If you chose *5) There is no difference, every day is equally as likely*, congratulations, you have good statistical sense, and are probably quite sure of your answer, but you are nonetheless wrong – just less wrong. The correct answer is 1), tomorrow.

Counterintuitive? Here’s why.

Yes, every day is equally as likely to hit the lottery. Namely, a 1% chance. So what is wrong?

Let’s look at the actual question. The question was not “what day am I most likely to win the lottery?” – it was “what day am I most likely to stop playing?”. At first glance the two questions seem to be the same, yet there is a subtle but very important difference.

Let’s say today is Sunday. Tomorrow (Monday) I have a 1% chance to win. The day after tomorrow (Tuesday) also carries a 1% chance to win. The same goes for Wednesday, and every day after that. However, while the chance I win on Tuesday is 1%, the chance that I *stop playing* on Tuesday is less than that, because *I must not have already won on Monday*. If I had gotten lucky on Monday and won, I wouldn’t even have had a chance to play on Tuesday, because I would have stopped already.

Each day after that, the chance that I *stop* on that particular day decreases accordingly, not because I’m less likely to win on that day, but because I cannot have already won any day before then. Therefore, the most likely day that I will end up stop playing is tomorrow, which carries a 1% chance. Every day after that carries a chance of less than 1%.

This is a good example of how our intuitions fail us. I stated clearly that it is not a trick question, but “*you just need to understand the question*”, and for good reason. The question asked was “what day am I most likely to *stop playing*?”, which many people immediately substituted for a much easier question, “what day am I most likely to *win*?”. There is a subtle but important difference, which is the hard-to-spot implied condition of previous losses. To stop playing on a day does not just mean you win that day, but also that you cannot have won before that day.

The last option “*There is no difference, every day is equally as likely*” is so appealing because it is a true statement. The statement just happens to be irrelevant to the question. It is a red herring to throw you off the trail. Similar to a mental sleight of hand, it’s a powerful technique, widely used by marketers, politicians, monthly question askers, and boyfriends/girlfriends.