A Method for Winning at Lotteries

22 Pages Posted: 15 Jul 2017 Last revised: 24 May 2018

See all articles by Steven Moffitt

Steven Moffitt

Stuart School of Business, Illinois Institute of Technology

William T. Ziemba

University of British Columbia (UBC) - Sauder School of Business

Date Written: May 21, 2018

Abstract

We report a new result on lotteries --- that a well-funded syndicate has a positive expectation risk arbitrage strategy in an equiprobable lottery with no take and no carryover pool. We prove that an optimal strategy for a syndicate in an equiprobable lottery with many uncoordinated bettors consists of betting one of each ticket (the ``trump ticket''). We show a similar result obtains for proportional ticket selection in non-equiprobable lotteries. The strategy can be adjusted to accommodate lottery taxes and carryover pools. No ``irrationality'' need be involved for the strategy to succeed (beyond the decision of the crowd to bet anything at all) --- it requires only that a large group of non-syndicate players each bet a few tickets without coordinating their choices.

Keywords: Lottery, Nash Equilibrium, Gambling, Optimal Betting Strategies, Efficiency, Parimutuel, Lotto, Trump Ticket

JEL Classification: C70, C71, C72, G14, Z23

Suggested Citation

Moffitt, Steven and Ziemba, William T., A Method for Winning at Lotteries (May 21, 2018). Available at SSRN: https://ssrn.com/abstract=2999480 or http://dx.doi.org/10.2139/ssrn.2999480

Steven Moffitt (Contact Author)

Stuart School of Business, Illinois Institute of Technology ( email )

10 West 35th Street, 18th Floor
Chicago, IL 60616
United States
630-660-0400 (Phone)

William T. Ziemba

University of British Columbia (UBC) - Sauder School of Business ( email )

2053 Main Mall
Vancouver, BC V6T 1Z2
Canada
604-261-1343 (Phone)
604-263-9572 (Fax)

HOME PAGE: http://williamtziemba.com

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