Some sort of geometric distribution with no replacement.

Can any one help with the following problem please:

There are 237 snake in a pit, a head and a tail are chosen at random and the head made to bite the tail. If the head and tail belong to the same snake you achieve a loop if they are from differing snakes both are discarded. Repeat the process until no more snakes remain.

What is the expected number of loops?

Basically the expected number of attempts where a head and tail is picked belonging to the same snake, bearing in mind that a failure means 2 snakes are discarded!

so basically this is as far as i could get:

the probability of a loop on the nth attempt provided you have had z previous succeses (loops achieved) is= 1/(237 - 2(n-1) + z)

Thank you