POW #12 - Eyeballing Game Link
Complete seven estimates with an average score below 2.75. Submit a screenshot to ejohnson@fessenden.org and also post to your mathematics folder.
Monday, December 12, 2016
Thursday, December 8, 2016
Friday, December 2, 2016
The Prisoner's Dilemma
I love teaching on the day before a break. The boys are loud, enthusiastic and happy to be in class with the knowledge that we won't have a quiz or any graded assignment. We are almost always missing a few boys due to travel plans but that doesn't stop us from exploring something interesting. I use these days to investigate a concept that is tangential to our curriculum and won't further our curriculum to the detriment of the boys that can't be there.
The day before Thanksgiving is the first of these opportunities during the year and last week we explored a favorite topic of mine, Game Theory. We do this through the exploration of the Prisoner's Dilemma. I start by telling a story of how two boys in the class were "busted" for a crime and are now awaiting sentencing in separate cells in the local jail. However, they can reduce their sentence if they "rat" out their accomplice on a second crime. The boys love the fiction and we discuss their options and possible consequences. We quantify decisions by optimizing results through use of the Nash Equilibrium (made famous in the Oscar Award winning movie, A Beautiful Mind with Russell Crowe).
We then move on to a British game show based on the Prisoner's Dilemma called, Golden Balls. We watch a few videos that have great opportunities to discuss first impressions, psychology, greed and the Nash Equilibrium. The outcomes are often quite surprising for such a simple game.
And then we get to the best part of the day. We play the game of Split or Steal at the front of the classroom with two boys going head to head at a time. I place a bag of candy between the two of them and give them each two discs (one says split and the other says steal). The goal (I think??) is for them both to put the split disc as then they split the candy evenly. If one puts split and the other puts steal, then the one that puts steal gets all the candy. If they both put steal, neither gets the candy. The drama builds when the boys try to persuade each other to put the split disc and culminates with the reveal of their choices.
I preface our investigation carefully with the boys so that it is understood that we are just dealing with a bag of candy and the consequences are not so great. That said, feelings are sometime hurt when someone chooses to steal the bag. In my five years of playing this game though, the boys report that it was of the best days of the year.
For those that are curious, the Nash Equilibrium says to always steal! This is because when you choose steal you will either win 100% or 0%, meaning an average of 50%. If you always pick split, then you will win 50% or 0, meaning an average of 25%.
A video of one of our Split/Steal duels... Link.
The day before Thanksgiving is the first of these opportunities during the year and last week we explored a favorite topic of mine, Game Theory. We do this through the exploration of the Prisoner's Dilemma. I start by telling a story of how two boys in the class were "busted" for a crime and are now awaiting sentencing in separate cells in the local jail. However, they can reduce their sentence if they "rat" out their accomplice on a second crime. The boys love the fiction and we discuss their options and possible consequences. We quantify decisions by optimizing results through use of the Nash Equilibrium (made famous in the Oscar Award winning movie, A Beautiful Mind with Russell Crowe).
We then move on to a British game show based on the Prisoner's Dilemma called, Golden Balls. We watch a few videos that have great opportunities to discuss first impressions, psychology, greed and the Nash Equilibrium. The outcomes are often quite surprising for such a simple game.
And then we get to the best part of the day. We play the game of Split or Steal at the front of the classroom with two boys going head to head at a time. I place a bag of candy between the two of them and give them each two discs (one says split and the other says steal). The goal (I think??) is for them both to put the split disc as then they split the candy evenly. If one puts split and the other puts steal, then the one that puts steal gets all the candy. If they both put steal, neither gets the candy. The drama builds when the boys try to persuade each other to put the split disc and culminates with the reveal of their choices.
I preface our investigation carefully with the boys so that it is understood that we are just dealing with a bag of candy and the consequences are not so great. That said, feelings are sometime hurt when someone chooses to steal the bag. In my five years of playing this game though, the boys report that it was of the best days of the year.
For those that are curious, the Nash Equilibrium says to always steal! This is because when you choose steal you will either win 100% or 0%, meaning an average of 50%. If you always pick split, then you will win 50% or 0, meaning an average of 25%.
A video of one of our Split/Steal duels... Link.
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