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## 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.

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.

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.

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.

Thanks Mike, for sharing such a cool link!