Learn / Library / Market making

Larger die payoff

Market makingMedium

$2$ fair $6$ -sided dice are rolled independently. A contract pays, in dollars, the larger of the numbers (if they are equal, that number). What is its fair value in dollars? Give an exact fraction.

Checking an answer needs JavaScript. The hint and the solution open without it.

Hint

Count the outcomes in which the maximum equals each value k.

Solution

The maximum equals k in $2 k - 1$ of the $36$ equally likely outcomes.
The sum of $k \times (2 k - 1)$ for $k$ from $1$ to $6$ is $1 + 6 + 15 + 28 + 45 + 66 = 161$ .
The fair value is $\frac{161}{36}$ .

Answer: $\frac{161}{36}$

Next question Back to the library