# Dice Duels

Students explore even and uneven distribution and bias using dynamic, interactive tools in a range of dice-based tutorials, activities and games

### Dice duels: go-kart race

Students select a go-kart and observe how it performs in a race where the go-kart's progress is determined by the roll of a dice. They look for any patterns in the results of 100 races, increase the distance of the races and then observe the distribution of winners. Students consider how many rolls of the dice are required to get a winner of an individual race.

### Dice duels: fair or unfair?

Students predict the result for 12 tosses of a fair dice. They observe what happens and record what they think about their prediction and the observed outcome.

Students increase the number of tosses up to 9999 and observe the graph of the results. Students consider the following: Are these results reassuring that the die is fair? How would you know if the die is not 'fair'? Should such variation in the distribution of outcomes be expected in what is referred to as an even distribution? If the die is loaded, what would repeated runs of 9999 tosses show?

### Dice duels: uneven distribution

Students predict the result for 11 tosses of a pair of fair dice and observe what happens. They record what they think about their prediction and the observed outcome.

Students increase the number of tosses up to 9999 and observe the graph of the results. They then consider the following: Are these results reassuring that the dice are fair? How would you know if the dice are not 'fair'? Should such variation in the distribution of outcomes be expected in such an experiment? If the dice are loaded what would repeated runs of 9999 tosses show?

### Dice duels: bike race

Students select a bike and observe how it performs in a race where the bike's progress is determined by the roll of two dice. They look for any patterns in the results of different bikes and in the results of 100 races. Students increase the length of the races and observe the distribution of winners. They consider how many rolls of the dice are required to get a winner of an individual race and consider if there any patterns emerging.

### Dice duels: lucky 16 game

Students choose where to place 16 counters on a grid of numbers 2 to 12. Two dice are rolled and the sum calculated. One of the 16 counters is removed. The goal is to find a strategy to minimise the number of rolls required to remove all 16 counters from the grid.

Students apply known underpinning mathematical theory or learn from experience. Either way there are variations from what might be expected.

### Dice duels: airport addition

Students choose which airport runway for your plane to queue in while waiting to take off. At Pot Luck airport the runways are numbered 2 to 12 and the order of take-off is determined by the toss of two dice and adding the faces. The task is to choose a runway that improves your chance of a prompt take-off. Knowledge of the underpinning theory relating to uneven distributions (included as a tutorial option) helps, but sometimes there are unexpected delays.

### Dice duels: airport subtraction

Students choose which airport runway for a plane to queue in while waiting to take off. At Pot Luck airport the runways are numbered 0 to 5 and the order of take-off is determined by the toss of two dice and taking the difference between the faces. The task is to choose a runway that improves the chance of a prompt take-off. Knowledge of the underpinning theory relating to uneven distributions (included as a tutorial option) helps, but sometimes there are unexpected delays.

### Dice duels: load one dice

'Dice duels: load one dice' provides a tool for loading one face of a single dice. Students carry out one or more of the suggested investigations or test their own conjectures and theories. The 'What's the theory' option assists with the underpinning mathematical ideas.

### Dice duels: load a pair of dice

'Dice duels: load a pair of dice' provides a tool for loading one or two faces (the same number or different numbers) of two dice. Carry out one or more of the suggested investigations or test your own conjectures and theories. The 'What's the theory' option assists with the underpinning mathematical ideas.

### Dice duels: find the bias

Students use dice to explore relationships between bias, proportions, sample size, random variation and statistical distributions.

### Dice duels

This is an aggregated learning unit combining 'Dice duels: load one dice', 'Dice duels: load a pair of dice' and 'Dice duels: find the bias.