## Wednesday, 25 September 2013

### The Unfair Game

One of the activities from our Week of Chance and Probability - which seems to have spilled over into a second week - is the make "The Unfair Game".

Here is an example of an Unfair Game from one keen student.

Here is how he set out his page - instruction, calculations, data - the thinking is very easy to see.

A clear set of rules - this is how he chose to make a game that is unfair.

Oh yes! The stuff he forgot!

And a bit of reflection and explanation to clarify the process.

He got very excited when he was tabulating the possible results from throwing 2 dice. He found that...

....there is only one way to roll 2 = 1 + 1

....there are 2 ways to make 3 = 1 + 2 or 2 + 1

....there are 3 ways to make 4 = 1 + 3 or 2 + 2 or 3 + 1

....there are 4 ways to make 5 = 1 + 4, 2 + 3, 3 + 2, 4 + 1

"When is this going to peak?!" he asked excitedly.

Well, here are his data and results. You and I probably both knew that it would happen when he got to 7. Now he knows it too and will probably always remember that "Ah-ha!" moment.

Why? Why did we go to all this trouble to make an unfair game?

Well, I think it shows really clearly what you understand about chance and probability if you can manipulate different variables to the advantage of one player. And the student's understanding is demonstrated explicitly here in this example.

And - yes - it was fun.