Meaning of Damemoto(ダメ元)

Damemoto(ダメ元) is an abstraction for “Dame de motomoto(ダメで元々)” which means “Even if it doesn’t go well, it won’t change the original state, so let’s do it!”
“Dame de motomoto(ダメで元々)” is an idiom.
Dame(ダメ) means fail and motomoto(元々) means originally.

Example Conversation

A: Hikaru is transferring to another school…
B: Seriously? You like him, right?
A: Yes… Umm… Should I ask him out on a date damemoto(ダメ元)?
B: You should! Go for Broke!

A: ひかるくん、転校しちゃうんだよね…。
B: え、ひかる君のこと好きだったよね？
A: うん…。あー、もうダメ元でデート誘うべき？
B: 誘っちゃえ！当たって砕けろだよ！