### The Math of Bedroom Compatibility

On OKCupid, one of the match questions is the following:

“Once you are intimate, how often would you and your significant other have sex?

– Every day

– About every other day

– Once or twice a week

– A few times a month or less”

On OKCupid, you choose your own answer and then pick what answer you’d like potential matches to answer. It seems straight-forward – if the other person picks the same answer as you, it’ll be fine. But will it?

Let’s make the following assumptions.

- A person is either in the mood to have sex on a given day, or they are not.
- Two people only have sex if both are in the mood.
- If someone is in the mood and has sex, they are happy. If they are not in the mood and don’t have sex, they are happy.
- If someone is in the mood and does not have sex, then they are unhappy.

If both people choose “Every Day,” then it will be fine; both people will be happy every day.

If both people choose “Every other day,” let’s assume they are in the mood 4/7 days of the week. So on a given day, there is a 4/7 chance of being in the mood.

It follows, then, that on any given day the chance of both people being in the mood is 16/49, or ~32.65%. And so the probability of having sex 4/7 a week is 7C4*(0.3265)^4 * (0.6735)^3 = 12.15%.

So that’s an 88% chance of not being satisfied in a given week. Well, that didn’t work out.

(Of course, the assumptions aren’t perfect – mostly because being in the mood might carry over if the itch wasn’t scratched.)