Arrange students in groups of two and give each group 2 coins. Tell students that they will play a game with the coins. Here are the rules:

• One person will be the Flipper—in all rounds of the game, the Flipper flips the coins.
• If both coins land on the same side, the Flipper wins. But if one coin lands on heads and the other coin lands on tails, the Challenger wins.

Ask students if they think this game is fair. That is, are both players equally likely to win? After some quiet think time, invite students to share their reasoning about whether the game is fair. (There are four equally likely possible outcomes, In two of them, the Flipper wins, and in the other two, the Challenger wins, so this seems fair.)

After a few have shared, invite students to test whether the game is fair by playing a few rounds and recording the results. Individual groups do not need to play many rounds, because the results from the whole class will be used to determine whether the game is fair.

Make a table to record the outcomes for all to see—for example, by using two columns with the headings “Flipper Wins” and “Challenger Wins.” Invite groups to record the results in the table—for example, by adding tally marks to each side. When all groups have recorded their results, ask students, “Do the results support your opinion about whether the game is fair?” (Out of the 50 rounds that we played, the Flipper won 28 times and the Challenger won 22 times, which is close to a 50% chance of winning, so this supports my opinion that the game is fair.)

An important point to highlight in the discussion is that playing the game can reveal which conjectures about the probabilities are plausible. Still we need to make a mathematical argument to prove whether the game is fair, because the results we get when we actually play the game might not match the mathematical odds perfectly.

Tell students that, in this task, they will decide whether certain games—such as the one they just played—are fair, and then they will design their own fair games. If they struggle to decide whether a game is fair, they can play it for a while and record their results in order to get a rough idea.