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[sitnaltax]

In the extensive discussion of the ratings of cards, one of the most important topics that comes up is: What makes one card "better" than another? Is it the probability that it will serve any function during a game? Is it the probability that it will be make a big impact on the game? Is it the degree of the impact it makes?

I propose introducing the idea of a "key card": a Kingdom card that was important to its deck. For the purposes of analysis, I'll define below a mechanical way of determining key cards. One important note is that a deck can have multiple key cards. For example, in a Duke/HT game, both Duke and Horse Traders will be key cards. (Conversely, in a BOM game, a deck may have no key cards.)

My imagined uses of this "key card" idea are: first, looking at the overall statistics, we can rank cards as a fraction of (times it appears as a key card in the winning deck) / (times it appears in the Kingdom). Therefore, we can rank cards by how often they are an important part of the winning strategy. Second, for an individual player, we can rank cards in the same way, for both wins and losses. Therefore a player can see what cards they tend to succeed and fail with.

A Kingdom card is a key card if it meets ANY of the following criteria:

1. The player voluntarily gained at least 4 of the card.
2. The player voluntarily gained at least 2 of the card, and not more copies of any other Kingdom card.
3. The player did not voluntarily gain any card of equal or greater value first.
4. The player gained the card on Turn 1 or 2.

Note that none of the rules require that the card stay in the deck--if it is trashed, passed, or returned to the supply, the gain is what counts.

Rule 4 is to ensure that cards like Courtyard, Chapel, Masquerade, and Ambassador can count as key cards in, say, a Silver/Chapel opening where the Kingdom card is typically bought second.

For the purposes of Rule 3, Peddler is a $0 card. (If Peddler is indeed an important card in a deck, Rule 1 or 2 should cover it.)

For Black Market, I propose the guideline that every card purchased using a Black Market counts as a Black Market for Rules 1 and 2.

To test whether these rules are good, I examined a few of my recent games. I have called out the key cards in the winner's deck and, to differentiate this from the naive method of simply examining what was gained, cards that were gained but not key cards. I have chosen my most recent games as of today, leaving out only ones that were resigned.

http://councilroom.com/game?game_id=game-20120729-203828-ca73603f.html
Baron and Fool's Gold. Not Herbalist.

http://councilroom.com/game?game_id=game-20120729-142344-41d900e7.html
Cartographer only. My opponent brain farted his Golden Deck; if he had not, he would have won and it would have been Lookout and Bishop.

http://councilroom.com/game?game_id=game-20120729-140110-cb33ac4b.html
Bridge, Festival, Embargo, Vineyard. Not Noble Brigand. Embargo looks a little off here, but they kept my opponent's Pirate Ships in check, provided cash, and provided a cheap pile to destroy. Vineyard was not a big deal, but if my opponent had gone for Provinces, it might have become one.

http://councilroom.com/game?game_id=game-20120729-134926-023a437f.html
Jack of all Trades, Laboratory, Bank; not Nobles

http://councilroom.com/game?game_id=game-20120729-134313-c9ca1c6c.html
Smithy and Farmlands; not Grand Market or Explorer. I absolutely agree that Farmlands was critical here; note the 1-point victory margin.

http://councilroom.com/game?game_id=game-20120729-133711-5ffec986.html
Remake, Mountebank, and Worker's Village; not Market, Scheme, Steward, Cellar, or Militia. The omission of Scheme is my biggest concern, but otherwise I agree.

http://councilroom.com/game?game_id=game-20120729-132325-d64af0f0.html
Jack of All Trades only, unsurprisingly; not Haggler, Forge, Tunnel.

http://councilroom.com/game?game_id=game-20120729-131709-748d6103.html
Gardens, Oasis, Minion; not Apprentice, Lighthouse. Gardens is a weird choice here because my opponent meant to buy Island instead, and I still lost horribly. Minion and Oasis, definitely.

http://councilroom.com/game?game_id=game-20120729-070702-62f6fb83.html
Fool's Gold, Festival. The 5/2 split was good to me.

http://councilroom.com/game?game_id=game-20120729-070206-f5cfe296.html
Trading Post, Hamlet, Goons, Crossroads, Mining Village. Not Swindler, Trade Route, Royal Seal. The rules work well here, with the possible exception of Crossroads, which I attacked to end the game.

[chwhite]

A Kingdom card is a key card if it meets ANY of the following criteria:

1. The player voluntarily gained at least 4 of the card.
2. The player voluntarily gained at least 2 of the card, and not more copies of any other Kingdom card.
3. The player did not voluntarily gain any card of equal or greater value first.
4. The player gained the card on Turn 1 or 2.

I like the idea of trying to figure out what cards are "key cards", but I don't think you can really just figure it out with hard and fast rules.  For example, a Goons engine deck will very often drain the Pearl Diver stack, but unless you're getting all your +Actions from Kinged Pearl Divers it's probably not a "key card".  Of course, if your Actions do come from Throning and Kinging Pearl Divers then maybe it is key!

[werothegreat]

I can object to this just with the First Game kingdom.

I always open Miltia or Mine, depending on the split.  If I get 5/2, I'll get Militia on my 3rd or 4th turn.  Sometime later, I will pick up a Remodel.  According to your rules, Remodel is not a key card.  However, Remodel is what gets rid of those pesky Estates, and turns your Mined Golds into Provinces later on.  Remodel really is a key card in my deck for that setup.

[sitnaltax]

A Kingdom card is a key card if it meets ANY of the following criteria:

1. The player voluntarily gained at least 4 of the card.
2. The player voluntarily gained at least 2 of the card, and not more copies of any other Kingdom card.
3. The player did not voluntarily gain any card of equal or greater value first.
4. The player gained the card on Turn 1 or 2.

I like the idea of trying to figure out what cards are "key cards", but I don't think you can really just figure it out with hard and fast rules.  For example, a Goons engine deck will very often drain the Pearl Diver stack, but unless you're getting all your +Actions from Kinged Pearl Divers it's probably not a "key card".  Of course, if your Actions do come from Throning and Kinging Pearl Divers then maybe it is key!

Of course I don't think you always can. Also, I'm sure the rules can and should be refined. For instance, you could stipulate that non-VP cards gained during the last shuffle--that aren't IGG or Noble Brigand--don't count. In particular, this would mean that a worthless pile you drive away with say Throned Bridges won't usually count. The cost is extra complexity, which I didn't particularly want to inflict on everyone--especially since there will always be more details to consider, and considering a few just invites everyone to look harder for the ones I missed, which isn't the point.

But a mechanical way to look at a card over many, many games--including most, which aren't quirky--is exactly what I'm hoping for. If there is a quirk where Pearl Diver gets rated a smidge too highly because it tends to get bought out in Goons games, that's a quirk that can be looked at.

[sitnaltax]

I can object to this just with the First Game kingdom.

I always open Miltia or Mine, depending on the split.  If I get 5/2, I'll get Militia on my 3rd or 4th turn.  Sometime later, I will pick up a Remodel.  According to your rules, Remodel is not a key card.  However, Remodel is what gets rid of those pesky Estates, and turns your Mined Golds into Provinces later on.  Remodel really is a key card in my deck for that setup.

Would you really play the board very differently with Remodel absent?

Geronimoo's engine featured on the front page of ds.com uses Remodel aggressively to pick up its engine pieces and Remodel really should be featured as a key card of that deck. However, if you're picking it up later... it's definitely a good card in the deck, but I don't think it's key. Your game isn't that dramatically different than if you had to buy another Militia instead. I'm more concerned with the fact that Remodel doesn't get marked as key in Geronimoo's engine if it opens 5/2 Market/Cellar. I considered proposing the rule to be "you gain it on the first turn where you gain any card of that cost," but I thought that let in too many questionable 4s.

[werothegreat]

We keep trying to make specific formalisms for all these different parameters we find.  Remember when we tried to define "cantrip"?  Most of these concepts we're all able to understand, but trying to pin them down, almost into "if/then" clauses of a computer program, just makes it all confusing.

[Geronimoo]

The beauty of Dominion is that every card can have its moments. Like Phil Stone and Herbalist are awful but combined can dominate the board. So it's pretty pointless to actually rank the cards out of context. Of course, it's only human to want to rank the cards anyway because a n00b will ask a pro if Market is better than Highway and it'd be annoying to hear "it all depends, man".

Here's how I'd see the utopian ranking system (it's not practical...):

See how much win rate the optimal strategy loses on average to the big money baseline if the card we want to rank is removed (considering all possible random boards)

So we'd get this ranking:

-Cards that cause massive fluctuations on a big % of boards (Mountebank/Goons will dominate almost all boards)
then
-Cards that cause small fluctuations on a big % of boards (Cellar because most decks will want one, but they're not super important)
then
-cards that cause massive fluctuations on a small % of boards (Workshop on a board with Gardens/Silk Road)
then
-cards that cause small fluctuations on a small % of boards (Thief on boards with really nothing going on)

[Markov Chain]

A Kingdom card is a key card if it meets ANY of the following criteria:

1. The player voluntarily gained at least 4 of the card.
2. The player voluntarily gained at least 2 of the card, and not more copies of any other Kingdom card.
3. The player did not voluntarily gain any card of equal or greater value first.
4. The player gained the card on Turn 1 or 2.

Criterion 4 probably makes too many cards key.  In a 5/2 start, you may buy a harmless Pawn or Pearl Diver with the 2, but you probably won't develop your strategy around it.  I do agree that a 5/2 with Chapel certainly makes the Chapel key.