A Method for Winning at Lotteries
31 Pages Posted: 15 Jul 2017 Last revised: 2 Dec 2021
Date Written: May 21, 2018
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: Suggested Citation