Duchess, like Peddler before it, is a card you almost never want at full price. Since the deck-inspection feature is enjoyed by all players--none of whom had to play Duchess, except you--the card’s sole net benefit is + $2. This means that although Duchess is cheaper, it is strictly worse than every other terminal silver card. Fortune Teller, for example, also attacks your opponents. Chancellor can grant you a fortuitous reshuffle. Both of these cards are terrible. That’s not a great sign for the Duchess.
And yet, Duchess is considerably underrated, since you can gain it for free whenever you gain a Duchy. This is (usually) a great deal, and can ease the decline of a once-great deck choking on green.
Typically, you're reaching for Provinces (or Colonies) and only dip into Duchy territory when you need green at all costs, toward the end of the game. But once you do, take the Duchess. Your odds of colliding it with a better Action are much lower once you’re greening heavily. There are exceptions of course: Terminal Draw Big Money (where the Duchess is just another dead card standing between you and your Treasures), and Golem decks (where Duchess isn’t an Action you want Golem to find), among them.
Occasionally, Duchess serves as an appealing opening on a 5/2 split. $5 Actions like Laboratory, Stables, Governor, Apprentice and Hunting Party are just begging to be paired with an early source of money, and Duchess's $2 for $2 is the best bang for your buck if you find yourself opening 5/2.
But Duchess’s moment in the sun really comes in situations where Duchies are part of the plan, rather than just consolation prizes. Such decks most commonly include alt-VP cards like Duke, Gardens, Silk Road, and Vineyard.
Duchess’s synergy with Duke is fairly obvious: You get to add terminal sources of money to your deck as it takes on Duchies. A bloated Duchy-Duke deck is happy to have more sources of money thrown in, and +$2 is all you need when your target price is $5. As a plus, the deck inspection helps you a bit more than your non-mirroring opponent, since you will have more junk to discard.
Silk Road and Gardens strategies often dip into Duchies to score cheap points, boost the value of SRs, and empty a third pile. And since you can drain the Duchy and Duchess piles at the same time, the 3-pile ending--an important thing for alt-VP decks--gets even easier. That’s an important general point about Duchess, actually; any game where your strategy hinges on pile-driving--going for Duchies instead of Provinces in a no-trashing Sea Hag game, for instance--is aided by Duchess.
Duchess can even play a role in Vineyard strategies. Vineyard always loves cheap Action cards, but Duchess solves the typical late-game Vineyard “actions or points?” dilemma by providing you a way to pick up 3-points and an extra Action card without needing $7 or +buy.
Duchess even gives a boost to the oft-overlooked Transmute. It’s well known that if you want Duchies, burning off valuable Action cards with Transmute isn’t a great way to get them. But with Duchess, you can create a self-sustaining loop for it. Just Transmute Duchess into Duchy, gain Duchess, and repeat. This may not be the most game-warping strategy out there, but it’s certainly less demoralizing than transmuting Hunting Parties into Duchies.
It’s true, nobody will ever sing songs about the Duchess, or celebrate her awesomeness in articles titled “Duchess: Better Than Wharf?” or “Step Aside, Chapel, She Has Arrived.” But even on-gain, Spy-variant, Duchy-accomplices can shine from time to time.
Works With:Duchy!
Alt-VP strategies: Duke, Silk Road, Gardens, Vineyard
3-pile rushes
Transmute
Scrying Pool (sort of)
Doesn’t worth with:Decks where you never buy Duchy
Terminal draw
Venture
Edit 1: Added 5/2 opening considerations.