BankBank is a lovely card, but it can also be a trap for many new players. While it's true that in practice it's often better than Gold in that it needs only 2 other Treasures to give you the same $3 it's also a bit random. If you ever end up drawing your Bank dead it gives you just $1 where Gold would still have given $3. But a hand with just 1 Treasure is often a dead hand anyway so the Bank vs. Gold wouldn't have that much of a difference.
The thing with Bank is that it's often overkill on its own, it needs its biggest friend:
+BuyIf you have a hand with 5 Banks you have 1+2+3+4+5 = $15 yet you can still only buy 1 Colony or Province.
And remember that Bank only gives you more than Gold if it's the 4th or higher Treasure played. This means Bank needs hands with lots of Treasures.
So what cards can Bank look to as a partner in crime?
Wharf, Council Room and MargraveWharf is awesome and Council Room and Margrave are quite good as they give you not only the needed +Buy, but also a good draw. Drawing cards equals more Treasure cards equals higher worth Banks. Wharf is the best there is. Council Room gives you 4 cards and your opponent 1, while Margrave gives you 1 less card, but your opponent has to drop 2 cards. All in all Margrave may be slightly better because of the attack.
Using rspeer's Dominiate simulator (Geronimoo's doesn't work on my PC with Java 7) it seems Margrave wins about 60% vs. Council Room if we let the sim just buy that card on every $5. Wharf beats both, it beats Council Room with about 65% and Margrave with about 60%.
Other terminal drawers can be good, but then you have to get the +Buy from somewhere else.
You could use cantrips for your +Buy like Market and Worker's Village coupled with non-terminal drawers like Lab and Stables.
Coupling a +Buy with other terminal drawers is risky business and you need quite a bit of luck to really be able to make use of it.
Tactician may work as well.
Trash for Benefit and Cost AdvantagesBank is a $7 card. That means most Trash-for-Benefit cards get a little extra out of it over Gold.
You can Upgrade Bank into a Province or Remake two Banks into two Provinces! Or Develop it into a Province and a Gold.
You can Remodel (or Expand/Farmland) it into a Platinum or Apprentice it for 7 cards.
Salvage it and you get +$7.
When it gets Saboteured you could grab a Duchy and when it gets Swindled there are often no other $7 cards around so you get it back.
Bank is even funnier with Governor, because you could grab a Province on your opponent's turn.
And to boot it even can't be Smuggled!
With Haggler you could buy Bank and a $6 card like Goons or Grand Market.
It can't be stolen with Noble Brigand since that chooses only Silver or Gold.
When Not to Choose Bank over GoldIf your hands are going to be cluttered with terminals and you will hardly ever reach the "4th Treasure" mark, stick with Gold. This can happen very easily. If every hand has exactly one terminal (like BM-Monument), your other cards
need to be Treasures for Bank to make it worth your while over Gold and even then it's hardly more effective than Gold.
For example: A hand of Monument ($2) + 3x Copper can buy a Province with both a Gold ($3) and a Bank ($4), so there's really no difference here. Often you will see a hand of Monument + 2x Copper and in this case both Gold and Bank get you to $7 so again there's no real difference.
Using Bank instead of Gold in decks without +Buy is an effort in futility.
In strategies where your deck will green very early (Duchy-Duke), a lucky early Gold may be better than a lucky early Bank.
When Not to Choose BankThis is pretty easy: Engines that depend on action cards for their money have no business with Bank as they have no business with Treasure cards in general. A long KC-Grand Market chain doesn't want it and double Tactician decks also don't need it. Just like any Treasure can throw a wrench in money from actions based engines, so can Bank.
And obviously your classic rushes don't need Bank and you'll probably never even be able to afford it anyway.
Works with:- +Buy terminal drawers (and possibly Tactician)
- +Buy form a Market-esque card (possibly even Worker's Village) with non-terminal hand size increasers (Lab, Stables)
- Cost-based Trash for Benefit
Doesn't work with:- BM+X style decks (no real advantage over Gold)
- Rush strategies
- Engines that rely on money from actions
- No +Buy