Brainteaser 1785: Back to front

From The Sunday Times, 1st December 1996 [link]

 

Given a row of eleven playing cards:

[J] [10] [9] [8] [7] [6] [5] [4] [3] [2] [1]

I wish to reverse the order to give:

[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [J]

To do this we are allowed at any stage to make a “move” of the following type:

remove any section of adjacent cards from the pack and move them elsewhere.

For example, one possible move from the starting position would be to take:

[9] [8] [7]

and move it to the right to give:

[J] [10] [6] [5] [9] [8] [7] [4] [3] [2] [1]

What is the minimum number of moves required to reverse them?

This puzzle was included in the book Brainteasers (2002, edited by Victor Bryant). The puzzle text above is taken from the book and differs slightly from the original puzzle.

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