## CJam, <s>23</s> 21 bytes

    q~({(\a@+1$ff-m<(}h*!

[Run all test cases.][1]

If the assignment of truthy and falsy was the opposite I could save 3 bytes:

    q~{((\a@+1$ff-m<}h

### Explanation

>! Putting the cards face up under another pile is a red herring. We might as well remove them from the game and keep playing until the current pile is empty. So that's what I'm doing: the code simply plays the game until the current pile is empty and then checks if any cards are left.

    q~    e# Read and evaluate input.
    (     e# Pull off the first (current) pile.
    {     e# While the current pile is non-empty...
      (\  e#   Pull off the top card and swap with the remaining pile.
      a   e#   Wrap the pile in an array.
      @+  e#   Prepend it to the list of piles
      1$  e#   Copy the drawn card.
      ff- e#   Subtract it from all all remaining cards.
      m<  e#   Rotate the stack to the left by the drawn card
      (   e#   Pull off the top pile as the new current pile.
    }h
    *     e# The top pile is empty. Joining the other piles with it, flattens them.
    !     e# Logical not, turns an empty array into 1 and a non-empty array into 0.

 [1]: http://cjam.tryitonline.net/#code=cU4veycsLTpROwoKUX4oeyhcYUArMSRmZi1tPCh9aCohCgpdb30v&input=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