Rock, Paper, Scissors and 2-Way Tables

Last weekend, the evil Michael Fenton posted a link to an online applet which will now occupy you for the next 2 hours.  It’s not too late to run away now…

Still with me? An adventurous soul, you are.  Anyway, the NY Times online Science section has shared an online game of “Rock, Paper, Scissors”, where you can play against a choice of computer opponents.  The “Novice” opponent has no understanding of your previous moves or stratgey.  But, the “Veteran” option has gathered data on over 200,000 moves, and will try to use its database to crush your spirit.

RPS5

My Advanced Placement Statistics class today was preparing for their first chapter test, where topics include 2-way tables and marginal distributions.  Time to abandon my planned review and play!  Here’s what we did:

Each group (I have 6 groups of 4) was given a netbook computer and the NY Times site.  Half of the groups were told to play against the “Novice” player, while the other half challenged the “Veterarn”.  Each group played 20 times, and pride was on the line as groups considered their moves carefully.  Class data was gathered and compiled into a 2-way table.

RPS1

But just how good are we at outsmarting the computer opponent?  In round 2 of this activity, groups again played 20 games, switching their opponent.  This time, however, I directed groups to choose their moves RANDOMLY.  Groups used their graphing calculator to generate a random number from 1 to 3, which determined their move.  The NY Times site provides some info regarding randomization:

A truly random game of rock-paper-scissors would result in a statistical tie with each player winning, tying and losing one-third of the time. However, people are not truly random and thus can be studied and analyzed. While this computer won’t win all rounds, over time it can exploit a person’s tendencies and patterns to gain an advantage over its opponent.

Groups played 20 more times, and a new table was created for this “random” round.  Last round strategy was labeled the by “guts” round.

RPS2

With the data now on the board, groups were given a few minutes to summarize their findings.  Did we improve by being random?  Did we improve in any particular area?  This turned out to be an engaging review of marginal distributions, and a good opportunity to discuss ribbon graphs, which come up in AP Stats as a useful graphical display.  Below, Excel can be used to compare the “Veteran” opponent results.

Ribbon Graph

Thanks Mike, for sharing such a cool link!

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22 responses to “Rock, Paper, Scissors and 2-Way Tables

  1. Love this!! Thanks for sharing. Just a couple of quick questions. Is the comparison graph only for the veteran player group (random and gut)? Can you give any reflections on what went well and what you would do differently next time? I was just wondering if I should have the entire class (in groups) play against only the “vet” player? Lastly, how did it work with 4 students to 1 computer?

    Thanks
    Kathy

    • This is something I really threw together at the last minute. Woud rather have more students playing. Also, would ensure an un-equal number of plays each time, as students knew we had 60 trials each time, so they settled on counts, rather than proportions.

      The graph is only for the vet level, and we could certainly compare the other group. What I would do differently is have students take the data and provide either a class period, or as a HW assignment, compare and summarize. Also, I can see revisiting this later as a chi-squared opener: is there a significant difference between a “gut” method and a “random” method.

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  3. I’m a little confused. Is the “W” column a win by the computer or by the person playing against the computer?

  4. Michael,
    Thanks for the idea and concept. A fellow teacher saw your blog and pointed it to me the week prior to two-way tables. Perfect timing. I took your idea and had students do 40 trials for homework (10 novice/guts, 10 novice/random, 10 veteran/guts, 10 veteran/random). I have about 120 AP Stats students, so it generated lots of data.

    I had my students fill out a google form that you can see here:https://docs.google.com/a/galileoweb.org/forms/d/1wKqfzrXDYJeqsIMl3rg1ZxdK-S_alozs2wCcNRrw2us/viewform

    and the results go into a Google spreadsheet here:https://docs.google.com/spreadsheet/ccc?key=0AmtJuxTQgCC8dGl6WVhaUm15aW05Rm9ZRjhHNUxETGc&usp=sharing

    Please feel free to copy the spreadsheet by using the “file” menu and “make a copy”. This should copy the sheet and the form for you. Of course you need to have a gmail or googles apps account.

    Enjoy and Thanks

  5. Bob,
    In looking at the student data with the students, it was a very compelling discussion. Since my classes are so large, we generated lots of data over 4,300 games!

    What you might expect played out in the data. In the Novice category (especially since on 10 games were played each time), our gut was better than random. But in the Veteran games, random was clearly the better choice. However the random selection didn’t quite lead the forecasted one-third for W, T and L. But that will come up later in Chi-Square!

    Here’s a link to a worksheet I created as well: https://docs.google.com/file/d/0B2tJuxTQgCC8TFBKZFNWYURsdzg/edit?usp=sharing

    Doug

    P.S. Sorry about the name confusion 😦

    • Wow, you really flew with this one. I am really looking forward to circling back to this applet when we look at experimental design, and again during Chi-squared. I am sharing this lesson with a local stat-teacher group next week, do you mind if I “borrow” your sheets?

  6. Not at all. They were tailored for my results, but whatever you’d like to use or leverage feel free to use. Thanks for getting the ball rolling. I’m glad I could advance it a little.

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  8. Bob and Doug,

    I love what you guys have done with this problem. Much cooler, and much more depth, than I originally imagined. Fair warning: I’m stealing (with attribution, of course) all of your ideas for another stats workshop I’m leading on Monday. 🙂

    Awesome work!

    P.S. I look forward to seeing what you do with chi-squared when you get to it.

    P.P.S. I googled “evil Michael Fenton” to find the post this afternoon since I never bookmarked it after first coming across it when Bob posted in September. Believe it or not, this is the seventh result. Hmmm…

  9. Bob,
    Well, I’m back. I just finished covering Chi Square with my students and now I need them to determine the proper test and conclusions to make. While is seems easy, there is always confusion regarding which Chi Square Test to use. I wanted this exercise to touch on that issue. I decided on the interest of time to use the same data that my students generated previously.

    I have included the worksheet in case anyone is interested. Enjoy
    https://drive.google.com/file/d/0B2tJuxTQgCC8ZUJoODg4bzg2Wk0/edit?usp=sharing

    If you have any interesting results or suggestions, please let me know

    Doug

    • I’ll take a deeper look at this tomorrow, as I am also starting Chi-Squared. Still wrapping my head around the best apparoach as well; really thinking of it as independence – are the proportions in the “vets” table as they would be if the computer had no real advantage? Intriguing questions abound!

  10. I think the issue of Independence or Homogeneity is a challenging one in this instance. I think this exercise really teases out the essence of the difference between the choices. I originally thought it’s independence because the students all answered the questions in one survey, but actually they didn’t (at least the way I instructed them to do it). They played 10 games in each option separately (gut/novice, random/novice, gut/veteran, and random/veteran). Even though they summarized the data in one survey, I think any 2-way table test is going to be a test of homogeneity, because they were separate samples. Do you see it that way, or am I off the mark here?

    Doug

    • I see it as homogeneity as well. The main difference between tests of association and homogeneity is that of one sample vs two samples. Here, we will have two sample, and want to compare the sameness of the responses.

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