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In the United States, state-run lotteries have raised some $502 billion for state governments. This seems like a lot, but when you put it in the context of actual state government spending and revenue, it’s just a drop in the bucket. Moreover, it comes with a lot of unintended side effects, including gambling addiction and the exacerbation of inequality.

Lotteries were initially designed to provide government with revenue without especially onerous taxes on the working class. In fact, a few cities, such as Montreal, even offered a lottery as a voluntary tax for residents. For a $2 “donation” you would get the chance to answer four questions about Montreal in order to win a prize of silver bars.

But lottery commissions have moved away from that message, and now rely on two messages primarily. One is to emphasize that playing the lottery is fun, which obscures its regressivity, and the other is that winning is a matter of luck. These two messages are linked because of a fundamental misconception about how lottery odds work.

A lot of people don’t understand that there are actually two sets of odds involved in a lottery, and they differ by how much money is being invested. These differences are crucial for understanding how the odds of winning vary between lottery games. In this article, we explain how to determine these odds and how to use them to make better bets.