Answer to November Question – Daily Lottery

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.

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