The card game, war. Have you played it? Long ago, perhaps as a small child, you played it. It's silly, right? You just flip cards out of the deck and see who has the highest card. That person takes both cards, repeat. It's not even a game, it's just an activity. Neither player can affect the results, there is no strategy, no skill, only pure luck.
Children sure do enjoy it though. How can they enjoy something they have no control over that has almost no benefit? I believe there are two forces at work here. One is a childhood thing, the other a psychological thing.
Children don't know how things work. At some point we learn a lot of common-sense things such as "you cannot change the top card of a deck just by thinking about it," but each of us has to learn that for ourselves. War can be fun for kids who haven't yet reached that conclusion. They think they can somehow be good at this activity through willpower or some imaginary skill. Does flipping the cards faster help? Does concentrating help? Does calling out a card or yelling at the deck or jumping up and down help? Even if you (as a child) know these specific things don't work you may still not have learned that there is nothing at all you can do against a shuffled deck of cards. Perhaps a ghost will help you. Eventually we all (almost all) learn that you can't win at war (the card game) and stop playing it (until we have children of our own, perhaps).
Psychology brings an exciting development to this story. Humans are inherently pattern-finders. Finding patterns is one of our huge advantages and we love to do it. By finding a pattern we become able to predict the outcome and many times this brings us a huge reward. Learn the spawning pattern of salmon? You can get a lot of fish if you come to the river on the correct days of the year. Learn the attack pattern of an enemy warrior? You can block his attack and win the fight. Yet this is also a place in which our brains can trick us. Some random systems scream out "there's a pattern here" when there is not. Attach a big enough reward to the random system and the human need to learn the pattern so it can predictably get the reward takes over. Enter the slot machine, or any other gambling environment that relies on a pure-luck event. Even if you know how it works, the reward is big enough that part of your brain says "keep watching this, we can figure it out, try again, I can almost predict it." Some study I read about but am too lazy to find the reference to postulates that too much of this subconscious brain activity is what predisposes some people to be compulsive gamblers. Even of those who don't "have a problem" there are many who play the slot machines even though it's just war, and the odds are not in your favor at all.
I'm sure this has something to do with game design.