Stop Buying Lotteries. Here Is Why

Let’s look at the following two games:

A: you pay $6 to flip an unbiased coin, and get $8 if it lands on head. Nothing otherwise.

B: you pay $3 to flip a biased coin. With probability 0.0001 it will land on head and you get $1000. Otherwise, you get nothing.

Game B is way more attractive than Game A, for a lower entry fee and a potentially much higher reward. Let’s compare the two games’ expected reward, which is the amount of money you receive/lose in each play.

For Game A, the expected reward is 0.5*8–6=-2, which means you are expected to lose $2 in each play. For Game B, the expected reward is 0.0001*1000–3=-2.9, which means you are expected to lose $2.9 in each play. What does this expected reward mean? It means if you play a game (e.g., Game A) for a infinite number of times, you get the expected reward (in the case of Game A, $-2) in average. And this is the Law of Large Numbers.

Now we see that the more attractive Game B is worse than Game A, and this is how lotteries work. You pay a low entry fee, and may get a very high reward with an extremely low probability. In expectation, the more you play, the more you lose.

Do I buy lotteries? Yes, but at a very low frequency (less than five times a year) and with $10 or below, for fun. If you always feel the urge to buy, use the money you save from regular expenses, for example, Medium membership. In this way, you will feel the price you pay for the lottery ticket!