You have a bag with 50 lengths of string inside it.

You pull out one end of one piece of string, leaving the rest of that piece in the bag. You pull out a second end of string, possibly the end of a different piece of string and possibly the other end of the piece of string you’re already holding. You tie the two ends together before dropping them back in the bag. Repeat this 50 times, until no ends remain untied.

After all the ends have been tied to some other end, what is the expected number of loops in the bag?