Installing Copied games/Games not loading!?

Hello
I just wanted to know peoples thoughts and opinions about something thats driving me mad at the moment

I have downloaded 2 versions of Assassins Creed 3:


And so Far Ive used 6 DVDs. (Verbatim)

Each time I try the game either to play or install. I get disc errors. from BOTH versions.... Ive just played a version then for 10mins without installing the game. I then go to install the game and straight away it says disc cannot be read, straight after I click on install again... and it starts (its installing as im writing this 43% so far)

However the other 5 DVDs didnt get to 43% and the other wouldnt even load from the disc. So I was thinking bad batch of DVDs? Ive got 3 different batches, but all the same make of Verbatim.

So far ive been trying different combinations

Verified version + DVD from batch 1
Verified version + DVD from batch 2
Unverified Version + DVD from batch 3

etc... you get the pick
I just thought that if a game installs to the hard drive 100%, then the game will load all of the time?? 100%

is the above theory correct? or does anybody else get the same problems as im having? I just thought if the games installed to the hard drive then it should play all the time with no errors.

If a game wont install to the hard drive and gave errors... yet the game loaded off the disc... would it be safe to say that when playing that game it would eventually give you "cant read disc" errors at some point?
All games that Ive installed 100% play fine all the time. So I use the basis that if a game does NOT install to the hard drive then there must be an error. Am I right?

Sorry for the long post. But I am getting totally fried here lol
Thanks for your time



EDIT: The game installed 100% however it gave errors the first time I tried to install it as I mentioned. But now the game is on the hard drive will it be all okay? or could it at any point still give cannot read disc errors?