Dominion: Prosperity
Mint is a card with two very different abilities that synergize well with each other.
First, Mint’s “trash-all-Treasures” ability is a considerable asset in the early game when you need to get rid of your Coppers (or Loan). It’s less useful if you have good trashing through Chapel or Steward, but without other options (and especially with good card draw) it can considerably streamline your deck. (Keep in mind that you can selectively play Treasures; if you draw a Gold and 7 Coppers, you can play only the Coppers and use the Mint buy to trash all 7 of them. Indeed, with 4 Coppers and a Silver, it’s usually worth trashing the Silver to trash the 4 Coppers with it.) But buying a second (or third) Mint for the trashing is usually not that helpful; there are better terminal Actions, and unless you can Remodel/Salvage/Expand the extra Mints, it’ll probably end up getting wasted.
Occasionally, with a $5/$2, you’ll see people open with Mint to trash 5 Coppers. Personally, I don’t think it’s a great idea; you’re really set back by the loss of all those Coppers, and unless you have a $2 like Lighthouse, Embargo, or Pawn, it’ll be tough to get to and Mint Silvers quickly enough. It’s a viable option if there are no other $5’s, but probably not otherwise.
Of course, if you gain Mint (through Expand, Remodel, Smugglers, etc.), this ability doesn’t trigger. This is useful if good trashing has already thinned your deck into high quality Treasures.
Mint’s minting ability is more straightforward. It tends to avalanche; the more Golds you Mint, the more likely you are to draw Gold with Mint. Try to avoid using it on Silvers unless you have no other choice; bloating your deck with Silvers nullifies the whole point of Mint, which is essentially to run Big Money on steroids. Naturally, Mint works really well with Platinum; it also does well with other cards that benefit from high-quality Treasure decks (Adventurer, Venture, Grand Market) or lead to high-quality Treasure decks (Mine, Hoard). In the late game, when you can’t really count on the reshuffle, Mint is usually too slow (exception: Harem and Watchtower); look to Salvage or Remodel it instead.
Works with:
- Platinum games
- Harem
- Hoard
- In the absence of other trashing, can be a good way to get rid of Coppers
- High-quality Treasure decks (e.g., Mine/Adventurer/Venture)
- Treasure Map (trashing to activate them, Minting for additional Golds)
- Watchtower (which turns Mint into something like a Mine)
- Grand Market
- Loan/Talisman/possibly Quarry, if you have no need for them past early game
Conflicts with:
- Low-quality Treasure decks
- Very big decks that take a while to reshuffle
- Coppersmith, Counting House (although theoretically you could use Counting House to trash dozens of Coppers at once …)
Dominion Strategy 
As a general rule, I don’t buy a Mint until I have at least one Gold in my deck, or can be certain that I’ll have one before my next reshuffle.
I’d say Mint synergizes well cards that enable you to reliably get most of the Copper in your hand at once for buying Mint, such as Laboratory, SmithyDuJour/VillageDuJour, etc.
Mint also likes to work with early +coins like woodcutter, swindler, embargo, etc, to get you to the point where you can afford the mint without trashing your early treasure buys or getting a lucky 5 copper hand, when card draw is less available
I thought about mentioning that, but to be honest I like the trashing ability so much I’d rather pass up a couple turns if it means I can trash all my Coppers at once, rather than trashing just 2 or 3.
Of course, if you draw your Swindler and 4 Coppers, the Steward’s +$2 would be quite amazing for getting the Mint.
I tried opening Mint/Secret Chamber once. It seemed like it should have worked really well, since every hand with Secret Chamber guaranteed me $4->Silver, but I lost handily. Either I got bad draws, or it’s just too slow.
I think this graph actually tells a pretty nice story with regards to mint.
http://councilroom.com/win_weighted_accum_turn.html?cards=Mint
You really want to pick it up after the first or second shuffle, where you can still shatter a lot of Copper with it, but after you have picked up a Silver or even Gold to help boot strap it.
I may be mistaken, but I don’t think the graph shows that hoff’s strategy was a bad one. In most games an early Mint (in the first two turns on a 5/2 split) is a huge mistake – I know from experience. But there are a few $2 cards that make the strategy plausible: Lighthouse, Embargo, and Pawn. As far as I can tell, the Councilroom graph doesn’t break its results down based on the other cards that are available. Even if the Mint + LH/E/P is the best strategy ever, on average we would still expect buying a Mint in the first two turns to lead to losses – simply because there are so many more situations where it is a losing strategy than where it is a winning strategy.
I’ve won with a first shuffle Mint. You have to make sure the $2 card is something that can buy you silvers.
Mint/Pawn: http://councilroom.com/game?game_id=game-20101205-200607-965531a6.html
Mint/Secret Chamber: http://councilroom.com/game?game_id=game-20110127-082250-a4fcb2b5.html
Of course if there was a salvager/remodel out there then your method probably would’ve won, without a good trashing source those estates can just be too annoying to grab the mint
An early Tactician is also a good setup for the Mint. Tactician helps you get early Gold, then it can be used to draw out all your Coppers to trash in buying the Mint. Then you just Mint Gold until you have a bundle of them, and away you go.
I think that Horn of Plenty eats some of the userbase of Mint. You can use Horn of Plenty to gain more Horns of Plenty when yo have a sufficient variety of cards in hand, and you can use Mint to gain a Horn of Plenty if you already have a Horn of Plenty and an action to spare. While gaining $5 cards with the Horn can be done on a regular basis, gaining $6 and more expensive and more is harder. So I’d say Mint is not too interesting when pursuing a Horn strategy, but has its upsides when Platinum is in play.
Mint/Fool’s Gold: incredible opener.
This is a case where trashing 5 Coppers right off the bat is not crippling. The 2 Coppers you have left are enough to buy another Fool’s Gold and Fool’s Gold itself is worth $1 to make it just that much easier. The early deck thinning from Mint means you can likely have a turn or two in which you both buy AND mint a Fool’s Gold. Have +Buys? The second Fool’s Gold you play buys you two more Fool’s Gold (ON TOP of minting one if you’ve got the actions to pull it off). Combine with your favorite drawing engine and +Buys and it seems like a clear winner.
CouncilRoom stats would seem to agree: http://councilroom.com/openings