Rock-Paper-Scissors

For me, as a little kid, the game Rock-Paper-Scissors was ALWAYS the deciding factor to see who went first in practically anything.  It was always "best out of three", and sometimes it just didn't seem fair when I'd always lose.  Is the commonly played game fair?  Or does it leave one person a higher advantage in winning?

In my Math 157 class, we looked deeper into the question of fairness.  We conducted an experiment!  I partnered up with my friend, Jessica, and we played the game 45 times.  We made sure that we kept the right tallies for our outcomes (we are competitive).  Our experimental probabilities were all about the same number.  The probability that I would win was 15/45 (simplified to 1/3).  The probability that Jessica would win was 16/45.  The probability that we would tie was 14/45.

So the question still remains, is the game fair?

Since we figured out the experimental probability, we decided that we needed to figure out the theoretical probability.  The difference between the two is simple.  Experimental probability is determined by observing the outcomes of an experiment.  Theoretical probability is the outcome under ideal conditions.  It is what "should" happen in the experiment.

The way that we figure out the theoretical probability is that we filled out a matrix, which looks like this.

In this matrix, the probability that A wins is 1/3.  The probability that B wins is 1/3.  The probability of a tie is 1/3.  Since the probabilities are equal, each party is equally likely to win.
When we go back to our experimental probabilities, even though they don't simplify to 1/3 exactly, the numbers are all within close distance of each other to almost equal 1/3.

So after all the math, the answer to our question above is...Rock-Paper-Scissors is a FAIR game!  Each person would have an equal chance to win.  So that means, we can keep using the game to determine who goes first, or even who gets the last cookie from the cookie jar.

Source for the matrix was found here

Source for the activity:
Klassen, Rosanne. Class lecture. Mathematics for Elementary Education Teachers II. Mesa Community     College, Mesa, AZ.