### Roulette Experiment

Roulette wheel
Distribution graph

#### Description

The American roulette wheel has 38 slots numbered 00, 0, and 1-36. Slots 00 and 0 are green. Half of the slots numbered 1-36 are red and half are black. The roulette experiment consists of rolling a ball in a groove in the wheel; the ball eventually falls randomly into one of the 38 slots. The roulette wheel is shown in the left graph panel; the ball is shown on each update.

One of seven different bets can be selected from the list box:

1. Bet on 1. This is an example of a straight bet, a bet on a single number. The bet pays $$35:1$$.
2. Bet on 1, 2. This is an example of a split bet, a bet on 2 numbers. The bet pays $$17:1$$.
3. Bet on 1, 2, 3. This is an example of a row bet, a bet on 3 numbers. The bet pays $$11:1$$.
4. Bet on 1, 2, 4, 5. This is an example of 4-number bet, and pays $$8:1$$.
5. Bet on 1-6. This is an example of a 2-row bet, a bet on 6 numbers. The bet pays $$5:1$$.
6. Bet on 1-12. This is an example of a 12-number bet, and pays $$2:1$$.
7. Bet on 1-18. This is an example of an 18-number bet, and pays $$1:1$$.

Random variable $$X$$ gives the outcome of the experiment and is shown graphically in the first panel and recorded numerically in the data table. Random variable $$W$$ gives the net winnings for the chosen bet; this variable 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 are recorded in the distribution table.