Ask Notch (the developer of Minecraft) anything
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I tried the single player and don't see what the fuss is about, perhaps I'm missing something?
I compare the feeling of playing this to that old DOS game "The Incredible Machine", but mixed in with some mining/resource-collection, crafting/construction, and the all-too-popular-lately retro 8-bit graphics.
See http://en.wikipedia.org/wiki/Open_world
Also http://en.wikipedia.org/wiki/System_Shock_2 http://en.wikipedia.org/wiki/SimCity_4 http://en.wikipedia.org/wiki/Dwarf_Fortress http://en.wikipedia.org/wiki/Little_big_planet
Also http://www.youtube.com/user/davidr64yt#p/c/E005D335B57338D1 - A play through of the game from a first time users perspective
http://www.youtube.com/watch?v=DS3s4iVijpA - Minecraft Calculator
http://www.youtube.com/watch?v=f6JqoE7MZEE - Minecraft 16bit adder using sand.
For me, the game is genius because it enables me to make it what I want: I'm the kind of guy that starts building a house, and then wants to make it bigger. And then wants better stuff. And then needs to explore. The 'do anything, no goal' side of it means I'm truly free to make my own goals.
Notch has said that eventually there will be a way to 'win', though. It _is_ still in alpha, after all...
Of course, that's also the part that makes it hard to put down: you'll start off just adding a few torches for visibility and end up building a lighthouse or similar.
Myself, I'm enjoying the multi-player with friends. We just dig, explore and build, which has been a hoot. Though we're kind of itching to actually fend off monsters from our complex, once that gets implemented.
Here's why it's so engaging: it successfully combines the ideas of LEGO, zombies, swords, model trains, spelunking, and electric circuits. It's like a 6 year old boy's idea of paradise. (I'm considerably older than that, but still interested in all of those things.)
It does take a little while to get started and get a stable base of operations up and running, but once you have one, you can do some really cool stuff.