#15, which is not a Sequence, by Gobleteer

All values in "Logics". ;)

Rankings:

TheExalabur 5 Logics
AngryGrasshopper 5 Logics
Gobleteer 0 Logics, Current Puzzler

Puzzle # 5, Open
There is a game called "Fill". On each turn, a player fills in any 1, 2, or 3 of 15 bubbles. There can be no ties. Which player wins in a perfect game, and why?
If I can't understand you, you're wrong; remember I'm in high school. :P

Puzzle #4
1, 1, 2, 3, 5, 8, 13, 21, 34
+5 Logic AngryGrasshopper.

Puzzle #3(Gobleteer), Closed
1, 1, 1, 3, 5, 9, 17, 31
Come ON. Someone needs to answer one of these sequences. I know someone can figure them out.
+5 Logic Exalabur, 0 Logic AngryGrasshopper.

Puzzle #2(Gobleteer), Open
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 8, 8, 23, 49, 72, 163, 315, 550
This sequence starts at the 3. Hope you read the hint I hadd up, as I've deleted the illegal version!

Puzzle #1(Gobleteer) , Open
4, 3, 3, 2, 1, 3, 1, 2, 1, 2, 1, 1, 1, 1, 1
Please post any answers that would work minus the first number as well. As a hint, I'm continuing roughly the same vein as AG at first.
As a hint, another sequence.
1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0