How Many Lottery Tickets Should I Buy?

When lottery jackpots are at record highs, as they are this week at $1.6 billion, I’m usually asked by friends, family, and colleagues for the same advice – should I buy a lottery ticket, and if yes, how many should I buy?

Being trained in economics and a risk manager by trade, one would expect me to say that lottery tickets are a waste of time, money – or, maybe a rant on how the lottery is a regressive tax on the poor. Not this economist/risk manager. I’ve spent a good deal of time studying odds at craps, horse races, and roulette tables in Vegas and the answer lies in understanding a little bit of probability theory.

First, look at this problem in terms of the expected value of buying a lottery ticket, which is based on the probability of winning and how much you could win. The expected value of the Mega Millions drawing on Tuesday, October 23rd, is $5.53, for a $2 ticket. It’s quite rare for the expected value of a game of chance to exceed the price of entry. Economically speaking, you should play this lottery on Tuesday.

The question remains, – how many tickets?

To answer this question, think of the problem this way: how much money do I need to spend to increase my odds? If you don’t play the lottery, the chance of winning is near-zero*. Buying one $2 ticket increases your odds from near-zero to 1 in 302 million. What a deal! You can increase your odds of winning by such a colossal amount for only $2, and the expected value exceeds the price of a ticket! Here’s the trick – the second, third, tenth, hundredth ticket barely increases your odds over 1 in 302 million. You could buy enough tickets to demonstrably increase your odds, but at that point, you would have to buy so many tickets, the expected value would be below $2.

The answer: one ticket. Just buy one. One is a good balance between risk and reward.

Not coincidentally, knowing how to calculate expected value is a superpower for risk managers when trying to optimize investments and expenditures. 

(*Near zero, not zero because it’s possible you can find a winning lottery ticket on the ground, in a jacket at Goodwill, etc. It’s happened.