Seven Chains in a Row

From Fallen London Wiki

Not sure what it takes to clear your New Newgate hand in between visits. If you do all Seven Chains in close succesion, it's pretty easy to end up with a full hand of bad cards (Gaoler, Bilge, Starvation in my case, without the items for any of the less damaging options) that won't go away.

You'll either have to take the Attributes hit from playing them (granted, that's par for the course with Seeking) or only play storylets for the rest of your Chains visits. Alternately, stock up on things like Whispered Hints and Favours: Criminals in between visits...