I would suspect that you probably have better than average observation of patterns and trends. I'd wager that some do have a brain that readily picks up on patterns and then extrapolates them, giving rise to an idea of having a "6th sense."
First scenario: this one probably isn't so much observation of trends as it is luck. I'd be more inclined to be "wow!" if you predicted one of the other kids in the class. We have a tendency to pick ourselves (either first or last), so that's what I suspect is going on there. Luck plus your brain either being excited (I KNOW IT!) or fatalistic (It'll be me....-.-)
Second scenario: I'd need to hear more about the situation.
Third scenario: you seem to be a pretty avid gamer, so I suspect that your brain has probably picked up on the randomizing programs that may be in the game. Even if you hadn't been to that level before, there are only a certain number of combinations that occur, and if you have played enough, you most likely will pick up on where things "should" be according to the program. I know that when I've had some gaming marathons, that's kinda happened to me.
So, in short: yes and no. Yes, I'd suspect that your observation and pattern-sensing skills are better than average, but I'm not going to mark it down to something supernatural like esp. :]
"Suppose we have only dreamed, or made up, all of those things—trees
himself. Suppose we have. Then all I can say is that, in that case, the made-up things seem a good deal more important than the real ones[." - Puddleglum, The Silver Chair
"I have had to believe a great deal in God because I have lost my belief in men." -Elias, Noli Me Tangere
"The price of freedom is learning to coexist with that which you hate." -- My
cousin.*rapes* I love you, Izzy.