Dice Game

https://www.desmos.com/calculator/lsio1fj9o1

Here’s the game. You can choose any number n of dice that you want and the dice are rolled. If any of the dice show a 1, you get zero. Otherwise (if no 1) you get the sum of the outcomes.

 How many dice should you choose to maximize your average payoff?

Generating some data.

We got out our box of 100 dice and had the students play the game many times with different numbers n of dice from 1 to 16. The average payoffs for each fixed value of n are plotted below.

By extending the grade 8 understanding of independent events, we can even find the equation of the theoretical curve that the data should fit.