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One may cause to argue that Fun activities are solely based off psychological and physical identification with certain activities, but surely there is a deeper analysis on why we find things fun.
Furthermore, what is the relationship of personal experience to what an individual finds fun. Some argue that what we find fun is solely defined by personal experiences, but what about activities that many individuals find fun- regardless of personal experiences.
I would argue that a positive emotional experience is something that evolved for conscious organisms in order for consciousness to function in a way that supports survival and reproduction (thus, sex and eating are pleasurable experiences).
Once having this system, an organism can then find other ways to trigger it that may not lead to better survival or reproduction, but still don't compromise survival and reproduction. Often, this may be through human invention. For example, our love of sugar evolved in a world where sugar indicated health (high energy foods that help you survive). Now, we're able to produce the sugar by itself with technology; it no longer occurs only in the context of nutritional food.
Thus, humans are able to exploit their reward systems and "fun" need not pertain to healthy activities, but may have roots in the evolutionary purpose of pleasure.
I think that a person finds something fun if it is challenging (it makes you learn something new, grow, etc.), yet he/she has a talent for it so he/she is doing well at it. Isn't that fun. On the other hand if you do something and it's hard and you're just not getting it, it's not fun and you'll probably consider exploring something else.
I think that some things are fun because our brain knows that the activity can make you happy and release dopamine.
For example, say you're going to play a game that you've never seen or played before. At first you probably won't be that in interested in it. But when you start playing it, you start to like the game. Then your brain documents it as fun, So when you see that game or think of it and start playing it, you will experience fun.
The reason why your brain probably thought of it as fun is because it's a game, and games are triggers for dopamine release when you win, advance in the game, get more points, etc. This is all due to primitive behaviors relating to triggers of dopamine.
Now say you're a kid and you're playing around with your friend. I think the reason that playing around with someone makes you happy and is fun is because that particular person makes you happy. So doing things with them such games will let you have fun.