The Mathematics of Conventions, Part 3: Room Stuffing

With FanimeCon opening their hotel blocks to the masses this week, the question of "to room stuff or not to room stuff" always comes up around this time up until the actual convention. Of course, we all know why most people room stuff: splitting a hotel room eight ways seems a lot cheaper than splitting a hotel room two ways or even four ways. We also know the risks and consequences associated with room stuffing: people can get kicked out of the hotel room, and often room stuffing will be used as an excuse to raise room rates for the next convention.

But my question is this: is it mathematically reasonable and economically viable to add in that next person when you already have a full room?

For this example, we'll look at how much I spent last year. Last year, a single King-bed room at the Marriott ran for $88 a night. With taxes and fees, FanimeCon quoted me at around $400, although in the end it's always higher. So for now, we'll use the base value of $400.

If I stay alone, I pay the entire $400 for the weekend. If someone else stays with me, it's $200 for both of us for the weekend. If there are eight people in the room, it goes all the way down to $50 - a savings of 87.5% compared to when there was just one.

In fact, let's look at the split costs for this hotel room from one person to eight people - double the occupancy that the hotel allows:

# of People in Room	Cost/Person
One	$400
Two	$200
Three	$133.33
Four	$100
Five	$80
Six	$66.67
Seven	$57.14
Eight	$50

As noted before, go to from one person to eight, it will save each person 87.5% over the original price of the room. But, if you already have five people and you want to add a sixth person, then everyone is only saving an additional 16.66%. Let's look at the overall percentage savings when we add one person:

Adding One More Person	% Saved with One More Person
One -> Two	50%
Two -> Three	33.33%
Three -> Four	25%
Four -> Five	20%
Five -> Six	16.66%
Six -> Seven	14.3%
Seven -> Eight	12.5%

So you might think that adding that seventh or eight person might work out for everyone, but mathematically and economically the percentage saved by adding just that one extra person is minuscule compared to having another person staying a room that's just occupied by you.

I could go on about the moral and fire hazards room stuffing can bring up, but that's for another time.