Virtual Laboratories > Games of Chance > 1 2 3 4 5 6 7 [8]

8. Notas

Simulación

Es muy fácil sinular un dado justo con un número aleatorio. Recuerde que la  función "ceiling" ceil(x) da el menor entero que es al menos tan grande como x.

1. Suponga que U está uniformemente distribuída en (0, 1) (un número aleatorio). muestre que ceil(6U) está uniformemente distribuída en {1, 2, 3, 4, 5, 6}.

To see how to simulate a card hand, see the Notes section of Finite Sampling Models. A general method of simulating random variables is based on the quantile function.

Related Topics

• For several of the models in this chapter, the gambler either wins or loses, independently from game to game, and with the same probability. Such random processes are studied in detail in the chapter on Bernoulli Trials.
• Many of the games we have studied in this chapter can be viewd, in statistical terms, as sampling from a finite population. The chapter Finite Sampling Models has a thorough discussion of such sampleing models.
• In our expected value analysis of this chapter, we have assumed that the gambler bets consistently from game to game. Many gamblers believe that a winning strategy can be constructed by varying the bet, depending on the outcomes of previous games. Such strategies are doomed to failure, but nonetheless some are better than others. The chapter Red and Black has a thorough comparison of two very opposite strategies: timid play and bold play.
• One of the simplest strategies for varying bets is studied in the discussion of the Petersburg Problem.

Web Sites

• Gambler's Anonymous is a support group founded in 1947 to help compulsive gamblers.
• The Wizard of Odds is a great resource for information about gambling and games of chance. The site includes rules and odds for just about every casino game, as well as gambling etiquette and other gambling miscellany, and java applets for selected games.

Books

• A good elementary reference for the analysis of a variety of games of chance is The Mathematics of Games and Gambling by Edward Packel.
• For a good advanced mathematical treatment of gambling, see The Theory of Gambling and Statistical Logic, by Richard Epstein
• A good history of gambling and probability theory is Games, Gods, and Gambling by Florence David.
• A compelling fictional (but partly autobiographical) account of a compulsive gambler is The Gambler, by Fyodor Dostoyevsky.
• An interesting account of the colorful Cardano is given in Cardano, the Gambling Scholar by Oystein Ore.

Selected Answers for Section 2

2.15. 0.0287

2.16. 3.913 × 10^-10

2.17. Ordinal. No.

Selected Answers for Section 3

3.12. 0.2130

Selected Answers for Section 4

4.36. 0.09235

Selected Answers for Section 7

7.3. E(U) = 0.5319148936, sd(U) = 0.6587832083

7.4. E(U) = 0.5102040816, sd(U) = 0.6480462207

7.5. E(U) = 1.042553191, sd(U) = 0.8783776109

7.8.

7.9.

In the following keno exercises, let V denote the random payoff on a unit bet.

7.13. Pick m = 1. E(V) = 0.75, sd(V) = 1.299038106

7.14. Pick m = 2. E(V) = 0.7215189873, sd(V) = 2.852654587

7.15. Pick m = 3. E(V) = 0.7353943525, sd(V) = 5.025285956

7.16. Pick m = 4. E(V) = 0.7406201394, sd(V) = 7.198935911

7.17. Pick m = 5. E(V) = 0.7207981892, sd(V) = 20.33532453

7.18. Pick m = 6. E(V) = 0.7315342885, sd(V) = 17.83831647

7.19. Pick m = 7. E(V) = 0.7196008747, sd(V) = 40.69860455

7.20. Pick m = 8. E(V) = 0.7270517606, sd(V) = 55.64771986

7.21. Pick m = 9. E(V) = 0.7486374371, sd(V) = 48.91644787

7.22. Pick m = 10. E(V) = 0.7228896221, sd(V) = 38.10367609

7.23. Pick m = 11. E(V) = 0.7138083347, sd(V) = 32.99373346

7.24. Pick m = 12. E(V) = .7167721544, sd(V) = 20.12030014

7.25. Pick m = 13. E(V) = 0.7216651326, sd(V) = 22.68311303

7.26. Pick m = 14. E(V) = 0.7194160496, sd(V) = 21.98977077

7.27. Pick m = 15. E(V) = 0.7144017020, sd(V) = 24.31901706

Virtual Laboratories > Games of Chance > 1 2 3 4 5 6 7 [8]
Contents | Applets | Data Sets | Biographies | Resources | Keywords | ©