Cheater Checkers
Task Description
Students are asked to create a board game, where it is easier for you to win than your
opponent.
Students explore the concepts of likelihood and weighted outcomes in this open-ended
activity.
Key Mathematical Concepts



Problem solving
Likelihood
Weighted outcomes
Prerequisite Knowledge
Little background knowledge is assumed for this task. However, more advanced students
will draw on prior knowledge of probability, uneven outcomes and factors that influence
outcomes to create more sophisticated games.
Links to VELS
Dimension
Measurement, Chance &
Data (Level 2.75)
Measurement, Chance &
Data (Level 3)
Measurement, Chance &
Data (Level 4)
Standard
…investigation of the fairness of events such as gambling
and games through experimentation.
Students… describe the fairness of events in qualitative
terms. They plan and conduct chance experiments.
Students calculate probabilities for chance outcomes (for
example, using spinners) and use the symmetry properties
of equally likely outcomes. They simulate chance events.
Assessment
When working at Level 3, students will create a game where one outcome is more likely
than any other. The design of the game will not involve calculation of probabilities of
events at each player's turn, but will rely on one player having an easier task to undertake
than the other player, which then biases the overall outcome. It will possibly be obvious
that the game is biased. Student Work Example 1 demonstrates this level of work.
More advanced students will add complexities to their game, which includes assessment of
probabilities of the events, and exploiting/creating imbalances in this. An example could
be a modified version of roulette, where the 'payout' (or points collected) ratio is higher
than the real game, thus weighting it back to the player rather than the operator of the
game. Depending upon the level of complexity in the game design, students could easily
produce work at VELS Level 4. There are no student work examples provided at this level.
Possible Enabling Prompts
Design a board game where players have the same chance of winning.
Cheater Checkers
Extension Suggestions
1. If it is obvious that one person has an advantage, no one will play your game with
you! Therefore, an additional challenge is to ensure your bias is disguised so the
other players are not aware that you are more likely to win than they are.
2. Work out the probability that you will win, and the probability that your opponent
will win.
Solution
The open-ended nature of this activity means there are many possible correct solutions.
Student Work Example 1 adequately demonstrates a game that is biased towards one
player.
Cheater Checkers
Student Work Samples
Example 1
Working at VELS Level 3
Smileys
The students have designed the game so that the shortest path to the smiley from the
yellow starting point is one square shorter than the shortest path from the white starting
point.