The Jungles of Randomness: Online Biliography

A list of Web articles, books, and other resources that deal with various aspects of randomness.

General References

Beasley, J.D. 1989. The Mathematics of Games. Oxford, England: Oxford University Press.

Bennett, D.J. 1998. Randomness. Cambridge, Mass.: Harvard University Press. See http://www.hup.harvard.edu/catalog/BENRAN.html.

Ekeland, I. 1993. The Broken Dice and Other Mathematical Tales of Chance. Chicago: University of Chicago Press.

Huff, D., and U. Geis. 1959. How to Take a Chance. New York: W.W. Norton.

Peterson, I. 1995. The Jungles of Randomness: A Mathematical Safari. New York: Wiley.

Weaver, W. 1963. Lady Luck: The Theory of Probability. New York: Wiley.

Ivars Peterson's MathTrek

A Catalog of Random Bits http://www.sciencenews.org/articles/20041016/mathtrek.asp

Randomness, Risk, and Financial Markets http://www.sciencenews.org/articles/20041009/mathtrek.asp

Heads or Tails? http://www.sciencenews.org/articles/20040228/mathtrek.asp

The Bias of Random Number Generators http://www.sciencenews.org/articles/20030927/mathtrek.asp

Card Shuffling Shenanigans http://www.sciencenews.org/articles/20021116/mathtrek.asp

Rainbow Randomness http://www.sciencenews.org/articles/20020330/mathtrek.asp

Lava Lamp Randomness http://www.sciencenews.org/articles/20010505/mathtrek.asp

Disorder in the Deck http://www.sciencenews.org/20001014/mathtrek.asp

Tilt-A-Whirl Chaos I
http://www.sciencenews.org/20000422/mathtrek.asp

Tilt-A-Whirl Chaos II
http://www.sciencenews.org/20000429/mathtrek.asp

Unfair Dice http://www.sciencenews.org/pages/sn_arc98/10_24_98/mathland.htm

A Penny Surprise http://www.sciencenews.org/pages/sn_arc97/12_13_97/mathland.htm

Deep in the Jungles http://www.sciencenews.org/pages/sn_arc97/9_13_97/mathland.htm

Gambling

Catlin, D. 2002. Non-random randomness. Part 1. Casino City Times (June 1). Available at http://catlin.casinocitytimes.com/articles/1243.html.

Heidel, R. 1996. Slot machines. Scientific American 275(August):112.

Koeppel, D. 2002. Money wired. Popular Science 261(November):76-86.

Mezrich, B. 2002. Hacking Las Vegas. Wired 9(September):130-139. Available at http://www.wired.com/wired/archive/10.09/vegas.html.

Orkin, M. 1991. Can You Win? The Real Odds for Casino Gambling, Sports Betting, and Lotteries.. New York: W.H. Freeman.

Scarne, J. 1986. Scarne's New Complete Guide to Gambling. New York: Simon & Schuster.

Wykes, A. 1964. The Complete Illustrated Guide to Gambling. Garden City, N.Y.: Doubleday.

Odds on Slot Machines
http://www.acesguidetogambling.com/slots/odds.html
Ace's Guide to Gambling

History of Slot Machines
http://slots.freewebpage.org/slot_history.htm
http://www.noehill.com/sf/landmarks/cal0937.asp

Chaos

Ditto, W.L., and L. Pecora. 1993. Mastering chaos. Scientific American 269(August):78-84. See http://www.fortunecity.com/emachines/e11/86/mastring.html.

Kautz, R.L., and B.M. Huggard. 1994. Chaos at the amusement park: Dynamics of the Tilt-A-Whirl. American Journal of Physics 62(January):59-66.

Lorenz, E.N. 1993. The Essence of Chaos. Seattle: University of Washington Press.

Shinbrot, T., et al. 1992. Chaos in a double pendulum. American Journal of Physics 60(June):491-499.

Kautz, R.L., and B.M. Huggard. 1994. Chaos at the amusement park: Dynamics of the Tilt-A-Whirl. American Journal of Physics 62(January):59-66.

The Sellner Manufacturing Company, which makes the Tilt-A-Whirl, has a Web site at http://www.whirlin.com.

To learn more about the mathematics underlying chaos you can try The Chaos Hypertextbook at http://hypertextbook.com/chaos/ or visit the University of Maryland's Chaos Group Web site at http://www.chaos.umd.edu/.

Pinball History
http://www.flipperit.net/tkalliok/flipperi/history_en.html

Random Number Generators

Bauke, H., and S. Mertens. Preprint. Pseudo random coins show more heads than tails. Available at http://xxx.arxiv.org/abs/cond-mat/0307138.

Ferrenberg, A.M., D.P. Landau, and Y.J. Wong. 1992. Monte Carlo simulations: Hidden errors from "good" random number generators. Physical Review Letters 69(Dec. 7):3382-3384. Abstract available at http://link.aps.org/abstract/PRL/v69/p3382.

Hayes, B. 2001. Randomness as a resource. American Scientist 89(July/August):300-304.

______. 1993. The wheel of fortune. American Scientist 81(March/April):114-118.

McNichol, T. 2003. Totally random. Wired 11(August). Available at http://www.wired.com/wired/archive/11.08/random.html.

Mertens, S., and H. Bauke. Preprint. Entropy of pseudo random number generators. Available at http://xxx.arxiv.org/abs/cond-mat/0305319.

Warnock, T. 1987. Random-number generators. Los Alamos Science 15:137-141.

Information about the lavarand random number generator is available at http://www.lavarnd.org/.

Dice

Diaconis, P., and J.B. Keller 1989. Fair dice. American Mathematical Monthly 96(April):333-348.

Coin Tossing

Ford, J. 1983. How random is a coin toss? Physics Today 36(April):40-47.

Keller, J.B. 1986. The probability of heads. American Mathematical Monthly 93(March):191-197.

Klarreich, E. 2004. Toss out the toss-up: Bias in heads-or-tails. Science News 165(Feb. 28):131-132. Available at http://www.sciencenews.org/articles/20040228/fob2.asp.

Peterson, I. 2003. Flipping a coin. Muse 7(April):19. Available at http://www.sciencenewsforkids.org/pages/puzzlezone/ muse/muse0403.asp.

______. 1990. Islands of Truth: A Mathematical Mystery Cruise. New York: W.H. Freeman.

Vulovic, V.Z., and R.E. Prange. 1986. Randomness of a true coin toss. Physical Review A 33(January):576-582. Abstract available at http://link.aps.org/abstract/PRA/v33/p576.

For a mathematical introduction to coin tossing, see http://mathworld.wolfram.com/CoinTossing.html.

2004. Magician-turned-mathematician uncovers bias in coin flipping. Stanford University news release. June 4. Available at http://www.stanford.edu/dept/news/pr/2004/diaconis-69.html.

Card Shuffling

Aldous, D., and P. Diaconis. 1986. Shuffling cards and stopping times. American Mathematical Monthly 93(May):333-348.

Bayer, D., and P. Diaconis. 1992. Trailing the dovetail shuffle to its lair. Annals of Applied Probability 2:294-313.

Berger, P. 1973. On the distribution of hand patterns in bridge: Man-dealt versus computer-dealt. Canadian Journal of Statistics 1:261-266.

Diaconis, P. 1996. The cutoff phenomenon in finite Markov chains. Proceedings of the National Academy of Sciences 93(Feb. 20):1659-1664. Available at http://www.pnas.org/cgi/reprint/93/4/1659.pdf.

Folger, T. 1991. Shuffling into hyperspace. Discover 12(January):66-67.

Keller, J.B. 1995. How many shuffles to mix a deck? SIAM Review 37(March):88-89.

Klarreich, E. 2002. Coming up trumps. New Scientist 175(July 20):42-44.

Kolata, G. 1990. In shuffling cards, 7 is winning number. New York Times (Jan. 9).

______. 1985. Prestidigitator of digits. Science 85 6(April):67-72.

Mackenzie, D. 2002. The mathematics of . . . shuffling the Stanford flip. Discover 23(October):22-23.

Trefethen, L.N., and L.M. Trefethen. 2000. How many shuffles to randomize a deck of cards? Proceedings of the Royal Society, London A 456(Oct. 8):2561-2568.

A brief outline of the mathematics of card shuffling can be found at http://mathworld.wolfram.com/Shuffle.html.

Randomness

Bassein, S. 1996. A sampler of randomness. American Mathematical Monthly 103(June-July):483-490.

Compagner, A. 1991. Definitions of randomness. American Journal of Physics 59(August):700-705.

Eckhardt, R. 1987. Stan Ulam, John von Neumann, and the Monte Carlo method. Los Alamos Science 15:131-137.

Kac, M. 1983. What is random? American Scientist (July/August):405-406.