Hostname: page-component-76fb5796d-2lccl Total loading time: 0 Render date: 2024-04-26T09:53:18.047Z Has data issue: false hasContentIssue false
  • English
  • Français

A long game – Racing random walkers

Published online by Cambridge University Press:  01 August 2016

T. G. Dankel  and
J. L. Brown
T. G. Dankel
Affiliation:
University of North Carolina at Wilmington, 601 S College Road, Wilmington, NC 28403 emails: dankel@uncwil.edubrownj@uncwil.edu
J. L. Brown
Affiliation:
University of North Carolina at Wilmington, 601 S College Road, Wilmington, NC 28403 emails: dankel@uncwil.edubrownj@uncwil.edu
Get access Rights & Permissions [Opens in a new window]

Extract

In this paper we analyse a game that was published in the 1996 Burger King Kid’s Club calendar. This calendar included an activity for each month, and for the month of September the activity was called the Mountain Bike Rally. To begin the game, each player places a marker on day 1. A turn consists of each player flipping a fair coin. Each player whose coin comes up heads moves his marker forward one day. If a player’s coin shows tails, then he moves his marker back one day, unless his marker is on day 1, in which case it stays there. The object is to be the first player to reach square 31. We never played the game because it was clear that it would take a long time to complete.

Type
Articles
Information
The Mathematical Gazette , Volume 88 , Issue 511 , March 2004 , pp. 57 - 67
Copyright
Copyright © The Mathematical Association 2004

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Grimmett, G. and Stirzaker, D. Probability and random process (2nd edn), Clarendon Press, Oxford (1992).Google Scholar
2. Grenander, U. and Szego, G. Toeplitz forms and their applications (2nd edn), Chelsea, New York (1984).Google Scholar
3. Spitzer, F. Principles of random walk, van Nostrand, Princeton (1964).Google Scholar
4. Feller, W. An introduction to probability theory and its applications, vol. 1 (2nd edn), Wiley, New York (1957).Google Scholar
5. Dette, H. On the generating functions of a random walk on the non-negative integers, Journal of Applied Probability 33 (1996) pp. 1033–1052.Google Scholar
6. Paul, W. and Baschnagel, J Stochastic processes: from physics to finance, Springer, Berlin (2000).Google Scholar
7. Barber, M. N. and Ninham, B. W. Random and restricted walks: theory and application, Gordon and Breach, New York (1970).Google Scholar
8. Lawler, G. Intersections of random walks, Birkhäuser, Boston (1991).Google Scholar
9. Chandrasekhar, S. Stochastic processes in Physics and Astronomy, reprinted in Wax, N. ed., Selected papers on noise and stochastic processes, Dover, New York (1954).Google Scholar
10. Montral, E. W. and Shlesinger, M. F. On the wonderful world of random walks, in Lebowitz, J. L. and Montral, E. W., eds., Nonequilibrium Phenomena II: from stochastics to hydrodynamics, Elsevier, Amsterdam (1984).Google Scholar
11. Vajda, S. Fibonacci & Lucas Numbers and the Golden Section: theory and applications, Ellis Horwood, Chichester (1989).Google Scholar