Competitiveness and fairness/"trickiness" as factors in solving math problems—compare Cosmides and Tooby on Wason tests and cheater detection

Condition A:

**New York Times NUMBERPLAY column**

**"Tricky Dice"**

APRIL 21, 2014

You and an opponent are to play a game with three dice. Your opponent starts by choosing one of the three dice, and then you choose one of the two dice that remain. You both then roll your chosen die, and whoever rolls the highest number wins. Our challenge is the following: design three dice (each with three distinct numbers between one and nine, with opposing faces identical) so that no matter which die your opponent chooses, you’ll always be able to choose a better die. That is, you’ll always be able to choose a die that will beat your opponent’s die on average. What set of three tricky dice will do this?

Condition B:

From the numbers 1 through 9, pick three sets A, B, and C that satisfy the following properties:

- Each set is made up of three of the nine numbers;
- All nine numbers are used, with each number used only once;
- The probability that a randomly selected number from set A will exceed a randomly selected number from set B is greater than one half;
- The probability that a randomly selected number from set B will exceed a randomly selected number from set C is greater than one half;
- The probability that a randomly selected number from set C will exceed a randomly selected number from set A is greater than one half.

Hypothesis: Solving times and accuracy will be significantly better for condition A than for condition B.