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Puzzles and Challenges / Best polynomial asymptotic point scoring
« on: January 24, 2020, 01:29:25 am »
This puzzle is related to the Best Asymptotic Point Scoring and Asymptotic analysis of kingdoms puzzle.

As in those puzzles, we have a kingdom with unlimited piles, and piles that have differently named cards have their contents repeated. You can choose the repeating order of any of these piles as long as it is a possible legal order in a normal game.

For this puzzle, you can also assume you have perfect luck, and one opponent whose choices you control, but cannot buy or play cards on their turns. For every kingdom, either it is possible to get an unbounded number of points on some turn, or there is a function f(n), where n is the number of turns, that bounds the maximum number of points that you can get by turn n.

For example, with only Bishop in the kingdom, you can trash down to a deck with Gold-Silver-Silver-Bishop-Province, and trash and buy a Province every turn for 5 points. This will give you f(n) = 5n - c, for some constant c that is related to how long it takes to build that deck.

For this puzzle, we are interested in kingdoms whose f(n) is bounded by a polynomial. Out of kingdoms whose f(n) is asymptotically bounded by a polynomial, what is the highest degree polynomial that can be achieved? For example, that Bishop kingdom can achieve O(n). A kingdom of only Gardens can achieve O(n^2). A kingdom of only Gardens and Embargo can achieve O(n^3).

Note that it's pretty easy to have a kingdom that's above polynomial. For example, with only Market in the kingdom, you can play all your markets every other turn (your starting 10 cards are all stop cards), and multiply the number of markets you have by 1.2, giving f(n) ~= 1.2^(n/2) ~= 1.095^n.

I propose two versions of this puzzle:

A) 10 kingdom piles, any number of sideways cards. Black Market is banned.
B) Any number of kingdom piles allowed, any number of sideways cards allowed. Black Market is banned.

Dominion General Discussion / Dominion Wavelength
« on: January 10, 2020, 10:12:25 pm »

I made a little mini project that I thought you all might enjoy. It is based off of the board game Wavelength.

The basic way it works is:
- The clue giver gets a category, which is a two-ended spectrum (e.g. Buy none -- Buy them all) and a random position on the spectrum. The clue giver has to name a card/card-shaped object that they think falls at the given position on the spectrum. They can share their clue with a URL for other people to guess.
- Other players look at the clue and guess where on the spectrum it actually was. The closer they are, the better they did. In the real game, the middle blue band is 4 points, the adjacent orange bands are 3 points, and the outside bands are 2 points.

To make your own clue, hit the "Make a Clue" button, type your clue in the box, then hit "Make Link!" and copy/paste the link that comes out. The link should automatically go to your clipboard so you can even skip the copying part. You can press the "Make a Clue" button again if you don't like the criteria you were given to get a newly generated one. (though in a real game, getting stumped is probably part of the fun?)

To guess on a clue, go to a clue link, then move around the slider and hit the "Guess" button.

The website is at:
Here's a sample clue that is probably not too hard or controversial:

Let me know what you think! Also, if you have any suggestions for new categories, that would be great! (If you're curious, the list of all categories is at

Puzzles and Challenges / Asymptotic analysis of kingdoms puzzle
« on: March 23, 2019, 08:44:26 pm »
Hi f.ds, sharing a puzzle that a friend and I made (well, mostly my friend) for another friend of ours. You probably won't enjoy the puzzle unless you like both dominion and math, but hopefully everyone here likes at least one of the two. :)

The rules of our puzzle's asymptotic dominion are similar to those in, but the main difference is that in our puzzle, you can assume you will have perfect luck, as it asks about the best possible score. Also, this puzzle was made before Renaissance came out, so no Renaissance cards are in any of the kingdoms.

The puzzle is at Each of the 13 bullet points on the left is a separate kingdom to consider. Most of these kingdoms might not have exactly 10 kingdom cards (in fact, one has none), but should be considered as if that were the kingdom anyway. Each of them matches with an answer on the right, and taking the corresponding letters will spell out a message. The eventual goal is to have a final answer, which is a word or phrase.

Feel free to ask for any hints or clarifications here, and I hope you enjoy!

Note: Based off a sample size of 1, this puzzle may take quite a while to complete.
Edit: Adding some extra info here.

Some basic kingdoms and their answers, to get the idea across.
  • Market, Chapel. Answer: 1.2^T
  • Market. Answer: 1.2^(T/2) = 1.095^T

A list of sets that I think are easier, since completing the whole puzzle is probably unreasonable.
In approximately increasing difficulty:
  • Potion cost
  • Durations
  • Reactions
  • Artisan, ...
  • Hamlet, Watchtower
  • Debt cost

A kingdom I would say is pretty fun and decently approachable is Artisan, ....
Here's some other kingdoms not included in the puzzle that are fun, and not toooo crazy to analyze:
  • Bishop, Cursed Village, Seaway
  • Bridge, Hunting Grounds, Donate, Canal, Inheritance

Rules Questions / Multiple donates in the same turn
« on: November 01, 2018, 04:19:44 pm »
What happens if you buy donate multiple times on the same turn? Do you get one donate phase at the end of your turn for each time you bought Donate?
Not that you would want to most of the time, but hey, maybe there's Tomb + Fortress or something.

Some of you may remember a puzzle from the old days: assuming perfect shuffle luck and a kingdom of your choice, empty your entire deck in as few turns as possible. The old puzzle post is here:, and back then, it was possible to do it in 6 turns.

Of course, there are a lot more possibilities now. How few turns can you do it in? I can get x=5, and I think one turn fewer might be possible, since I can find a x turn solution that gets really close.

Some silly side puzzles to go along with this, each of which is a condition that can also be satisfied with an x turn solution (not simultaneously, each is its own puzzle).

1) No cards from Guilds.
2) No cards in the Native Village or Island mat at the end of the game.
3) Gain a Fortress at some point.

Goko Dominion Online / (please delete)
« on: July 04, 2013, 02:33:19 am »
(post edited away)

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