"After a few turns it seems that you've reached a dead-end..."
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You turned left.
Welcome to another E.B.O.N.Y. special -- a room that doesn't make any kind of sense.
There's a table with cards on it, why not take a closer look? Seems to be a game going on. If you're able to make sense of it, perhaps you'll find a way out of this place.
What game is it? Maybe you can find an egg page that will lead you closer to the solution. What do these cards mean in the game? A rose by any another name is just as sweet... but only one name can open up a way for you to leave.
Hint 1
Hint 2
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Spoiler: As you can't take the front door, take the opposite