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In-Class Assignment May 6, 2019
Modeling the game: Pass the Pigs
Rules:
Each turn involves one active team throwing two model pigs, each of which has a dot on one side only.
The team will earn points for their “turn score” based on the way the pigs land (see below). Each turn
lasts until the active team either rolls “Pig Out” which wipes out their current “turn score” or the active
team decides to stop their turn at which time they add their “turn score” to their “total score” and pass
the pigs to the next team. The winner is the first team to get a “total score” of at least 100 points.
Scoring: Note, each pig can land in one of 7 ways:
1. Dot: The pig is lying on its side with the dot showing.
2. No Dot: The pig is lying on its side with the all pink side showing.
3. Razorback: The pig is lying on its back.
4. Trotter: The pig is standing upright.
5. Snouter: The pig is leaning on its snout.
6. Leaning Jowler: The pig is resting on its snout and ear.
7. Other: The pig is resting on its back and one ear with the dot showing. (Reroll)
The score of each roll is computed by looking at both pigs as follows:
Pig Out - If both pigs are lying on their sides, one with the dot facing upwards and one with the dot
facing downwards the score for that turn is reset to 0 and the turn changes to the next team
Sider - The pigs are on their sides, either both with the dot facing upward or downward - 1 Point
Single Razorback - One pig on its side and one Razorback. - 5 points
Single Trotter - One pig on its side and one Trotter. - 5 points
Single Snouter - One pig on its side and one Snouter. - 10 points
Single Leaning Jowler - One pig on its side and one Leaning Jowler. - 15 points
Double Razorback - The pigs are both lying on their backs - 20 Points
Double Trotter - The pigs are both standing upright - 20 Points
Double Snouter - The pigs are both leaning on their snouts - 40 Points
Double Leaning Jowler - The pigs are both resting between snouts and ears - 60 Points
Mixed Combo - A combination not mentioned above is the sum of the single pigs score above.
1Chart I: Histogram of Rolls
Keep track of how many times you get each type of roll over all games in a histogram here. Mark one box
starting at the top for each type of roll you see. Note: If any other type of roll occurs, keep track of that
too. I might have missed another possibility! For the sake of the game, you will need to keep track of the
current turn score and the total score too.
DotSide NoDotSide Razorback T rotter Snouter LeaningJowler Other
2Chart II: Histogram of Incremental Scores After Each Turn
inc.score all +1 +5 +10 +15 +20 +40 +60 other value
Summary of scores:
P igOut Sider S.Razor S.T rot S.Snout S.Lean D.Raz D.T rot. D.Sn D.Lean. OtherV alue
inc.score all +1 +5 +5 +10 +15 +20 +20 +40 +60 various
Other Values: there are 6 types of rolls corresponding to the 2-subsets of {Razor, T rot, Snout, Lean}.
The points for these are the sum of the two scores for the single rolls. If you get one of these, note the
score in the histogram.
3Your name:
Team members
Due in class today Monday, May 6: The goal of this exercise is to estimate the probability of each
type of roll(s) and to determine an effective strategy for playing. We will use this data later to determine
an optimal strategy for winning.
1. Collect data: In teams of 2 (if possible) play one game of Pass the Pigs. Record the results of every
single pig roll on the Chart I (whether or not it was your turn). Record the result of the score after
every pair of pigs are rolled in Chart II. What were the final scores?
Us: Them:
2. Hypothesize an optimal strategy for when to stop rolling and discuss it with your partner. Test one of
the strategies you discussed. Play one more game using your proposed strategy. Continue to record
the results of every roll on Charts I and II. What will your strategy be this time?
3. Was your strategy effective?
4. Probabilities: Using the data on your Chart II, approximate the probability distribution for each
possible incremental score.
5. Expected values: Assume the probability of each score computed in Problem 4 is correct. Say you
currently have x points accumulated on this turn, write down the formula for the expected number
of points you will have after 1 more roll.
4
In-Class Assignment May 6, 2019
Modeling the game: Pass the Pigs
Rules:
Each turn involves one active team throwing two model pigs, each of which has a dot on one side only.
The team will earn points for their “turn score” based on the way the pigs land (see below). Each turn
lasts until the active team either rolls “Pig Out” which wipes out their current “turn score” or the active
team decides to stop their turn at which time they add their “turn score” to their “total score” and pass
the pigs to the next team. The winner is the first team to get a “total score” of at least 100 points.
Scoring: Note, each pig can land in one of 7 ways:
1. Dot: The pig is lying on its side with the dot showing.
2. No Dot: The pig is lying on its side with the all pink side showing.
3. Razorback: The pig is lying on its back.
4. Trotter: The pig is standing upright.
5. Snouter: The pig is leaning on its snout.
6. Leaning Jowler: The pig is resting on its snout and ear.
7. Other: The pig is resting on its back and one ear with the dot showing. (Reroll)
The score of each roll is computed by looking at both pigs as follows:
Pig Out - If both pigs are lying on their sides, one with the dot facing upwards and one with the dot
facing downwards the score for that turn is reset to 0 and the turn changes to the next team
Sider - The pigs are on their sides, either both with the dot facing upward or downward - 1 Point
Single Razorback - One pig on its side and one Razorback. - 5 points
Single Trotter - One pig on its side and one Trotter. - 5 points
Single Snouter - One pig on its side and one Snouter. - 10 points
Single Leaning Jowler - One pig on its side and one Leaning Jowler. - 15 points
Double Razorback - The pigs are both lying on their backs - 20 Points
Double Trotter - The pigs are both standing upright - 20 Points
Double Snouter - The pigs are both leaning on their snouts - 40 Points
Double Leaning Jowler - The pigs are both resting between snouts and ears - 60 Points
Mixed Combo - A combination not mentioned above is the sum of the single pigs score above.
1Chart I: Histogram of Rolls
Keep track of how many times you get each type of roll over all games in a histogram here. Mark one box
starting at the top for each type of roll you see. Note: If any other type of roll occurs, keep track of that
too. I might have missed another possibility! For the sake of the game, you will need to keep track of the
current turn score and the total score too.
DotSide NoDotSide Razorback T rotter Snouter LeaningJowler Other
2Chart II: Histogram of Incremental Scores After Each Turn
inc.score all +1 +5 +10 +15 +20 +40 +60 other value
Summary of scores:
P igOut Sider S.Razor S.T rot S.Snout S.Lean D.Raz D.T rot. D.Sn D.Lean. OtherV alue
inc.score all +1 +5 +5 +10 +15 +20 +20 +40 +60 various
Other Values: there are 6 types of rolls corresponding to the 2-subsets of {Razor, T rot, Snout, Lean}.
The points for these are the sum of the two scores for the single rolls. If you get one of these, note the
score in the histogram.
3Your name:
Team members
Due in class today Monday, May 6: The goal of this exercise is to estimate the probability of each
type of roll(s) and to determine an effective strategy for playing. We will use this data later to determine
an optimal strategy for winning.
1. Collect data: In teams of 2 (if possible) play one game of Pass the Pigs. Record the results of every
single pig roll on the Chart I (whether or not it was your turn). Record the result of the score after
every pair of pigs are rolled in Chart II. What were the final scores?
Us: Them:
2. Hypothesize an optimal strategy for when to stop rolling and discuss it with your partner. Test one of
the strategies you discussed. Play one more game using your proposed strategy. Continue to record
the results of every roll on Charts I and II. What will your strategy be this time?
3. Was your strategy effective?
4. Probabilities: Using the data on your Chart II, approximate the probability distribution for each
possible incremental score.
5. Expected values: Assume the probability of each score computed in Problem 4 is correct. Say you
currently have x points accumulated on this turn, write down the formula for the expected number
of points you will have after 1 more roll.
4