Rock-Paper-Scissors

Have you ever played Rock, Paper, Scissors? Have you ever felt that your opponent knew what you where going to choose, therefore your opponent always choosing the thing that will make you lose? Is this a fair game? What are the chances of you winning? Losing? Or even tying? Well before we go into how this all works here is a video that should help you understand a little more about how competitive this game really is...

Ok so now that we have that out of the way, lets learn how we can actually find out if this game is a fair or rigged game. Today in class we actually found out if it was a fair game or not, and here is how we did it.
First we got into groups of two and played  45 games of Rock-Paper-Scissors and kept track who won and lost with rock paper and scissors, and we also kept track of the ones we tied. Afterwards we added up (individually) how many times I won, my partner won, and how many times we tied. In my example I won 19/45, Tied 10/45, Lost 16/45 times. We then were asked to explain if it was fair or not. We both decided it was because There was not a huge margin between the wins. So theoretically it is a fair game. Here is the reason why....

If you were to make a 3x3 square and mark the first column and row with Paper, then the second column and row with Scissors, then finally the last column and row with Rock. Now Player A will be the column side and Player B will the row side. Fill out your 3x3 square with all the possible outcomes and mark where there would be a tie with T, if player A would win mark it with an A, likewise for player B but with B.
What is the probability of player A winning? = 3/9 = 1/3
What is the probability of player B winning? = 3/9 = 1/3
What is the probability of a tie? = 3/9 = 1/3

Here is a link to that will also provide another way of seeing if the game is fair or not.
         Is Rock-Paper-Scissors Fair?

You now can see that Rock-Paper-Scissors is a fair game.