This article is written by yaron. He is the Round 6 Champion of the BoardGameGeek Dominion League.
Suppose I have 9 cards in my draw deck: 3 Golds and 6 Victory cards. What is the probability of my next draw being a Gold?
Well, that’s an easy one: 3/9 = 1/3. You have a 1 in 3 chance of drawing Gold.
Now, suppose my right hand opponent played a Tribute, putting the top 2 cards of my deck into my discard pile. What is my probability of drawing Gold now?
Still 1 in 3. The third card from the top (which is the one you draw after being Tributed) is just as likely to be a Gold as the first one.
Doesn’t the answer depend on the specific cards discarded by the Tribute?
Sure. But coming in, no one knows what these cards will be. Averaging over all possible outcomes, your chance is still 1 in 3. The Tribute didn’t help or hinder your position.
Okay. Now suppose I played a Loan last turn, finding my first Gold and discarding it. What are my chances of drawing Gold now?
Just like before, 1 in 3.
Wait, that can’t be true! I’ve just discarded a Gold!
That’s true. However, you’ve also discarded some Victory cards on the way to that Gold. Your deck has 2 Victory cards for every Gold, so you discard an average of 2 Victory cards before discarding the Gold, leaving the proportion of Gold in your deck 1 in 3.
Okay, but that’s because I have a lot of junk. If my deck had more Gold and less victory cards, playing the Loan would definitely be bad for my next draws, right?
Wrong. If you had less junk, then yes, you would discard less junk on the way to your Gold. But you would also have less junk remaining in your deck afterwards. If 2 out of every 3 cards in your deck were Gold, then after playing the Loan, there would still be an average of 2 Gold for every 3 cards in your deck.
So the desirability of cycling has nothing to do with the quality of my deck?
Exactly. In a good deck, you’ll cycle away some good cards, but the cards you draw in their stead will be just as good. In a pile of Curses, you’ll cycle away a lot of junk, but the cards you end up drawing will be just as junky. It just doesn’t matter.
As an example, let’s look at the Adventurer. Which is a better buy, Adventurer or Gold?
The answer depends only on the Treasures in your deck. If your average Treasure is bigger than $1.5, and you have actions to spare, then Adventurer might be better for you than Gold.
However, the answer emphatically does not depend on the amount of Curses in your deck. If the average Treasure in your deck is worse than $1.5, then no matter how many Curses your deck has, the Adventurer is not worth it. The Adventurer’s cycling effect has no inherent advantage in a Cursy deck. The proportion of Curses drawn will be just the same, whether you play an Adventurer or not.
What if I track my discards, and realize that my best cards have yet to be drawn?
Sure, if you know that the one undrawn card in your deck is your only Platinum, it would make sense to skip playing the Loan. On the other hand, if you know there’s a Silver there, but there are Platinums in your discard pile, play the Loan to skip the Silver and get at the Platinum.
Note, however, that these considerations depend on the quality of your remaining draws compared to the rest of your deck. They have nothing to do with your overall deck quality. There’s no general reason to avoid playing your Loan when your deck is brimming with Gold and Platinum—your Loan is no better and no worse than a Copper.
How about cycling in order to draw my new acquisitions faster? Is that a good idea?
It is. In the early game and mid-game, you are adding cards to your deck that are better than your existing average. Cards that cycle your deck will make you reshuffle faster, getting your newest and best cards into your hand. However, in the late game, most of your new acquisitions are Victory cards. Cycling your deck becomes a bad idea at that point, because you’d rather not draw these new cards.
Again, this has nothing to do with overall deck quality. A trimmed monster that’s buying multiple Grand Markets and Platinums each turn can benefit from cycling, because the cards bought are even better than the existing average. On the other hand, you should try to avoid cycling when buying Estates with your pile of Gardens and Curses. The cards you are cycling away are bad, but the new Estates are even worse.