# Should I play the lottery?

## Should I play the lottery? Evaluating the risks, rewards, guarantees and probabilities...

The most popular answer to the question, “Should I play the lottery?” is always “No” and is typically based solely on the fact that the odds against winning are astronomically high. On the other hand, the risk:reward ratio can be low too and simply taking part in a lottery can be exciting & fun.

A lot of people do play their local and national lotteries so it’s worth attempting to understand why if for no better reason than learning more about how people make buying decisions.

### Simple fun

If your focus is on money, then it also makes sense that your entertainment would be derived from activities that directly concern money (and mathematics).

A lottery play can cost a fraction of the price of a movie ticket and can provide a real (if minuscule) justification to daydream about becoming fantastically wealthy. Provided it doesn’t become an obsession, this can be psychologically beneficial.

### Someone’s got to win

Not necessarily... Within any game, unless all the possible tickets have been issued, there is no guarantee that anyone will win - jackpots can be rolled over into the next game.

### There is a chance of winning, if you play

Even though the chances of winning are small, they are still better than zero. What is always guaranteed is that if you don’t play you definitely won’t win.

### Evaluating the odds correctly

The supposedly rational decision whether or not to play the lottery is usually based the mathematical probability of winning, assuming pure randomness in ticket selection and result, and nothing more. The justification for not participating is then supported by the very low value of this number or as it compares to some equally unlikely event such as being struck by lightning.

Here are two [more realistic] rationales for making that decision:

1. Avoiding real danger: If, for example, you’re already in a gas station and it is not obvious that staying the extra few seconds required to buy a lottery ticket is more dangerous than leaving as quickly as possible, then I say go for it. However, if you’re thinking of deliberately going near a road for the sole purpose of buying a lottery ticket, forget it.
2. Better use of time: If you can spend the time otherwise used for buying lottery tickets, dreaming about winning and checking the results on something that’s more likely to make money - which is almost anything - do that instead.

### Sharing the pot

Given that the numbers are - or should be - random, it makes sense to find out which are the most popular numbers and avoid using them. This way it will be less likely that you’ll have to share your winnings with others who chose the same numbers.

### Guaranteed win

When the pot is bigger than the stake and you can buy all possible tickets then you are guaranteed to win (and it’s not illegal).

In most lotteries you simply choose a set of different numbers from a limited range and their order does not matter.

For example, you have to choose two numbers from 1-5, they cannot be the same and choosing 4 & 3 is considered to be equivalent to choosing 3 & 4. The number of combinations* is therefore 10 and is derived from 5 (choices of the first number) multiplied by 4 (for each of the remaining choices of the second number) divided by 2 (because the order does not matter).

* Here is the formula for calculating the number of combinations (“combinations” is the formal mathematical term):

$\frac{n!}{r!\text{(}n-r\text{)}!}$

where n is the number of choices for each number and r is how many numbers being chosen (must necessarily be less than n).

So, in this extremely simple example, there are 10 possible combinations and we don’t need to care about that being a 1-in-10 chance because we can buy all 10 possible tickets: If tickets cost \$1 and a total of 20 ( including our 10) have been sold, the jackpot is \$18 (20 × \$1 less 10% organizer fees), guaranteeing a profit of \$8...

... unless someone else also manages to win, in which case the pot is usually split equally and we receive \$9. A loss of \$1.

So it’s a risk and in reality, when the number of possible tickets is in the millions, the sheer practicalities of acquiring all the tickets adds a level of difficulty such that only the most ambitious syndicates can attempt it (it has been done though).

### But if it feels right!

If you wake up with the unaccountable conviction that you are going to win big you should probably play.

### Interesting point of history

In the mid 18th century, a relatively early time in the development of lotteries, the [in]famous Giacomo Casanova successfully promoted the first state lottery in France.

This is described in detail in the 2003 Nora And Edward Ryerson Lecture, “Casanova’s Lottery” - transcript available at president.uchicago.edu.

“Lottery Syndicate and the Mathematical Advantage You Don’t Want to Miss” at lotterycodex.com

“Group Invests \$5 Million To Hedge Bets in Lottery” at nytimes.com (from 1992).

Lottery odds calculator at shouldiplaythelottery.com

“5 reasons you don’t really want to win the lottery” at creditcards.com