Batch 3 - Class 178 - Game of Pig and SKUNK (Probability)

• What if you wanted to color the tetrahedron vertices with two different colors. How many ways of doing that are there?
• 5 - Only the number of vertices with a certain color matter. All the "different" configurations with (say) 2 red and 2 blue vertices are rotationally the same

• 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

• 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 "1" 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 1" comes up, all points accumulated in prior column are also wiped out
• If "1" 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 "1" or "double 1" comes on the first roll of a round, that round is over and all players bear the consequences
• Try a practice game. At end, ask students what strategies they are trying. Try another practice game, and see how students are changing their strategy
• What is the chance and what is the choice in this game?
• How would you decide on whether to stand or sit in SKUNK?
• Since rolling a "1" is a disaster, it would be useful to know how many "good" rolls happen on an average before a "bad" roll. How can you find it out?
• Is this a good strategy or is there a better one?
• If a "1" isn't rolled, what is the average score you expect to get?
• Test it by rolling a pair of dice several times
• Ask students to describe the following strategies
• "Play it safe"
• Risky strategy
• What kind of scores might you get on both of above?
• Choose a strategy (some kids may do either of the two), play few games and analyze
• How well do the results agree with the objective (safe or risky)
• Let students create a 5-grade rating chart. How many points would they allocate for each grade range? Why?

• What are the similarities and differences in game of PIG versus game of SKUNK? Getting to 100 versus maximum score in 5 turns.

• Ten slips of paper, numbered 1 through 10, are placed in a hat. Three numbers are drawn out, one after another. What is the probability that the three numbers are drawn in increasing order?
• Answer: 1/6