OR Insight

, Volume 22, Issue 1, pp 31–44 | Cite as

Bitz & Pizzas: Optimal stopping strategy for a slot machine bonus game

  • Noelia Oses
Original Article


Slot machine games used to be very simple, often limited to just one spin of the reels, but have evolved to accommodate a variety of features that provide added excitement and the potential for greater wins. They also engage the players more by, quite often, requiring them to make choices. This paper presents one of these games, Bitz & Pizzas. This case study introduces a novel application of Operational Research (OR) and serves as evidence that as slot games, and their corresponding models, are becoming more sophisticated, the role of a well-trained OR professional is becoming more important and necessary in this industry. It also shows that OR practitioners are in touch with the needs of the gambling industry and understand current practices and legislation.


dynamic programming gaming optimal stopping of a finite-horizon Markov chain slot machines 


  1. Bather, J. (2000) Decision Theory: An Introduction to Dynamic Programming and Sequential Decisions. Chichester, UK: John Wiley & Sons.Google Scholar
  2. Bellman, R. (1957) Dynamic Programming. Princeton: Princeton University Press.Google Scholar
  3. Fey, M. (1994) Slot Machines: A Pictorial History of the First 100 Years of the World's Most Popular Coin-Operated Gaming Device. Reno, NV: Liberty Belle Books.Google Scholar
  4. Freeman, J.M. (1998) Gambling on HI-LO: An evaluation of alternative playing strategies. Journal of the Operational Research Society 49: 1278–1287.CrossRefGoogle Scholar
  5. Griffiths, M. (1993) Fruit machine gambling: The importance of structural characteristics. Journal of Gambling Studies 9 (2): 101–120.CrossRefGoogle Scholar
  6. Grimmet, G. and Stirzaker, D. (2001) Probability and Random Processes. Oxford: Oxford University Press.Google Scholar
  7. Nevada Gaming Control Board. (1959) Regulation 14.040 ‘Manufacturers, Distributors, Operators of Inter-Casino Linked Systems, Gaming Devices, New Games Inter-Casino Linked Systems and Associated Equipment’. Adopted 1 July 1959, and Current as of March 2006.Google Scholar
  8. Norris, J.R. (1997) Markov Chains. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  9. Oses, N. and Freeman, J. (2006) Hitting the jackpot with OR. OR Insight 19 (3): 21–30.CrossRefGoogle Scholar
  10. Ross, S.M. (1983) Introduction to Stochastic Dynamic Programming. London: Academic Press.Google Scholar
  11. White, D.J. (1969) Dynamic Programming. San Francisco: Holden-Day.Google Scholar

Copyright information

© Operational Research Society Ltd 2009

Authors and Affiliations

  • Noelia Oses
    • 1
  1. 1.NOF Consulting, Zorroaga pasealekua 23Euskal HerriaSpain

Personalised recommendations