In order to play multiplayer, spartan OPS, or forge it is REQUIRED that I install the disc to the Hard drive? I can’t play the multiplayer right off the second disc?
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You need to install mate
That is correct, you have to install disk 2.
you need to install it then the second disk is useless
Who the -Yoink- thought that up? sO now I have to buy another harddrive? Looks like I won’t be playing online for a while. 
If you had been listening to the halo news, you would know that it takes about 8gb. They said it months before it even released.
Get a USB key.