[skitout]

Or they can double spend some crypto, that is generally the main goal here

[pat2man]

As far as the block chain is concerned they cannot. No single branch can have a double spend. But of course with deep reorgs they can defraud exchanges or other parties who end up on the wrong branch.

[skitout]

As far as the block chain is concerned they cannot... when they are not under attack. The attack can rewrite part of the history to double spend some crypto

[pat2man]

They cannot rewrite history. But they can create multiple histories and switch between them.