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Should I install Xbox 360 games to my hard drive?
When I enter and see a game in the dashboard, I can press Y and see game details for it. There I can choose to install the game. What is this for? I can play the game without installing it.
Much like those in your computer, optical drives spin at varying speeds based on the data they're trying to read. It doesn't mean much, and in general should happen more on startup and loading screens. If it gets to be too loud or disruptive, you always have the option to install games to your hard drive. Note you'll still need the disc in the drive, but it will attempt to read data from the hard drive instead of the disc, making it generally faster and quieter.
I generally keep the game that I've been playing the most installed on my xbox and uninstall games I haven't played in a while to keep space free. I appreciate the faster load times and quieter operation, but it is by no means required that you install games to your hard drive.
This will allow you to install the game directly to a hard drive (if you bought one), or to an external USB device. This will load the game from that device, rather than from the DVD. It'll definitely cut down on any noise from reading the disc, and typically (but not always) results in faster loads for games. You do have to have the game disc in the drive when loading it up and playing though for security reasons.
Installing a game can avoid in-game problems that may occur from having a slightly-damaged disc, as described here. Depending on the extent of the damage, you may be able to install the game to your hard drive and then play from there, using the disc only to start the game.
If you can't install the game from your copy, then as the linked question suggests, you can try to find a friend with a working disc, use their disc to install, and use your disc to start. (If your disc is damaged to the point where it can't be used to start the game, then you still won't be able to play the game, even if you did install it to your hard drive.)
Another reason no one has mentioned: It reduces wear-and-tear on the optical drive. My wife plays a lot and has actually mechanically worn out more than one optical drive over the years.
I'm not too sure about the first part of your question but I can certainly answer the second part. You can indeed play games without installing it, if you don't install the game the game will simply run off the CD. If you do decide to install the game you will still need the CD to play the game (prevents users installing the game and then returning the game).
Installing the game has advantages: - Reduces game load times - Apparently helps prevent the "red ring of death"
