Which urinal should you choose? The maths of the men’s room

You open the door. There are five urinals. Two are taken. You have about a second and a half to decide where to stand before you become the man who stood in the doorway thinking about it.

Good news: there’s a method. It’s the one every man uses without being taught, and it’s the one our game scores you on. Here it is, written down.

The one number that matters

For every free urinal, count how far it is from the nearest man already there. Right next to someone is a distance of 1. One empty urinal between you is 2. And so on.

Then pick the urinal with the biggest number.

That’s it. That’s the whole unwritten rule. Everything else is detail.

Worked examples

🧍 is a man, [ ] is a free urinal.

Room 1. One man at the end.

[🧍][ ][ ][ ][ ]

Distances from left: –, 1, 2, 3, 4. Take the far end. Anything else is either Okay or, at the urinal right next to him, Awkward.

Room 2. Both ends taken.

[🧍][ ][ ][ ][🧍]

Distances: –, 1, 2, 1, –. The middle is the only good answer. It feels wrong, standing in the centre of the room. It isn’t. Both neighbours are two urinals away.

Room 3. Two men, unevenly spread.

[🧍][ ][ ][🧍][ ][ ][ ]

Distances: –, 1, 1, –, 1, 2, 3. The far end wins. The gap between the first two men looks tempting, but it’s right next to someone whichever side you take.

How the game scores it

In Urinal Rules Forever, every pick gets one of three grades. For an ordinary man, the Regular:

• Perfect: you chose the biggest distance available in the room.
• Okay: not the best spot, but at least one empty urinal between you and anyone else.
• Awkward: right next to someone, when you had a choice.

An empty room is a gift: every urinal is as far from everyone as it can be, so any choice is Perfect. Folklore still says to take an end, so the next man has room.

Not everyone plays by the same numbers. The Alpha doesn’t mind company: standing right next to someone is only Okay for him. The Shy needs space: anything closer than two urinals is Awkward, and if the door opens or someone is watching, even his best spot drops to Okay.

Things that change the maths

Real rooms aren’t just distances.

• Dividers. A partition between urinals makes a direct neighbour bearable. Next to someone becomes Okay instead of Awkward. Unless you’re Shy. Then nothing helps.
• What he’s doing. Stand next to the Peeker and it’s Awkward however good the gap elsewhere is. Next to the Caller, the best you can do is Okay, because you’re in his meeting. The Leaner has one hand on the wall, and the urinal under his arm is his too. Meet them all in The Regulars.
• Out of order. A blocked urinal is simply not an option. Sometimes it was the only good one.

The urinal problem

Here’s the twist. If every man always takes the spot furthest from everyone, the row can fill up sooner than it should. The xkcd blog called this the “urinal protocol vulnerability” in 2009.

Take seven urinals. In theory four men fit without anyone standing next to anyone: urinals 1, 3, 5 and 7.

Now let them arrive one by one, each being perfectly polite:

1. The first man takes an end: 1.
2. The second takes the other end: 7.
3. The third takes the middle, furthest from both: 4.

[🧍][ ][ ][🧍][ ][ ][🧍]

Now every free urinal is right next to somebody. The fourth man has no polite choice at all. Three men have filled a row built for four, and everybody did everything right.

That’s why the rules sometimes collide, and why a cubicle is always allowed. It’s also why the game gets hard: by the busiest airports, you’re not just picking the best spot, you’re living with everyone else’s.

Why we bother

Leaving a gap isn’t just manners. In a 1976 study, men with a stranger at the next urinal took noticeably longer to start. Choosing well is a small kindness to the bladder next to yours.

Read the full code in The Unwritten Rules, then try the six-room quiz on the home page. If you get Perfect every time, the full game has 54 airports waiting in Urinal Rules Forever.