Beemer (dr_tectonic) wrote,


Dominion, if you're not familiar with it, is a deck-building card game. You start off with a deck of ten cards; each turn you draw five cards, play them, and buy a card to add to your deck. Some cards give you the coins that you use to buy more cards; others do things like let you draw more cards or buy an extra card. Your ultimate goal is to buy cards that have victory points on them, because that's how you win the game.

The base game has 26 different "kingdom cards" in it. You pick ten of those to play with each time you play the game, so there are a lot of different ways to play the game. You play with one set of cards and get to know how they interact, and then you swap out half of a really good combo, or one card that countered another card, and now it's a very different game. So it has a lot of replay value.

There are now thirteen expansions, most of them as big or bigger than the base set. And you can use cards from any of them.

I did the math. There are 208,693,818,083,123,000,000,000,000 (2.09e26) configurations of the game.

That number is 208-some septillion, which is about 3,000 times the estimated number of stars in the entire observable universe.

So what I'm saying is, if you're looking for a pastime, it's got a lot of replay value.

Math details:

The 14 Dominion sets (plus the handful of promo cards) comprise 353 kingdom cards total. 353 choose 10 is 353! / (343!)(10!) = 353*352*...*345*344/(10*9*...*2*1) = 2.78e18.

There are also two binary options: whether to use Shelters from the Dark Ages expansion and whether to use Colonies & Platinum from the Prosperity expansion, which gives you another factor of 4.

Finally, there are 115 landscape cards (Events, Landmarks, Projects, and Ways) from the Adventures, Empires, Renaissance, and Menagerie expansions. You can in theory play with however many of those you like, though the designer recommends using only one or two. The website allows you to use up to 4, so that what I went with. That gives you an additional factor of 115*114*113*112/4! + 115*114*113/3! + 115*114/2 + 115 + 1 = 7166916.

2.78e18 * 4 * 7.16e6 = 2.09e26

I'm NOT adding any additional multiplicity for the Black Market promo card, which lets you draw from a special deck of cards from outside the kingdom, under the assumption that the contents of the special deck are just "everything else", so that's only a single configuration. I'm also not counting the orderings of stacks of differently-named cards like Knights and Ruins; those are different starting points for the game, but not different ways of setting it up. (Like whether your initial shuffle gets you a 3-4 split or a 5-2 split on your 7 starting copper.)

This post brought to you by my desire to post something just to break the long dry spell, even if I haven't mustered up the wherewithal to post about life in general. (Short version: things are fine, better now than before the change in administrations, but the pandemic still sucks.)

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