Let's consider such a two-piles situation:

111100

001111

is better for Ciel.

"1" means this card is picked by Ciel,while "0" by Jiro.

We know that better for Ciel means worse for Jiro.

So if

111100

001111

is better than

111000

000111

for Ciel.

Then when Ciel picked the first three cards from pile 1,Jiro can just pick the last three cards from pile 1 and finally lead to the result:

111000

000111

which is not better for Ciel.

Generally, if the final result is not balance(half from top and half from bottom) while balance is better than such result for Jiro, Jiro has the ability to adjust it to be balance.So do Ciel.

Therefore,it reaches balance.

I wander why this submission on F failed in only one test