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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.

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Snail Trails

This is a game for two players. You will need some small-square grid paper, a die and two felt-tip pens or highlighters. Players take turns to roll the die, then move that number of squares in a straight line. Move only vertically (up/down) or horizontally (across), never diagonally. You can cross over the other player's trails. You can trace over the top of the other player's trails. You can cross over a single trail of your own, but can never cross a pair of your trails (side-by-side) or trace over your own trail. To win, you must roll the exact number needed to finish in the target square. You can never pass through the target square. The game ends when a player ends his/her trail in the target square, OR when a player cannot move without breaking any of the rules.

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Odds and Evens

Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?

Flippin' Discs

Age 11 to 14 Challenge Level:

Here are two discs. Each disc is red on one side and green on the other.

You win if both discs show the same colour.

Complete one throw. Did you win?
Complete several throws and look at your results.

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Approximately how often do you think you would win if you completed $100$ throws?
Make a prediction and then check it by doing the experiment.

You should have won approximately half of the time. Can you explain why?

Now change the number of discs to $3$.
You win if all the discs show the same colour.

What is the probability of winning this time? Can you explain why?

What is the probability of winning with $4$ discs? Can you explain why?

Repeat for $5$ discs.

Do you notice a pattern in your results? Can you explain it?

Can you explain how to find the probability of winning for $n$ discs?