This course will become read-only in the near future. Tell us at if that is a problem.

Understanding uncertainty

Here is a small board game to get us thinking about uncertainty.   It's more fun if you have a number of players.


1. Identify 6-8 players (minimum).   Each player needs 6 coins.   Their task is simple.   They have to "make" heads.   They are to toss the coins (randomly) and count the number of heads.  If you are playing the game on your own, you will have to invent the players (which is kinda fun).

2. Find out how the players got on.   If you had one or two really good players maybe you should give them a bonus or promote them to positions of leadership.   If you have any players who did badly, you should sack them.

3. Repeat the game for a couple of rounds.   You might end up demoting your original managers.   You might end up sacking a few more people.


What you need to do now is summarise the experiment.   If the coins were fair, you would expect heads around half the time.   So in 6 throws, anyone getting 4,5 or 6 heads was just lucky.   Likewise, anyone getting 0,1 or 2 heads was unlucky.    So what we've done in the game is to promote lucky people and sack unlucky ones.   Does that sound fair?


With a bit of thought, we should be happy that this is a game of chance.   What is much harder is thinking about real life.   If we invest in stocks/shares and they go up, how much of this is luck?   How much of this iis skillful investment?    This last point is what we need to think hard about.   It's very obvious with coins how much is systematic and how much is luck.   Move away from coins and it gets more complicated.   But our first point of statistical literacy is that much of what we measure is to some extnt, in some way suject to random variation.   But we believe, if we are careful, we can umderstand and characterise that random variation.




Task: Please discuss what this silly game tells us about randomness being natural.   What do you work with that involves randomness?   How good a model is a coin toss?   I know it's not a a very good model, as it has probability of getting heads of 0.5, but what else is "wrong" with it?

Task Discussion