Craps Experiment

Die0 Die1
Distribution graph

Description

In the game of craps, the shooter rolls a pair of fair die. The rules are as follows:

  1. If the shooter rolls a sum of 7 or 11 on the first roll, she wins.
  2. If the shooter rolls a sum of 2, 3, or 12 on the first roll, she loses.
  3. If the shooter rolls a sum of 4, 5, 6, 8, 9, or 10, this number becomes the shooter's point. The shooter continues to roll the dice until the sum is either the point (in which case she wins) or 7 (in which case she loses).

Any of the following bets can be selected from the list box:

  1. Pass. This is the bet that the shooter will win, and pays \(1:1\).
  2. Don't Pass. This is the bet that the shooter will lose, except that an initial roll of 12 is excluded (that is, the shooter loses, but the don't pass bettor neither wins nor loses). The bet pays \(1:1\).
  3. Field. This. is a bet on a single throw. It pays \(1:1\) if 3, 4, 9, 10, or 11 is thrown, \(2:1\) if 2 or 12 is thrown, and loses otherwise.
  4. Craps. This is a bet that 2, 3, or 12 will come up on a single throw, and pays \(7:1\).
  5. Craps 2. This is a bet that 2 will come up on a single throw, and pays \(30:1\).
  6. Craps 3. This is a bet that 3 will come up on a single throw, and pays \(15:1\).
  7. Craps 12. This is a bet that 12 will come up on a single throw, and pays \(30:1\).
  8. Seven. This is a bet that 7 will come up on a single throw, and pays \(4:1\).
  9. Eleven. This is a bet that 11 will come up on a single throw, and pays \(15:1\.
  10. Big 6. This is a bet that 6 will be thrown before 7, and pays \(1:1\).
  11. Big 8. This is a bet that 8 will be thrown before 7, and pays \(1:1\).
  12. Hardway 4. This is a bet that \((2, 2)\) will be thrown before 7 or any other 4, and pays \(7:1\).
  13. Hardway 6. This is a bet that \((3, 3)\) will be thrown before 7 or any other 6, and pays \(9:1\).
  14. Hardway 8. This is a bet that \((4, 4)\) will be thrown before 7 or any other 8, and pays \(9:1\).
  15. Hardway 10. This is a bet that \((5, 5)\) will be thrown before 7 or any other 10, and pays \(7:1\).

Random variable \((X, Y)\) denotes the outcome of the first roll and random variable \((U, V)\) denotes the outcome of the last roll. These are recorded in the data table on each update. The intermediate rolls, if any, are shown in single-step mode, but not recorded. Random variable \(W\) gives the net winnings for the chosen bet of $1; 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 recorded in the distribution table. Finally, the number of rolls \(N\) is recorded in the record table on each update.