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.