### Chuck-a-Luck Experiment

Die 1 Die 2 Die 3
Distribution graph

#### Description

In the game of chuck-a-luck, a gambler chooses an integer from 1 to 6 and then three fair dice are rolled. If exactly $$k$$ dice show the gambler's number, the payoff is $$k : 1$$.

The three dice are shown in the first graph box on each update. Random variable $$W$$ gives the gambler's net profit on a \$1 bet and is recorded in the record table on each update. The probability density function and moments of $$W$$ are shown in blue in the distribution graph and are recorded in the distribution table. On each update, the empirical density function and moments of $$W$$ are shown in red in the distribution graph and recorded in the distribution table.