You may use this https://www.random.org/dice/?num=2 to play.
- Get kids to play and get to a realization that quitting too early or too late is not good. So there is some sort of a "good number" to quit
- Promote the notion of wanting to advance the score as much as possible on each turn (limit to only "one six" scenario)
- Help find the balance by introducing notion of "what you expect to gain should be more than what you expect to lose", hence arrive at 13 as the cross over point
- Using same argument, illustrate that its not worth worrying about double sixes. Also reason that as a risk which always remains regardless of whether you quit now or not
- What happens if we play with a single dice, and if it throws 6, then the turn score goes to zero?
- What happens if we play Game of Pig - Ones. If you roll one, the turn score goes to zero. If you roll double ones, your total score is reset to zero. Sixes are safe
- How about Big Pig - if you roll double ones, then you get 25 points.
- Would your strategy be different depending on the other person's score?
- If the competitor is sitting at 95, then you might have to take higher risk
- How should we think about the overall strategy in this case? When should you be aggressive, when should you be conservative?
- Can you start to put some quantitative model to thinking about this? What should be the inputs to this model (Answer: own score, opponent score, and turn score)
- http://www.durangobill.com/Pig.html for more detailed analysis and exact strategy
Homework:
Game of SKUNK http://www.mathwire.com/games/skunk.pdf
- Rules of Skunk - Each letter of SKUNK represents a different round of the game; play begins with the "S" column and continue through the "K" column. The object of the game is to accumulate greatest points over five rounds. Rules:
- At beginning of each round, every player stands. Then, a pair of dice is rolled (common for all players)
- A player gets the total of the dice and records it in his or her column, unless a "6" comes up, in which case play is over for that round and all the player's points in that column are wiped out
- If "double 6" comes up, all points accumulated in prior column are also wiped out
- If "6" doesn't occur, the player may choose to continue standing and try for more points, or to stop and sit, in which case they get to keep what they have accumulated.
- If "6" or "double 6" comes on the first roll of a round, that round is over and all players bear the consequences
- Think about the turn and game strategy for this game.
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