Why 30 tries is not enough

Flip a coin ten times. You might get seven heads. Does that mean the coin favours heads? Probably not. Small experiments are bumpy. Big experiments are smooth.

Experimental probability

When you do an experiment, the experimental probability of an event is the number of times it happened divided by the number of trials. If you roll a die 30 times and get a six 7 times, the experimental probability of a six is 7/30, which is about 0.23 or 23%.

Why results vary

Every set of 30 rolls is different. One group might get four sixes, another nine. That is not a mistake. It is exactly what chance looks like in small numbers. This is why you can't decide a game is unfair from just a few goes.

The Law of Large Numbers

The Law of Large Numbers says that the more trials you do, the closer the experimental probability usually gets to the theoretical probability. During the Second World War a mathematician named John Kerrich was held in a prison camp with plenty of time on his hands. He flipped a coin 10,000 times and got 5,067 heads. That is 50.67%, very close to one half.

If you plot the running percentage of heads after every 10 flips, the line swings wildly at first and then flattens out towards 50%. Your class can do the same thing by pooling everyone's results.

When theory can't help

Some things can only be explored by experiment. A paper cup, a bottle cap or an old knucklebone has sides of different shapes, so the chance of landing each way is not equal. The only way to find out is to try it many times. The same is true of a weighted or damaged die.

So next time you test a game, do not stop at 30 goes. Pool your results, aim for 100 or more, and watch the pattern appear.