When Should I Start Greening?

The article below was written by Titandrake and originally posted in the Articles section of the Dominion Strategy Forums. Quality articles posted to the forums will often find their way onto the blog with permission of the author, so feel free to post your contributions there if you’re interested!

A quick side note: Dominion Strategy blog articles will now regularly publish on Sundays instead of Thursdays. If you’re the type to religiously check the blog each week, adjust your schedules accordingly.

If you’re not familiar with Dominion slang, “greening” is when you start buying VP cards for points.

You should start greening based on how quickly you can improve your deck and your buying power. The faster you can improve it, the longer you should delay buying VP. The reasoning is simple: buying VP cards slows down your deck. Part of the problem is adding a junk card. The bigger problem is that $8 spent on a Province is $8 less that could have been spent on more money or Action cards. If the Kingdom supports faster growth, you’re better off investing into your deck now and buying points later.

If you’re playing a Gardens rush, then, well, for one Gardens rushes are not as strong as we thought they were 5 years ago and a lot of Big Money baselines compete with it. But sometimes they’re the correct choice, and in these cases you start greening right away. It’s not like your deck is going to do much better than hitting $4 for Gardens.

If you’re going for Duchy-Duke, then you want to start greening a bit later, late enough that you can somewhat reliably hit $5. But still much earlier than you would in a Province game.

If you’re playing a 1 buy a turn deck, you don’t have any reason to hit more than $8 for Province (or more than $11 for Colony), so you start greening when you think your deck can usually hit $8.

If you’re playing a reasonable engine, one that draws a lot of cards but not always your entire deck, you start greening around the point where you’re hitting $13 (Province + Duchy), $16 (2 Provinces), or $18 (Province + 2 Duchies, a useful option to have in endgames). Two Provinces a turn is a sweet spot where the game ends very soon if both players decide to start greening – 8 Provinces goes away in 4 turns, or 2 turns each.

However, if you’re playing a Kingdom with a strong engine, something like Wharf + Village + trashing, you may want to build even more. $24 for triple Province, $28 for 2 Province + 2 Duchy, maybe even $32 for 4 Provinces. On these boards, it’s common for high-level play to turn into a game of chicken that eventually ends in a low-scoring 3 pile. When both players believe detouring for points will cost them the game, they both buy actions instead, bringing the game closer to a 3 pile ending.

Finally, there are Bridge boards, Bridge Troll boards, and the like, where you play for the megaturn and buy all your points on the final turn. The scoring potential of these decks grows quadratically, and there’s really no reason to pick up points unless you have to (e.g. in order to avoid a 3 pile).

Here are some toy examples. In these examples, when I say a deck hits $N, I mean it always hits $N, even as Victory cards are entering their deck. Additionally, P1 is not necessarily the player who started the game, but is the player who goes first at the time the analysis starts.

Both decks can hit $8, and it takes 2 turns to build a deck into one that hits $16

Let’s say first player goes for Provinces, and 2nd player tries to build

P1: Province
P2: build
P1: Province
P2: build
P1: Province
P2: Province + Province
P1: Province
P2: Province + Province, both players have 4 Provinces, tie at game end.

So it isn’t any worse at hitting 4 Provinces. But in a real-life version of this scenario,

  1. P2’s deck is more reliable because they buy Provinces later, and
  2. if P1 misses $8 once, P2 can punish that bad luck more severely.

If P2 gets unlucky, then well, they lose. But if they didn’t build and got unlucky, they would have lost anyways, and P2 is less likely to get unlucky if they build their deck a bit more.

If we reverse the roles, and have P1 build, then P1 wins.

P1: build
P2: Province
P1: build
P2: Province
P1: Province + Province
P2: Province
P1: Province + Duchy (P1 has 3 Prov 1 Duchy, P2 has 3 Prov)
P2: “If I buy Province, P1 wins on Province. If I buy Duchy, P1 wins on 2 Provinces.” P2 loses.

Both decks can hit $16, takes 1 turn to build deck to one that hits $24

Say P1 goes for double Provinces and P2 goes for building.

P1: Province + Province
P2: build
P1: Province + Province
P2: “If I buy 2 Provinces, P1 wins on Province + Province”. Buys Province + 3 Duchies (costs $23)
P1: Province + Province (P1 has 6 Provinces, P2 has Province + 3 Duchies)
P2: loses

In this example, P2 loses because they don’t have time against a double Province player.

If we reverse the roles, P2 still loses.

P1: build
P2: Province + Province
P1: Province + Province + Province (P1: 3 Province, P2: 2 Province)
P2: “If I double Province, P1 wins on Province + Duchy. If I don’t buy any Provinces, P1 wins anyways on triple Province.” P2 loses. (In a real game I would buy Province + Duchy and hope P1 has a dud and hits less than $16.)

In fact, P1 wins even if both players go for double Provinces.

P1: Province + Province
P2: Province + Province
P1: Province + Duchy (P1: 3 Prov + 1 Duchy, P2: 2 Province)
P2: “If I double Province, P1 wins on a single Province. If I Province + Duchy, P1 wins on double Province”. P2 loses.

In this setting, P1 wins because they have first mover advantage. But what if we can build to $24 while picking up some points along the way?

Both decks can hit $16, takes 1 turn to build deck to one that hits $24, on the building turn you can afford buying 1 Province

P1 goes for double Prov, P2 builds

P1: Province + Province
P2: builds + Province
P1: “If I double Province, then P2 ties on triple Province. Can I win if I don’t allow the tie?”.

(P1 hypothetical)
P1: Province + Duchy (P1: 3 Provinces + 1 Duchy, P2: 1 Province)
P2: “If I buy 2 Provinces, P1 can end the game.” Province + 3 Duchies (P1: 3 Provinces + Duchy, P2: 2 Provinces + 3 Duchies)
P1 “Only 3 Provinces are left, so P2 can end the game no matter what I do. I should get as many points as possible.” Province + Province
P2: Province + 3 Duchies (P1: 5 Provinces + Duchy. P2: 3 Provinces + 6 Duchies. P2 wins)

P1: “Okay, I can’t, I take the tie”. Province + Province
P2: Province + Province + Province

If we give the option of picking up a Province while building towards $24, then P2 can turn a losing situation into one where they can get a tie instead, as long as P1 goes for the double Province strategy. But, if P1 builds, then P2 will once again lose no matter what they do.

P1 builds, P2 does double Province

P1: builds + Province
P2: Province + Province
P1: Province + Province + Duchy
P2: “P1 can end the game no matter what I do and I can at most get 4 Provinces, while they have 3 Provinces + 1 Duchy”. P2 loses.

P1 builds, P2 builds

P1: builds + Province
P2: builds + Province
P1: Province + Province + Duchy (P1: 3 Provinces, 1 Duchy. P2: 1 Province)
P2: “A 6-2 Province split is not beatable. If I buy a single Province, P1 can end the game on Provinces. Therefore I should deny all the Provinces I can.” Province + Province + Province
P1: Province + 3 Duchies (P1: 4 Provinces, 4 Duchies. P2: 4 Provinces)

These toy examples are far enough from reality that I would not follow them religiously. In particular, they’re missing a model of how your deck becomes less reliable as you add VP cards to it. What they do show is how the decision of when to build and when to green isn’t just “stop at $8” or “stop at $16”. It’s dependent on the context of how quickly your deck can become better, how many VP cards are left in the pile, and how well your deck can handle Victory cards.

Even though these examples aren’t perfect, they do show off the emergent complexity of Dominion endgames. It’s quite tricky to play them correctly, and there aren’t really any shortcuts besides thinking about the possibilities and seeing what happens in each one. But that’s a subject for another article.

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