Unbelievably means to such an extreme degree that it is hard to credit. Unbelievably cheap, unbelievably rude, unbelievably, he won.
It works two ways: before an adjective it simply intensifies, and at the start of a sentence it comments on the whole thing. Nothing so described is actually unbelievable, and the word has been worn down to meaning very.
1adverbunbelievablyTo such an extreme degree that it is hard to credit as true.
“The flat was unbelievably cheap for such a central location.”
unbelievably is a degree.
From unbelievable + -ly.
Etymology from Wiktionary, CC BY-SA