(Submitted by reader Jim Preston)
I went to my first ever The Amazing Meeting this year, held at the Southpoint Hotel and Casino in Las Vegas. It was not only my first TAM, it was my first skeptical meeting of any kind. When I arrived, I went to the front desk to check in. I asked if I could have a particularly quiet room, away from the ice machine and the elevator. That was the only input that I had into which room I would get. When the desk clerk told me my room number I was amazed that the four digits were the year I was born.
So what are the odds that I’d be given a room whose number is the year I was born? According to their website, the Southpoint has 2163 rooms. So the simple odds are one out of 2163. Now, if I was someone who travelled a lot and stayed in hotels with at least 19 floors a lot, I’d say that this was bound to happen sooner or later. But I almost never stay in a large hotel. I’ve probably stayed in a 19+ floor hotel less than a dozen times in my life. So the odds that one of those times I would get my birth year room is more like 12 out of whatever the average number of rooms in those dozen hotels is, probably something in the one to two thousand range. Still rather long odds.
What I find most interesting about this is how much, even though I was a good skeptic and I knew it was just a coincidence, I found myself wanting to believe that there was some kind of significance in getting my birth year as my room number at my first ever skeptical meeting.
But maybe it was just an opportunity to apply my skepticism. But see, I said “opportunity”; I’m still phrasing it in terms of some kind of meaning.
Below are the extended notes provided by Barbara Drescher for use in Skepticality Episode 212. Take a look and leave your comments below. Also, please be sure to listen to the podcast for our own sarcastic and hilarious commentary.
The author of this story did an excellent analysis himself. Even if we only consider the question of the odds of getting a single, specific room number on this specific occasion, at one in 2163, it’s much, much greater than winning the jackpot on any of the slot machines.
But the one thing that is most important to keep in mind is that it’s post-hoc thinking to even consider these odds. What if the room number wasn’t the year of his birth, but the last four digits of his SSN or phone number? Or his street address at home? Our lives are filled with numbers that hold significance for us. The odds of getting a room number that matches some other number of significance are actually quite high–much higher than if we chose one beforehand and tried to predict the incident.
An additional thing to remember with many large hotels is, the bottom few floors often have special functions (eg. conference rooms, gym, restaurant) and fewer guest rooms as a result. So getting a room number like “103” is probably considerably less likely in many such hotels than a room number like “1957” for example. Some hotels also avoid designating a 13th floor at all, for reasons that I’m guessing are amusing to readers here.
Also, with 2163 rooms, if the probability that an person will get a room number with their birthday, then the probability they won’t is 2162 out of 2163, or 0.9995. If the hotel is full, the probability that no one will have a room with their birthday is therefore 0.9995^2163, or about 37%. We could probably even work out how many rooms need to be occupied for their to be a 50% chance that someone will be in a room that has the same number as their birthyear. Add in the extra possible numbers as suggested, and it soon becomes extremely likely
I don’t think this is a random situation. Only the rooms on the 19th floor are in contention. (The 20th floor may be included if all residents of a room are considered, but I doubt there are any 113 year olds staying on the 18th floor.)
You also have to consider the distribution of ages of the people staying. That would depend on what was going on. A person attending an AARP Convention would have a much higher probability than the people there for motorcycle racing or even attending a TAM. In fact, if the 2163 rooms correspond to 63 rooms per floor, those between 13 and 50 (+/-1) can’t get a room equal to their birth year at all.
I realize this is overkill for the seriousness of this issue, but it was fun to think about it.