If, like me, you didn't get the joke at first:

Both of the first two logicians wanted a beer; otherwise they would know the answer was "no". The third logician recognizes this, and therefore knows the answer.

Unless one of those wanted two beers. Or 0.5 beer. Or -1 beers. Or 1e9 beers. Or 2147483648 beers.

He didn’t know perfectly, but he knew with great enough probability to place an order. In the very small chance that someone wanted two beers, someone would speak up.

This way is logically most efficient to work and involve the least communication.

Hopefully no one asks where the bathroom is.

You’re referencing the wrong joke

Right.

why is it three logicians? wouldn't it work with just two?

I recently heard this explained () in the following way: three is the smallest number where you can set up an expectation (with the first two) and then break it. This is why three is such a common number, not just in jokes but in all sorts of story-telling.

() In a lecture by the mathematician & author Sarah Hart.

[Three is always funnier](https://en.wikipedia.org/wiki/Rule_of_three_(writing)).

Three is a magic number. https://www.youtube.com/watch?v=0rdhqAZSRDc

That sounds like my old neighbour, a professor of logic from the university of science.

I've heard tell of the place. By chance, did he have a doghouse?

Found the QA engineer:

https://news.ycombinator.com/item?id=25851770

I do love a good joke, but this one falls a bit flat.

Logically speaking, the second bar tender could have thought to himself "no I don't want any beer, but one of these two other guys may want to double fist" and so there is really no way for the third logician to answer in the affirmative.

And the human bartender passes the check to the third logician.

The third logician never finishes his beer, his friends get more free beers. The bar overflows.

How much would that exploit be worth on the open market?

It's one you keep to yourself and your friends. Otherwise, it will get fixed up.