Freewill is a wonderful thing. And the ability to do what you want and to be in control is written into the definition of games themselves. If a game was not interactive it wouldn’t be a game, it would be a film, because you would have no control aside from the pause button on how the story progresses. In a game the experience will be different each time, even if the main plot is the same, things like the timing of jumps wont be exactly the same for every different player, will they? In a film, you get to decide if you want to stop the frames rolling or make them roll backward, but in a game you get to change the frames themselves.
Freewill is a beautiful thing and there are varying degrees of it. In Minecraft, there are many different things you can do and in many different orders, it is a chaotic pile of fun, or, as I like to put it, a VERY HIGH ENTROPY GAME.
Compare this to another very popular game, Portal 2. In Portal 2 there is a solid storyline that does not change, there may be still be a lot of ways to go about doing the puzzles but each players experience of the game as a whole will be roughly similar, therefore it is a LOW ENTROPY GAME.
When it comes to asking what is better game designers will almost always err on the side of high entropy. You see games boasting about their freedom but you rarely see games boasting about how little you can do, I am here to tell you the importance of keeping things restricted sometimes.
You see, both Portal 2 and Minecraft are excellent games but one of them very clearly outmatches the other on story. Portal 2 delivers a clear and powerful narrative with characters that you really care about, Minecraft has that really weird poem at the end but apart from that not much.
Lets think about this for a second. Films, as I think we can all agree, are very good at delivering stories. They also have very little in the way of entropy, as I said, aside from rewinding pausing muting and whatnot you pretty much have to take the story as it is. In general, the lower the entropy the easier it is to deliver a good story.
Why? You may ask. Well, all stories have an element of chance in them. The character is constantly being faced with coincidences however small. Be that surviving the big battle or losing a loved one or even just happening to bump into another character at the right time. If there was not this element of luck then everyone would have those kind of stories happening to them all the time. The chance that you will join Hogwarts is obviously extremely low because otherwise it would actually happen to people, so, if you gave the player all the freedom he has in this world then the chance this string of coincidences will occur becomes smaller and smaller.
Let’s use a new example, In Portal 2 there is a small sequence where you have to carry a small metal ball called Wheatley. Once you pick him up, the game does not let you drop him until the sequence is over, Valve took away that little bit of freedom because, can you imagine what would have happened if Chell just dropped Wheatley over the edge of a rail? GlaDOS would never wake up, you would never hear Cave Johnson, perhaps you would climb out of the facility and escape into the fresh outside world, one way or another, it would be a pain in the ass to code and probably not half as fun.
However, this really only applies to story-based games, and where high entropy games really win out is the replayability. Most people only play Portal 2 once, (or in my case 2 and a half times) which amounts to 10 hours of gameplay. Anyone who likes Minecraft will probably have spent 100 or even 1000 hours placing and removing those wonderful little cubes. I am not saying don’t make a high entropy game, but don’t try to make a high entropy game with a good story, it can be done, (Skyrim is high entropy but still has quite a good narrative.) but it is difficult. Also, keep in mind that Skyrim, while having high entropy in terms of the way you level up and so on, is very fixed for each individual mission, the missions are low entropy but the game as a whole is high.
So call me a fascist if you must, but when it comes to telling tales it may be best to leave your anarchic desires behind for a much more controlled environment.