The
old article is a bit outdated, so I feel like it's time to write a new article.
What is Counting House?It's essentially a +X Cards effect. Only it draws from your discard pile instead of your deck, and it always draws Coppers. You probably already knew this, but I wanted to say it anyway, because it is easy to focus too much on the Copper part and forget about the part that actually increases your hand size.
When should you ignore Counting House?Counting House is a card that's hard to utilize. As the old article mentions, just buying one in hopes of high +coins is going to fail in most decks — CH just isn't strong enough to be a big money enabler and in engines where you draw most of your deck anyway, it's not going to be of much use. In other words, you should never go for Counting House unless there is a particular reason why Counting House works on that board.
So, when is Counting House actually useful?
Counting House as a +$This is bad in most decks, but there are some edge cases. With great support, such as Beggar or Candlestick Maker, a strategy centered around this can do well in an otherwise weak kingdom, but not if there are other decent options.
Here's how you play it with CSM, and with Beggar, it's similar, but you don't need that many Beggars.
Another edge case is when you're getting hit by Copper junking attacks, such as Mountebank, and you can't deal with the junk otherwise. In this case, you definitely want the attack, and you probably want the Counting House later.
Non-terminal +buy can be excellent here, since it lets you buy extra Coppers and later, more green cards with your big Counting House turns. Terminal +buy is a lot worse, because you can't play both that and CH on the same turn without a splitter, and lining up the splitter, the +buy and the Counting House is difficult in a deck full of Copper.
These kinds of strategies are usually resilient to most attacks for obvious reasons, but you should watch out for Pillage and sometimes Enchantress. For the same reason why you're not too worried about junking, greening early is often a good idea in these games.
It's also usable in the Hunting Party stack (well, at least if the Hunting Party stack itself is better than other strategies on the board), where it guarantees a Province turn as long as you just have at least one Silver in your deck and are able to play enough HPs to discard your deck. The downside is that you don't get any other benefits, such as the +VP from Monument etc, and it's more expensive than many other alternatives for the terminal slot, but the upside is that you don't have to buy a Gold at all.
Counting House as a +CardThis has the potential to be
extremely good. There are two ways to utilize this:
1) Taking Coppers from your discard pile, then triggering a reshuffle mid-turn. This greatly reduces the number of cards you have to draw with other cards when you're trying to draw your whole deck, so it can be useful when you're having trouble drawing your deck given the kingdom. It needs a payload that really makes it worth it, though, and it should be noted that if your engine relies on this, you can't, pardon the pun, count on being able to go off every turn, so either it needs to be a megaturn payload or you need lots and lots of time.
2) Actually taking advantage of the Coppers in your hand. The most effective thing is if you can discard the Coppers for some benefit, then draw them with Counting House, then discard them again for more benefit (repeat as many times as you have +actions available). For example, you can use Counting House with Cellar to draw cards from your deck, allowing you to build an engine with no other +card, or Secret Chamber to give you lots of coins, letting you use that as your payload. Storeroom is great here, since it does both.
Here, Copper might or might not be a good addition for your deck. If your engine is strong, you can power up your Secret Chamber-style payload by adding extra Coppers, and for the Cellar draw engine thing, you want to maintain a good balance between Coppers, Cellar variants, Counting Houses and splitters. But if your engine isn't too strong, then adding extra Coppers has the potential to make it not work. If you're using it for making the Coppers miss the mid-turn reshuffle, then Copper is obviously bad as the purpose of your CH is to get rid of the Copper anyway.
Militia makes the Cellar thing a lot more clumsy, and these kinds of engines are also more vulnerable to junking than engines usually are.
Counting House with Travelling FairThis is a thing.
In generalAny strategy with Counting House in it becomes a lot better when you gain some control over when to draw your Counting House. Therefore, cards such as Watchtower, Inn, Scheme and Haven are good in Counting House decks. Colony games are usually more favorable for CH strategies, since they benefit from longer games.
So, that's it.