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The term RNG means Random Number Generator..... You will hear the phrase 'This RNG hates me!' a lot on world chat. This basically refers to the chances of getting the hardest mobs (to beat) when subjugating a dungeon that has randomized waves of encounters.
Many times you can get just plain lucky as well.... and you'll sail through a dungeon and onto the next [player] level because the RNG gods have smiled upon you and your good fortune means you've gotten the easiest waves possible or your Himes worked the way they're supposed to (in a perfect world.)
It can also refer to the chances to get an item to 'drop' or that desired Hime to be summoned from tickets.