Maximizing the Expected Value of a Lottery Ticket: How to Sell and When to Buy

TL;DR

This paper proposes a method to increase lottery ticket expected value by partitioning ticket space among vendors to reduce collisions, analyzing optimal jackpot ranges for positive returns.

Contribution

It introduces a novel partitioning approach to minimize collisions in distributed lottery sales, enhancing expected value without increasing jackpot size.

Findings

Partitioning ticket space reduces collision probability.

Expected value increases without raising jackpot size.

Positive returns occur for jackpots between $775.2 million and $1.67 billion.

Abstract

Unusually large prize pools in lotteries like Mega Millions and Powerball attract additional bettors, which increases the likelihood that multiple winners will have to share the pool. Thus, the expected value of a lottery ticket decreases as the probability of collisions (two or more bettors with identical winning tickets) increase. We propose a way to increase the expected value of lottery tickets by minimizing collisions, while preserving the independent generation necessary in a distributed point-of-sales environment. Our approach involves partitioning the ticket space among different vendors and pairing them off to ensure no collisions among pairs. Our analysis demonstrates that this approach increases the expected value each ticket, without increasing the size of the prize pool. We also analyze when ticket sales have maximal expected value, and show that they provide positive returns when the jackpot is between \$775.2 million and \$1.67 billion dollars.