Assuming I was lucky enough to mine the exact same address, could I get the privkey?
Yes, if you got the exact same address, then you would have one of the 7.9 X 10
28 (on average) working private keys for that address.
wait im not quite sure i understand, are you saying that every bitcoin address has more than 1 private key associated with it? I've always thought it was 1private key that links to 1 address
That is correct. There are 2
256 private keys with 2
256 public keys. The public key is hashed with ripemd160(sha256(pubkey)). Ripemd160 is limited to 2
160 possible solutions thus[1] there are 2
160 possible addresses with 2
256 private keys or 2
256/2
160 = 2
96 private keys per address. 2
96 ~7.9*10
28[1] under some minor assumptions like even distribution
Basically you have a better chance of winning the lottery AND being hit by lightning than guessing the correct private key for a given address. As pointed about in a prior post, the math can change drastically if a faulty RNG was used.