Wednesday, 20 May 2015

Engines' Economic Explosiveness

A point that I think a lot of players get to – and I know I certainly did – is to look at the world of Dominion in a Big Money Paradigm. What I’m talking about, in my case at least, is a concept I call “money density”. Basically, a rough measure of quality for a BM deck is something like “take your average coin production per card, multiply that by your average hand-size, and that gives you your average economic capacity per turn.”

This is perhaps a bit simplistic, but it really does give you a rough assessment of the capabilities of a big money deck. I will note that even when you are playing big money, there are lots of imprecisions to modelling things this way: card efficacy doesn’t, in general, scale linearly, unused money has no value, turn-to-turn variations are quite important, ancillary benefits of cards beyond coin-value are real, etc. Even within this Big Money Paradigm, there are lots of nuanced decisions to make.

When you are stuck in this mindset, it can be hard to think of why you would add “do-nothing” cards – a la Village – to your deck. Sure, the cantrip makes it not hurt so much, but it doesn’t actually help your money density, and you are potentially missing out on getting a better card – silver, at least, will do more for you. And in a Big Money deck, the extra action usually doesn’t do a lot for you – if you get to the point you’re needing one very often, you probably should have just bought fewer terminal actions. Or not play Big Money at all.

This is where the Engine Paradigm (or draw-your-deck if you want slightly less pithy but arguably more descriptive names) comes in. If you can get to the point where you are drawing every card in your deck every turn, the way you look at your economic output on a turn changes completely. Now, you don’t need to look at average coin per card; you can actually just add up the sum total of all economic production in your whole deck.

To illustrate this, let’s look at an example of adding a Gold (which is not what you want to do terribly often in engines, but is always available and gets the point across). Adding the gold in a Big Money Paradigm will increase your money density by the difference between $3 and your old average value, divided by the number of cards in your deck. So if you had a starting deck plus five silvers, your old density was 17/15 = 1.133, and you increase by (3-1.133)/16 = 0.117. Multiply that by 5 cards per hand, and you get .583 coin per turn on average. This is pretty good for a Big Money deck. It’s worth noting here that each successive gold will do less though – the next one only adds .103 per card, or .515 per hand. This is because the difference between where you were and the $3 of the Gold continues to shrink, and the impact of each card is less as your deck gets bigger.

If you’re drawing your deck, on the other hand, you simply get to add the full $3 to your ever-turn spending power. The next gold just adds $3 again, too. This is a lot more, and it gets to be a progressively bigger gap over time. So you can see that even treasures can get leveraged more if you are drawing your deck.

Now, there are reasons why it’s not quite so rosy for engines as the above might make it sound. As it relates to the discussion above, the most notable thing is that if you are adding payload cards which don’t help you to draw (like Gold), you will have to get more pieces that do so you can continue to draw your deck every turn (terminal payload also requires getting more villages). This diminishes the ability to really add as much economy as you might otherwise be able to. On the other hand, being able to add to your per-turn payload so quickly self-synergizes, exploding in on itself in a chain reaction – getting that extra $3 now means I have more that I’m able to spend next turn to keep increasing my economic capabilities without falling behind on draw. This ramping effect virtually always more than compensates for the need to get extra pieces to keep drawing, at least if you have the capability to get extra buys – otherwise making $30 on a turn doesn’t do much for me. On top of that, there are ancillary benefits – if there are cards which are much better in combination or in multiples, you get to reliably do that, and you get to hit them with your attacks every turn. Engines also give you better control of ending the game just when you want.

The real downside of engines, which might make you not want to go for one, is that they can be slow to set up. This, along with increasing the reliability of the engine, is why trashing and/or sifting is such a boon to the engine. It’s all about getting to that point where you are drawing your deck as quickly as possible, because once you are there, even if it takes a long time, even if you are forced in to buying victory points in less efficient chunks, the raw power of an engine’s chaining buildup, if one is possible on the board, is usually enough to overcome the potential speed deficit.

No comments:

Post a Comment