One thing you learn from playing with children - especially the very young - is that the fun you are having together is more important than the game you are playing. This is equally apparent when you play with the very old. What good is it to win if it makes the other person not want to play with you anymore? Or if it makes the other player cry? Or get angry? Sure, you can blame it on their immaturity (or post maturity), but, still, if your goal is to play together, the game has to end with your being together
In fact, that's how you have to measure the success of the game - the more together you are at the end of the game, the better the game. This is less apparent when you play with your peers. You tend to think of the game as being the ultimate arbiter of your relationship: "Let the best man win" and all that. When, of course, neither the game, nor your relationship has anything to do with who is the best person. Both, in fact, the game and your relationship are about your being better, together. Not better than each other. Better with.
On the other hand, for the sake of the game, we have to play as if one of us, or one team of us, will prove to be better than the other. It's called "winning." To make winning seem as important and meaningful as we possibly can - again for the sake of the game - we add officials and official rules, trophies and prizes, records and world standings. It makes the game seem more real (when we know it's nowhere as real as we are), more significant (when we know we're far more significant than a game could ever be), more permanent (when we know that neither the game nor any of us can last forever).
So, again for the sake of the game, we play as if it's not just a game, as if it's in fact more real, more significant, more permanent than we are. Which is fine. And fun. Unless we're playing with people who are much younger or older than we are. Because what they have to teach, all over again, is that when it comes to games, the people who are playing are more important.
If it's not fun, change the rules, change the goals or the way you keep score or the number of pieces you get or the number of players you have on your team or where you play it or how long you play or what side you're on. Or try a different game.
Sometimes, this is a very hard lesson. Because we want to make the game as real as we can. And we forget who we're playing with or why. And we hurt each other. But as difficult as it is, it's probably the most important lesson we can learn from playing with the elderly and youngerly. It's the reason we need to be playing with them whenever we can. To be reminded what games are really all about. Because otherwise, we forget. And the games get too important. And we play too hard. And we break.