Dominion Strategy

How about I kick off your working/studying/playing-dominion week with a few cool graphs and clever observations? I kind of had to after reading timchen’s request to simulate DG’s and Yaron’s game in the comments (you see, we at dominionstrategy really care for our readers…).  Let’s recap the game in question:

Yaron chose a pretty straightforward strategy of Masquerade into bigger and bigger money into Provinces, sprinkled lightly with a few Caravans. His opponent DG had a slightly different approach by going for the Remodel into Coppersmith/Caravans into big money and finally Provinces.

Simulating Yaron’s playing style was easy, because non of his cards involve difficult decisions. DG’s Remodel and Haven on the other hand gave my poor simulator fits. It kept making silly mistakes like Remodeling the wrong card at the right time and Havening away the right card at the wrong time. I’m not making much sense here, but hold on, the serious strategy is coming. Haven is an innocuous little card, but explaining to a computer how to set up future turns is a really hard thing to accomplish. As most of you will know even the crunchiest of number crunchers is dumber than the dumbest animal on this planet (google told me it’s a turkey):So unfortunately I wasn’t able to fully simulate DG and Yaron’s game. But seeing how a Coppersmith/Caravan and Masquerade/Caravan strategy match up should still prove interesting so here goes:

On with the games… a few thousand

Here are Yaron’s buy rules: Open with Masquerade/Caravan, buy Province if you have Gold, buy Duchy when there are 4 or less Provinces left in the supply, buy Estate when there is 1 Provinces left in the supply, buy Gold, Caravan and Silvers when you can.

DG’s buy rules are quite similar except for the opening (Coppersmith/Silver) and buying Duchies a little earlier (when there are 5 Provinces left in the supply). (These are the buy rules after optimising)

Here’s the delta-VP graph (which shows the average amount of Victory points gained each turn):

And here are the winning percentages (the ties bar shows how many games where tied):

So Yaron’s Masquerade strategy beats the basic Coppersmith/Caravan which shouldn’t be too surprising (just check out councilroom). This still doesn’t tell us if DG’s Remodel will tip the game in his favor, but I have a feeling it might not. DG is playing a “big money”-strategy and doesn’t really use his Remodel to build an engine, but rather cycle his deck a little faster (buy turning Estates into Caravans) and as an aid to win the late game race for Victory Points. As I’ve noticed from my simulations, trashing will only help “big money” strategies out a little or not at all:

Loan and Lookout are really terrible and will actually hurt you when you’re a Gold digger. Chapel will give a slight edge against an opponent who only buys treasures. Masquerade is a whole different story, but that’s because its draw-2 effect is very significant:

Remodel is a not a fast trasher like Chapel and doesn’t have any other direct benefits like Masquerade, so I’m guessing it will not have a big influence on your big money deck’s win rate. If you’re trying to build a real engine, it’s a completely different story! Take this solitaire game I played as an example: I built an engine to get to that one big turn where I played multiple Coppersmiths and bought 6 Provinces on turn 13. This would be impossible to achieve without the Remodels!

Skipping the Caravans

Although we’re just guessing at how good DG’s strategy was, we can try to improve Yaron’s. Here’s what happens when we don’t let him buy Caravans (just the one Masquerade and money):

Not jumping onto the Caravan results in a +15% win rate. This shows Masquerade’s similarity to Envoy which also hates to see other Action Cards in the same deck.

So why is it that one of the best players in this game (hello Yaron!) makes such an obvious mistake of buying extra action cards with his Masquerade? Is it because Caravan is such a sexy card: it’s got a different color than most cards, it gives you that adrenaline rush of drawing a card, not once but twice. And maybe most importantly it makes your starting hands bigger.  This might be a male thing: look, mine’s bigger than yours. Which brings me to something I’ve been wondering about. Is Dominion a game played mainly by guys? Please enlighten us and yourselves in this poll:

Hiatus! I didn’t want to let folks down because theory thinks he needs to study, so here is some light content:

Theory and I played a series of epic games a few weeks back, some of which will probably get written up while he is “studying”.

The least interesting of these was http://councilroom.com/game?game_id=game-20110408-191900-6a229632.html.

In this game, theory was upset that he drew a 5/2.  I sized up the board, and then executed one of the most boring strategies, coined as “Grand Envoy” (or Single Envoy Big Money if you prefer more specific names)

This strategy (with the goofiness of theories Penultimate Province Rule removed for readability) can be summarized as follows:

Do I have an Envoy?  Play it.  Opponent discards highest treasure.
Do I have 8 and at least 1 gold?  Buy Province
Do I have 5 AND the game is somewhere around half over (provinces <= 5ish) ? Buy Duchy
Do I have 2 AND the game is really over AND it might make a difference? Buy Estate
Do I have 6?  Buy Gold
Do I have 4 and No Envoy's? Buy an Envoy
Do I have 3? Buy Silver
Do Nothing

It was a predictably fast boring match… over in 14 turns, although theory didn’t even try to stretch the game out with duchy dancing. I had 5 golds by turn 8, and then it was province x2, gold, province x2, duchy, province. Theory tried treasure maps, hit them, but even by then I already had more gold.

I honestly don’t enjoy playing this way, but because because it was a ranked match with theory, I couldn’t really afford to experiment (see this match with yaron for an example where experimentation with bad cards failed in epic fashion)

Afterwards, in our typical debrief, we went though the logs to see what we could learn from this experience. Our gut feel was that there really weren’t alot of options here, especially for theory sitting on 5/2.

Possibilities:

•  Treasury is usually a slow engine card… very useful if you want to repeatedly buy mid cost cards to build up your engine.  Not great if you need to be green card rushing because your opponent will buy 5 provinces by turn 14.
•  Upgrade / Nothing looks like it might be slightly stronger than Native Village per the opening buy analysis, maybe move into Envoy with the upgrade after.
•  Treasure Map / Native Village is interesting?
• Envoy / Nothing is strictly worse than Envoy / Silver, but perhaps the p1 advantage might make up for it?

On the 4/3 side

• Nothing involving village will work here, the only thing that needs extra actions is Envoy.
• Treasure Map / Chancellor is a little crazy.  Crazy like a fox perhaps?

Without extra buys, we didn’t see anything that would realistically beat (as defined by win more often)  Grand Envoy.  Unfortunately, I don’t have any fully functional simulators, so I figured I could pose the challenge out to the simulator community…

On this board is Grand Envoy a “Dominant Strategy“?

I’m defining Grand Envoy is defined as any strategy (regardless of parameters) that only buys 1 Envoy, and the rest coins and victory, even if the parameters are slightly different than what I outlined above, as I make no claim to knowing for sure that the optimal parameters are.

It is going to be very difficult (if not impossible) to prove that this strategy is dominant, but it should be possible to demonstrate that it is not, if a strategy can be defined that beats it.

You’ll only get partial credit for winning if the answer is

Do you have 4/3? -> Play Grand Envoy
Otherwise buy Upgrade / Nothing -> Play Grand Envoy, with trashing states into Silvers.

Contact us if you think you have an answer and want to discuss further! Alternatively, discuss how you would play the set in the comments below.

Any ideas on what theory could have done differently besides treasure map desperation? I had luckier than average draws, IIRC Grand Envoy typically has 4 provinces by turn 14, not 5.