### Stop or Dare

All you need for this game is a pack of cards. While you play the game, think about strategies that will increase your chances of winning.

### Game of PIG - Sixes

Can you beat Piggy in this simple dice game? Can you figure out Piggy's strategy, and is there a better one?

### Three Spinners

These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?

# How Random!

##### Stage: 2 Challenge Level:

Full screen version
If you can see this message Flash may not be working in your browser
Please see http://nrich.maths.org/techhelp/#flash to enable it.

To get an idea of how this interactivity works, set the grid size to 10 rows and 10 columns, and the size of each trial to 10.

Click on "Randomise" a few times. Can you work out what is happening?

Clear the grid so that the red squares disappear.

Now click in the "Keep previous trials" box, still with the grid size at 10 by 10 and the size of each trial at 10.
This time, click "Randomise" exactly ten times. What happens? Is this what you expected?

Clear the grid once more and try the same thing again, clicking "Randomise" exactly ten times with the "Keep previous trials" box ticked.

Can you explain what you think is happening? You may want to repeat this several more times to test your ideas.

Clear the grid again and this time click on the "Toggle Shape Type" button. You'll see a shape appear on the grid. Make sure the "Keep previous trials" box is ticked again.

How many times do you think you'll have to click on "Randomise" in order for all the small squares you can see to be coloured red?
Try it and find out. How close were you?
Try the same thing again. Were you closer this time? Why do you think that was?

Once all the small squares you can see are red, how many small squares hidden by the shape would you expect to be white still?
Remove the shape and see whether you were right.

How would your estimate for the number of white squares left depend on the size of the shape?
You could choose some different shapes to try out your ideas.

This interactivity can be used to help estimate the area of a shape. Can you explain how?