Can I play Minecraft on a USB flash drive?
Where can I download minecraft from that will enable me to put it on a USB and load it from anywhere?
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Minecraft.net is the only site you can use to download the Minecraft game, so you will need a personal computer and an internet connection. However, after you download it, you can copy the game to an external drive, and play it from there. Sort of.
Note: the following is for a Windows machine.
If you want to transfer your saved data:
Once open texture pack folder' to open up a folder in your system. Go up a few directory levels until you get to %APPDATA%. You should see a folder called .minecraft (it may be hidden). That folder contains all of your previously saved Minecraft game data (worlds, version files, etc). Copy this folder to your USB stick.
Unfortunately, Minecraft will still try to look for the data in the same place on any computer you play it on, so you'll have to copy this folder to the same place on the new computer, and then copy it back to your stick when you're done if you want to be able to save your progress.
If you don't care about saved data
You can also get the client to create this directory like it did when you first installed it, when you run it on a new machine. When you run the client on a new computer, it should download, and store the files you need to play. If it doesn't, on the game's splash screen click 'options', and then check 'force update'. This will cause the game to update itself when you log in, and it will create the new directory in your %APPDATA% with all of the files Minecraft needs to run.
Either way, Minecraft is going to need to make, or use files buried in your system's %APPDATA% directory, so if you don't want to leave any game files on a computer, you'll have to go in and delete them when you're done. You cannot save, load, and play Minecraft entirely from an external USB stick.