Brainstorm quiz

Learned this quiz in class. Imagine that you have unlimited amounts of balls (to the left, right and bottom, NOT top). The goal is to get a ball as high as possible, moving them as you would in solitaire (You pick one ball, move it to an empty spot on the other side of a nearby ball, and remove that ball). In the pictures below, O is balls and O is empty space.

Example of a move:

You have:
OOOOOO

Pick the left ball, move it to the other side of the other ball:
OOOOOO

And remove the ball that you jumped over:
OOOOOO


I'll show the first steps: (red is the ball I'm going to move next time)

Pick a ball from the second row and move it upwards to reach the first level.
OOOOOOOOOO
OOOOOOOOOO
OOOOOOOOOO
OOOOOOOOOO
OOOOOOOOOO
OOOOOOOOOO
OOOOOOOOOO

Pick a ball as shown in the picture and move it to the empty location on the first row.
OOOOOOOOOO
OOOOOOOOOO
OOOOOOOOOO <-- You've reached level 1
OOOOOOOOOO
OOOOOOOOOO
OOOOOOOOOO
OOOOOOOOOO

Pick the same ball again and move it upwards to reach the second level.
OOOOOOOOOO
OOOOOOOOOO
OOOOOOOOOO
OOOOOOOOOO
OOOOOOOOOO
OOOOOOOOOO
OOOOOOOOOO


OOOOOOOOOO
OOOOOOOOOO <-- You've reached level 2
OOOOOOOOOO
OOOOOOOOOO
OOOOOOOOOO
OOOOOOOOOO
OOOOOOOOOO

And so on...

Question: How high can you get a ball using this method over and over again?
(I'll give you some time to think ;))

Isn't that like Pegged?:o

Sorry, I don't know what Pegged is... :(