A Method for Winning at Lotteries

TL;DR

This paper presents a mechanical strategy for syndicates to achieve significant expected returns in lotteries by betting on specific tickets, applicable even with taxes and carryover pools, without relying on irrational behavior.

Contribution

It introduces a Nash equilibrium strategy for syndicates in lotteries, extending to non-equiprobable lotteries and accounting for taxes and carryover pools.

Findings

Syndicates can achieve 10-25% expected returns using the strategy.

Optimal strategy involves betting on a 'trump ticket' and proportional ticket selection.

Strategy works without irrationality, relying on large groups of independent bettors.

Abstract

We report a new result on lotteries --- that a well-funded syndicate has a purely mechanical strategy to achieve expected returns of 10\% to 25\% in an equiprobable lottery with no take and no carryover pool. We prove that an optimal strategy (Nash equilibrium) in a game between the syndicate and other players consists of betting one of each ticket (the "trump ticket"), and extend that result to 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 --- it requires only that a large group of non-syndicate bettors each choose a few tickets independently.