How do I unlock Chained Cards?

Chained cards are introduced at level 51. 

Each chained card has 4 bits of chain, which are removed one by one as you clear cards. 

You need a run of four cards to unchain them, then you must remove them before you turn over another 
card from the deck.

For this reason you must be very careful when removing cards that you don't take ones which will match with the chained cards unless absolutely necessary.

Here you can see the chain is almost undone. I just need ONE more card to completely unlock it. 
Then it must be removed.

I have no moves left at this point so I have a choice of waiting to see if I can get another run to re open it, 
or using my joker to continue the run so I can take K,Q,J,10,9 & then the 8. 

It's more risky to let the chain re-lock and hope for another run, but it saves the joker for later in the game.

The choice is yours, depending on how difficult the level 
is and how many cards you have left in the deck.

On levels where you have less cards it's even more important to leave cards that will give you the 4 card run to unlock the chains and remove them. 

Save your joker if possible to remove the card once it's unlocked if it doesn't follow the run.

Remember, you don't HAVE to remove cards just 
because you can!

If you leave odd cards on the table they may match up with a run later to unchain the cards, 
and even if they don't they are worth more points 
on the table at the end than if you 
take them one at a time.