The following is a guest article by Geronimoo, who analyzes the steps in designing an “engine”, using one of the most popular Kingdom boards.
You’ve finally gotten your friends together to show them the awesomeness that is Dominion. Trusting Donald X., you carefully lay out the cards according to his “First Game” recommandation in the game rules:
Cellar, Market, Militia, Mine, Moat, Remodel, Smithy, Village, Woodcutter, Workshop
You’ll probably want to show off the two main strategies for this board: Smithy Big Money and the engine centered around Village and Smithy. I’d suggest you play this board twice and start with the Smithy BM deck. You’ll probably crush because your newbie opponents will buy too many actions and have no focus. Now, an observant friend might say this game is badly designed because you only bought one action card and won by a big margin while their cool action cards didn’t really help them much. “True”, you say, “let’s try this again!”
Chances are they’ll copy your strategy from the previous game and you can show off your engine building skills. Now, unless you’re a level +20 isotropic player your engine is not going to beat the Big Money deck. Embarrassing! Your friends decide Dominion is a game dominated by a brainless, broken and boring strategy and you have to resort to the horror that is Settlers of Catan for your IRL gaming fix while those Dominion boxes collect dust in the cupboard…
So, how do you go about building a successful engine for this board that beats the Big Money Smithy deck consistently? It’s not exactly rocket science and we’ll take this step by step. So my little n00b friend, let go of your fears and read on…
Warp or Impulse drive?
The first question you have to ask yourself is what kind of engine you’re going to build? Dominion features many types of engines: see here and here for some discussion. The Village/Smithy archetype should probably aim to draw the entire deck consistently and go for double Province buying turns. Since you’ll be drawing your entire deck, you only need exactly enough treasure to buy what you need. Extra treasures should be avoided because they will only clog up your engine and prevent you from drawing the entire deck. Greening too early is a bad idea because the Provinces/Duchies will clog up the engine like the superfluous treasure, but are also completely useless until the end of the game.
I’m going to use the simulator I wrote to find a good game plan instead of showing you real (isotropic) game logs. The simulator can play most big money strategies as well as an expert human player and even some engines with careful scripting. If you prefer advice from human players, remember that even an expert can make mistakes and unless he’s a Vulcan his brain, like yours, is very bad at probability.
This phenomenon makes players way too optimistic about how an engine will run while underestimating the power of a big money approach. The variance inherent in Dominion also means one game can never be proof that a strategy is better than another because luck plays such a large role (it’s like saying you’re better than Phil Ivey because you cracked his Aces once in a tournament). It takes tens and often hundreds of real games to find the best strategy and tweaking it to optimal would probably take a lifetime. The simulator does that job in mere seconds! Using this method I will be able to “prove” that a fairly simple engine beats the big money deck consistently in this particular kingdom. (You can download all the strategies in this article here by right clicking and saving, then load them into the simulator via File->Load and select them via “Created by user”).
Let’s start with the simplest implementation of the engine for this board. We’re just going to buy Villages and Smithies. Once we reach a critical mass we’ll be drawing the entire deck and can start buying Provinces. Since you start the game with 7 Coppers, you need to buy a single Silver to reach the needed $8 (you could even buy a Copper if you open $5/$2). According to the simulator the fastest route to 4 Provinces with this engine goes like this (run the simulation yourself by selecting the “Village/Smithy engine #1” in the simulator after loading the XML-file):
Open Smithy/Silver (or Smithy/Copper), then get a Village and from then on alternate between Villages and Smithies. Buy Province each time you reach $8.
One of the most important things about this type of engine is to get the balance right between Villages and Smithies. If you buy too few Villages you’re going to get a lot of terminal collision, while too many Villages will take you longer to reach the “draw the entire deck” stage. The simulator shows that you should have at least as many Villages as Smithies at all times. This gives the best risk vs reward ratio and the same logic can be applied to most “+actions, +terminal draw” engines.
The 18.5 turns it takes this engine to get 4 Provinces is pathetic compared to the Big Money deck which does the job in 15 turns. And it doesn’t really draw itself consistently (if I let the simulator wait until it does, the number of turns goes up to 20). This deck is so slow because it’s wasting $6 buys on Village and there are a lot of bad things that can happen like the all-Smithy-no-Village hand (terminal collision)
Here’s a view of this engine vs the Big Money Smithy deck (the graph shows the AVERAGE Victory Points gained each turn over 10,000 games which explains why there are no peaks to 6VP):
The Smithy Big Money starts to buy Provinces consistently from turn 6 while it takes the engine a bit longer to set up and has much less success overall getting VP consistently.
Market: The next generation
The engine clearly needs a lot of help! We have to do something about all the wasted economy and that’s where a source of +buy comes in. If we play a Market and have $7 we can buy Village + Smithy which will allow the engine to build twice as fast compared to the version without +buy. The simulator likes the following strategy for the Village/Smithy engine with Markets (select “Village/Smithy engine #2” in the simulator):
Open Smithy/Silver, get a single Gold, then quite a few Markets (5), then focus only on Villages and Smithies (keeping the right balance in mind). Once you have about 4 Smithies your engine should be firing consistently and you can start greening (often you’ll have reached a double Province buying turn by then). Make sure not to buy more than the single Silver and Gold because extra treasure will only clog up the engine.
This strategy is still 1.5 turns slower than the big money deck. Here’s what happens if we let the simulator play this engine against the big money deck (I added a few rules for Duchy and Estate buying of course):
This graph shows how the engine builds up during the first 11 to 13 turns of the game and then explodes with a few mega turns buying Provinces. However, the BM’s early VP lead is too big to overcome and the engine gets crushed winning only 1 out of 4 games. Why is the Big Money strategy so fast and consistent? Well, getting to $8 is very easy with just a few Silvers and the occasional Smithy and/or Gold. On top of that there’s hardly any wasted economy and no dead turns because of colliding terminal actions.
Shields down? Attack!
Instead of trying to speed up the engine, we could try to slow down the Big Money deck. Slower games means attacks and luckily Donald included a decent attack for this first game in the form of Militia. Here’s the engine + attack plan laid out:
Open Militia/Silver, get a single Gold, then Markets (stop at 5), then get the Villages and Smithies (you probably want an extra Village here because Militia is a terminal action). I also added Cellar (buy only if you have $2 to spend and don’t buy more than two) which adds some crucial filtering to counter the possible terminal collision and also speeds up deck cycling so your recent buys become available more rapidly. Once you have 5 Smithies start buying Provinces. Duchies should be bought if there are about 3 Provinces left (so a bit later than the Big Money deck because they clog the engine up more than the BM) and Estates when there are about 2 left.
You want to open Militia instead of Smithy because the early attacks hurt the most, often disabling a crucial Gold buy. After a while you’ll be able to play the Militia each turn crippling the Big Money deck even more as is clearly seen in the BM Smithy graph which is a lot flatter than the previous. (select “Village/Smithy engine #3” in the simulator)
According to the simulator this engine is on par with the Big Money deck (it even has a slight advantage winning about half of the games).
The final frontier
Now we have most of the crucial elements of a successful engine in place: +actions, +draw, +buy, filtering and an attack. There’s just one thing that’s holding the engine back. Drawing itself so often means it’s always stuck with the 3 starting Estates. These hurt the engine much more than the Big Money deck which cycles far less often. The Coppers are less problematic, because they provide some economy to buy engine pieces. If only there was a way to get rid of those Estates…. The more astute reader will have figured out by now that this kingdom has the perfect card for us: Remodel. It will transform the Estates into useful engine pieces and can even be used to speed up the end game by trashing Golds into Provinces. Here’s the final engine’s game plan:
Open Remodel/Silver (or Market/Cellar). Get 2 Golds (these can be Remodeled into Provinces in the end game). Get a single Militia, then again focus on Markets (stop at 4). The Villages and Smithies can be acquired fast by Remodeling Estates and all the +buys from the Markets. Get Cellar at $2 (or Remodel a Copper). Once you have about 5 Smithies your engine is fit for greening. Duchies can wait until there are 3 Provinces left and Estates when 2 are left. If the game is very close to ending use Remodel agressively to transform cards into VP (most notably Gold into Province).
(select “Village/Smithy engine #4” in the simulator) Here’s the buying script that the simulator uses (it is evaluated from top to bottom for each buy):
- $8 or more to spend: Province (if you have 5 or more Smithies)
- $5: Duchy (if there are 3 or less Provinces left)
- $2: Estate (if there are 2 or less Provinces left)
- $6: Gold (max 2)
- $5: Market (max 5)
- $4: Remodel (1), otherwise Militia (1), otherwise Village (if you have less Villages than terminal actions), otherwise Smithy
- $3: Village
- $2: Cellar (max 2)
According to the simulator this strategy beats the big money deck almost 3 out of 4 games. The Remodel is really key to put this deck over the top even though the simulator plays the trasher rather poorly (check the “sample games” in the simulator). I expect an expert human player will be able to get at least an 80% win rate against the big money strategy. The bot can be improved with extra buy rules and conditions, but I kept it basic so you can easily copy the play pattern in a real game and be certain of a good outcome. The actual optimal strategy for this board is unlikely to ever be found, but it’s probably similar to what I came up with using the simulator.
So now you know how to play the engine decently for this board you’ll have no trouble convincing skeptical friends and people everywhere that big money is not the be-all and end-all for base Dominion. Even far from it when you add all the expansions!
(this paragraph was added later)
When this article was first published I created a challenge on the forum to give people a chance to find a better bot than what I was able to come up. I expected someone to reach the proposed 75% win rate, but michaeljb surpassed all my expectations and created a bot that gets 89% win rate vs the Smithy bot. That’s huge and knowing the simulator plays some cards suboptimally a human expert should easily win 9 out 10 games using his strategy. How did he do it? It’s complicated, but in short: use Mine to improve Treasures rather than buying Treasures, use Remodel and Workshop to pick up engine pieces, wait until you have a few Smithies to get a Militia, pick up Villages early and often, sprinkle in some Markets, and grab up to 3 Cellars. Check out the challenge on the forum if you want the full detail.
Boldly go where no man has gone before…?
I haven’t touched the case where both players are going for the engine, but that is quite a complex subject and best handled in a separate article (…and then there’s multiplayer which is probably harder than rocket science)
This article shows you an example of how to build a successful engine. This is just the tip of the engine building iceberg in Dominion, and there are plenty more to explore. If enough ingredients are available and you mix them in the right order you should be able to beat nearly all Big Money decks with them (especially in Colony games). Some of these can be simulated well, while you’ll have to figure others out for yourself or get advice on the forum from expert engine builders like Marin, chwhite or DG. And here‘s some more engine reading.
Ensign Geronimoo signing off!