Every so often, a lottery jackpot will get so high that I'll hear about it on the news or from a friend. Whenever that happens, I instinctively do two things: daydream about winning the jackpot and think about the odds. It's pretty easy to intuit that the odds of winning the jackpot are really low (understatement!), but I recently got more curious about some of the math here, specifically questions like:
- How many tickets would I have to play to win the jackpot?
- How do the odds change with more or fewer numbers to choose?
- What if we change the pool of numbers to choose from?
This tool is broken up into two sections: Setup and Simulation. The Setup section lets explore probabilities for an existing American lottery or for your own lottery with custom rules. The Simulation section lets you pick some numbers and play up to thousands of tickets per second, and visualizes the returns for you. Note that this tool makes some simplifying assumptions, like that there's only one jackpot winner and that taxes are ignored.