When I was a teenager, I used to read fortunes with a deck of tarot cards (still have it). With tarot cards, you don't necessarily just tell a future, you also tell a person their influences from the past and the present, fears and so on. When I did this to people, I was usually right on the money, often to the point where they were scared because it was so accurate. However, when I tried reading my own fortune several times in a row, I also felt that the cards were right over and over agian, more often than not. But, there was the occasional blooper.
A strong component in why they worked so well is that the interpretation of the cards are actually quite vague and people are almost eager to believe in them. For example, I might get a card like the devil and tell someone that something has come between them and another person, something which is splitting them apart. They will then take that information and mentally search for something in their lives which they can attach it to. For example, if they have a boyfriend which is going away, they'll apply it to that. If they've had a row with one of their parents, they'll apply it to that. If someone died, they'll apply it to that. For every card, it's almost always possible to find something and so people end up basically doing much of their card reading for you. You just help them down a mental path they construct themselves and then finally give them a fortune reading based on the cards, but rooted in what they've told you.
I think if people were more aware of stuff like this, how we are prone to thinking and interpreting stuff and how vulnerable we are to
suggestion, more people would be sceptics.