Could You Game a Lottery?
Late last year, I joined this advantage gambling event out of curiosity about how the world depicted in the movie 21 operates in real life. The speaker covered various games and strategies to exploit them. The biggest surprise came when he discussed lotteries. I had always thought lotteries were only for idiots since the expected value should be negative.
Expected value (EV) is calculated as (Reward * Probability) - (Penalty * Probability). In the case of a lottery, it represents the chance of winning multiplied by the prize, minus the ticket price.
How can you have a positive expected value (EV) in lotteries? You won’t achieve this by purchasing your tickets early. However, as more tickets are sold and prizes are distributed, there may come a time when the EV becomes positive because the probability of winning might increase with enough prizes remaining.
How do you get information about the prize and probability? Apparently, lottery players scrape lottery websites to fetch this information and then calculate the EV. This repo parses scratch-off lottery ticket data from state lottery websites, for example. The EV calculation has to be more complex than this repo’s calculation when you consider things like taxes and multiple winners (you might have to split the prize), but it’s certainly doable if you are willing to put in some effort.
In practice, prize distributions may be designed in a way that you can’t beat the system, and the logistics can be challenging. But still, buying a lottery ticket may not be idiotic when you figure that the EV is positive.