Thanks for the clearcut explaination.
So it got me thinking, Can't this kind of attack happen at the mining pool level? Let say a certain pool of miners has more than 51% of the mining power ( which usually is very likely with certain new blockchains) and they decided to carry out the attack or it just has to done by an individual miner who thinks his mining power is more than 51%?
Yes, it can be implemented by a pool of colluding miners. In fact it can be implemented by multiple colluding pools. The only problem with this is that humans are not the Borg. The more people you have involved in the conspiracy, the more likely it will be that someone diverges from the plan or becomes a rat. In order to properly implement a double spend, it must be done on the sly. To quote from Ben Franklin, "Three can keep a secret if two of them are dead." Furthermore, the gang of thieves are going to somehow have to divvy up the bounty. I'm sure someone would end up getting royally screwed over.