Nerd Alert: the word リベンジ、pronounced rebenji, is a katakana word. Katakana words are words that are borrowed from foreign languages. In this instance it is derived from the English word for revenge. Usually the pronunciation and meaning are similar to the original word, but occasionally they slightly differ.
Revenge is a word I've been using a lot lately. But it doesn't quite mean what you're probably thinking.
In Japanese, this word is used to mean to try something over again. There's no nuance of malice. Rather, it's a determination to overcome a previous failure.
Most recently I used this word in the context of meeting my friend at a “flower park”. This place is about an hour away from where I live, but I really wanted to go, so I invited my language exchange partner to go with me. We agreed to meet in front of the building since I was going by train and she was going by bus. Miraculously we arrived at the same time. Just in time for us to both have the same disappointed look on our faces as we saw a sign saying it was closed. I couldn’t believe it! I didn’t check the hours of operation ahead of time, and I felt so bad because I was the one who made the plans. Instead we went to a nearby cafe and talked about our next meeting, to which she said, リベンジしよう！Let's get revenge!
Thus we went a couple of weeks later and had a grand time taking tons of pictures and celebrating her birthday.
So whether it's making plans to go back to a place that was unexpectedly closed, deciding to make a new attempt at a failed house project, or generally taking another stab at any faux pas (which, let's face it, I make a ton of), I have used this word a lot.
Those times may be しょうがない (can't be helped/that's just the way it is), but Japanese people seem to be such a determined group that they also have phrases like 頑張って(do your best) and ファイト(fight) that they very commonly say to one another. So rather than getting bogged down and wanting to quit, they have a fighting spirit. And I have to admit, saying, “I'll try again next time” will never get me as fired up as saying “I'm going to get revenge!”