### 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.

### 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.

### 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?

# Who's the Winner?

### Why do this problem?

This problem offers the opportunity to use probability in an authentic sporting context. It introduces the idea of using a probability model to make predictions, and then to refine the model using real data.

### Possible approach

Introduce the idea of two equally matched teams (teams who are equally likely to score the next goal).
"If two goals are scored in a match, what different results are possible?"
"What are the probabilities of the different results?"

Give students time to work out the probabilities. While they are working, circulate and see what methods are being used.

Bring the class together and share different approaches (this may include approaches based on the incorrect assumption that win, loss and draw are equally likely).

With some classes, it may be appropriate to simulate the matches using dice. For example, the even numbers could correspond to one team scoring and the odd numbers could correspond to the other team scoring.

Next, introduce Charlie's and Alison's models, and allow some time for students to discuss their "gut feelings" about which might be more accurate, based on their own experiences.
Then allow time for students to simulate the matches using dice again, or to work out the probabilities using one of the methods discussed earlier (perhaps drawing attention to the efficiency of tree diagrams).

Students may be curious to know how accurately the models reflect reality; the possible extension below suggests how this can be explored.

### Key questions

Why are the results "win", "draw" and "lose" not all equally likely?
Is the second goal independent of the first goal?
What data could be collected to evaluate the models?

### Possible extension

Students could find data (perhaps from school or local teams) and decide on criteria for identifying "closely matched" teams. Then matches between closely matched teams where exactly two goals were scored can be analysed to see which model best fits the data.
Students could refine the models based on the data, and could critique the models and the assumptions made in evaluating them.

### Possible support

Ask pairs of students to simulate the different models using dice, and collect together all the results. Then introduce tree diagrams to explain the results of the simulation.