In my case, the addiction comes from setting up techniques (submissions, sweeps, takedowns, anything) and actually making them work against a resisting opponent. Even better if it is against someone more experienced, like a higher belt or someone that has been training for significantly longer than me. There is also a lot of satisfaction in the act of making someone give up or submit. Of course people should be good training partners and hopefully should not have big egos, but somewhere deep inside being capable to decide to break a limb or bring about unconsciousness is a powerful feeling.
Jiu jitsu is sometimes referred to as “human chess”, which is a good enough analogy. However, anyone who trains and has played chess at least once knows that jiu jitsu is much more complex and open. In chess we have six types of pieces for each player: one king, one queen, two rooks, two bishops, two knights and eight pawns; and these pieces can move in some predetermined manner in an eight by eight grid. In jiu jitsu, a purple belt probably will be able to name twenty types of guards. Even though this same purple belt will not know how to play them all, he probably has a general passing strategy that will cover most types of guards. Therefore jiu jitus is more like a game of chess with fifty types of pieces played in a giant grid. We need to remember that chess is played in turns, but in jiu jitsu both players take their actions at the same time, in other words, jiu jitsu is more dynamical and open than chess.
This analogy with chess can be expanded upon to explain another aspect that makes it so addictive to strangle your friends: in jiu jitsu we can create our set of fifty types of pieces. This is called “having a game” or “developing a game”. I do not need to ever play spider guard to be an absolute killer in the mats. One does not need to be super flexible to play an effective game. Do you have short arms? No problem. Got long legs? Fine. The fact that we have such freedom to develop strategies, pick moves and even express ourselves through a recognizable style is mind blowing. This makes the possibility of creating techniques and variations almost endless and two completely different renditions of the same move can both be extremely effective. In a way you are creating your own style of jiu jitsu that takes into account your body type, your injuries, your strengths, your weaknesses, your preferences, and the style of jiu jitsu you have seen from other people. This process of creating a style is extremely rewarding and addictive, I believe.
Another factor that accounts for the addiction we feel towards jiu jitsu is also common to sports in general, specially combat sports. We can see sports as a means of simulating combat and expressing aggression in a non aggressive form or, at least, in a non lethal, controlled way. This type of thing is very beneficial for humans and can be explained in philosophical and psychological senses. By engaging in sports we can control stress and disposition for violence. This is one of the reasons why people who train regularly are usually calm and do not engage in fights so easily. Having a controlled environment where we can let out undesirable characteristics of human nature really makes us feel better and be better in everyday life.
There are other factors to consider, like the hormones on the brain when people exercise, but what I wrote so far is what I wanted to say.