Does it Pay to Buy the Pot in the Canadian 6/49 Lotto? Implications for Lottery Design

TL;DR

This paper analyzes the Canadian 6/49 Lotto's payout structure to determine when a syndicate can profitably buy all tickets, offering insights into lottery design and strategies for maximizing expected returns.

Contribution

It provides a formula for the expected return of buying the pot and identifies conditions for profitability, informing lottery design considerations.

Findings

Buying the pot can yield positive expected returns under certain conditions.

A formula for the syndicate's expected return is derived.

Implications for lottery design are discussed.

Abstract

Despite its unusual payout structure, the Canadian 6/49 Lotto is one of the few government sponsored lotteries that has the potential for a favorable strategy we call "buying the pot." By buying the pot we mean that a syndicate buys each ticket in the lottery, ensuring that it holds a jackpot winner. We assume that the other bettors independently buy small numbers of tickets. This paper presents (1) a formula for the syndicate's expected return, (2) conditions under which buying the pot produces a significant positive expected return, and (3) the implications of these findings for lottery design.