Dominion Things

Those of you around Seattle know that I'm a big fan of the card game Dominion. I recently bought a fourth set of the game and just last night had some people over to play it, and there are some strategic thoughts and concepts that I want to discuss about it.

First, for those of you who don't know what the game is, I'll try to explain it fairly succinctly. Dominion is a deck-building card game in which you try to earn the most Victory Points. Victory Points are normally accrued through purchasing cards in the game that are worth 1, 3, or 6 Points. Cards are purchased with Treasure Cards with values of 1, 2, and 3. Cards are put in your discard pile after you play them. As your deck runs out, you take your discard pile, shuffle it, and start drawing again from your new deck. Now the tension within the game is that when you start drawing Victory Point Cards into your hand, they're functionally worthless.

In order to help you in your quest to get Victory Points, there are ten "Kingdom Cards" dealt before every game. These cards can be purchased and allow you to draw more cards into your hand, or steal Treasure Cards from your opponents' decks, upgrade the value of your own Treasure Cards, give you Treasure points for this turn,
or any number of other Actions. Typically, you can only play one of these per turn, unless the effects of an Action Card allow you to play more Actions. It's how these cards interact that dictates the style of play of each game.

At the beginning of the game, all players are given a deck of 10 cards, seven Copper (worth 1 Treasure each) and three Estates (worth 1 Victory each). Each player takes his/her hand of five cards and you begin. What I want to do now is get into it a little bit here and figure out some math.

Assuming you buy one card each of your first two turns, you will have 12 cards in your deck. That means that any given card has a 41% chance of showing up in your hand. If you buy two cards, the chance that they will BOTH show up in your hand on the third turn is 15%. Suppose you bought a Smithy, which allows you to draw three cards when you play it, and you also bought a Village, which allows you to draw a card and play an additional Action. Fifteen percent is really good for you, then, because you'll end up drawing four more cards into your hand. But if you get the Smithy and not the Village in your hand, it's a bit of a bummer.

After taking your five-card hand, there are seven cards left in your deck. If you draw three cards, the chance of any specific card being within that three is 42%.

That's where I went wrong in the last game we played Sunday night. If you're going to take a Smithy early, you should resist buying other action cards until your deck is large enough that it becomes relatively unlikely that you'll pick up the extra Action Card while drawing three.

The other thing I notice is that a Village card is not all that useful in the early-going of a game. Village cards become more useful when your deck is full of actions, but until then all you get from it is a single card. You recall the odds of two specific cards being in your hand on your third turn being 15%. Trouble is that every time I play Dominion with folks and Village is in play, it gets bought up quickly because it can become a lot more useful later on in the game. I'm going to try to avoid Village the next time it comes up and see if I can make it work.