# Dominion Strategy Forum

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1
##### Puzzles and Challenges / Re: Best asymptotic point scoring per "action"
« on: March 05, 2021, 04:55:49 pm »
I don't know if cards set aside by Prince should count as plays every time or not. Either way, it should be possible to keep growing the number of Treasure Hunters every turn to increase our performance.

For example, we could put a +Buy token on Page, then once we can hit \$18 every turn:

(All Treasure Hunters that have been set aside by Prince get played.)
Play two Pages.
Play Prince, setting aside a Treasure Hunter.
Buy Page, Prince, and Donate, paying all debt.
Clean-up: exchange a single Page for Treasure Hunter.
Donate: Trash all Silvers.

This can be accomplished with the kingdom Page, Peasant, Prince, Donate, Tomb.
After N turns of this, we do O(N) playing/buying steps, or O(N^2) if we count the start of turn Prince effects. We will score O(N!) points though, and no matter which denominator we pick, we will have an (N-O(1))! points/actions ratio.

2
##### Puzzles and Challenges / Re: Best asymptotic point scoring per "action"
« on: March 05, 2021, 04:38:21 pm »
Here's something silly that uses multiple turns.

Kingdom: Page, Hireling
Landmarks: Donate, Tomb

Setup: Pick an integer K >= 9. Over many turns, obtain K Treasure Hunters and K-5 Hirelings, and play all the Hirelings (so that starting hand size will be K every turn). Set up your deck so that you gain at least one card on a turn and are guaranteed to draw at least 8 Treasure Hunters next turn. (e.g., Donate down to only K Treasure Hunters, then buy anything. Next turn you will draw at least K-1 Treasure Hunters).

Every turn:
Play K Treasure Hunters. (or K-1 the first time)
Buy Donate, paying off all debt.
Donate down to K Treasure Hunters.

On the first turn you start this, you'll gain at least 1 Silver, then on every subsequent turn, you'll gain K times more Silvers than the previous turn, and trash them all.

After n turns, this gives O(K^N) points and takes O(K) actions, giving an O(K^N) points per action performance for any K of our choosing.

3
##### Puzzles and Challenges / Re: Best Asymptotic Point Scoring
« on: February 27, 2021, 02:29:20 pm »
A N -> (2^(2^(2^N))) growth should amount to f(n) = 2 ↑↑ 3n growth, which seems like the best so far if I'm understanding correctly. The triple up arrow seems elusive again though

Great work on your part as well! I think it's a lot harder to build out the solution from nothing than to try to improve it.

4
##### Puzzles and Challenges / Re: Best Asymptotic Point Scoring
« on: February 26, 2021, 08:08:36 pm »
TL;DR: +Ironworks -Forager +Squire should still be finite and boost it up to N -> (2^(2^(2^N))).

Looks neat! I'm a little confused at the end of the Buy phase since Conquest should only give 2 silvers, which of course can be remedied by exchanging instead of trashing on the second-to-last buy and leaving 6 money to buy the Conquest last. (Also, you only need to do this on the last turn anyway.) This shouldn't affect any of the calculations, of course.

I think we can improve this by removing Forager and adding Ironworks (which gets Seawayed), which is a gainer that works with Capitalism but can't gain Mandarins (or Scrying Pools or Universities). Since Ironworks can gain a copy of itself, we have to be careful that this doesn't introduce any infinite loops. I believe this is okay because

1. You cannot gain Scrying Pools or Universities mid-turn (or take them out of play).
2. Without using a University, you cannot gain a Cultist or Mandarin midturn, and cards stay in play.
3. Without playing Scrying Pool or University, the only plays that don't decrease handsize are playing our single Scheme/Fortress/Watchtower, trashing a Cultist, or playing a Cultist, or playing an Ironworks on Estate. We have a finite bound on all these actions besides the Ironworks play. The Ironworks play strictly decreases the number of "available" (in hand + deck + discard) Ironworks. No other play (besides playing University) can increase the number of available Ironworks.

With this, the action phase loop looks like:

play Scrying Pool, drawing entire deck
play Black Market
play all Priests, trashing the Fortress
play all Ironworks, gaining either Priest or Ironworks (I think the best thing is all Ironworks until the second-to-last loop where you get some ratio of Priests)

(The last loop is analogous to pitythefool's solution, as are the remaining phases.)

Analysis:
At the start of the turn, say we have:
N       Ironworks
<= N Priests (exact amount doesn't really matter)
U       Universities
U+1   Scrying Pools
Every time we play a Pool and University, we double the amount of Ironworks, and on the last step we can give ourselves an equal number of Ironworks and Priests, giving 2^U * N Ironworks and 2^U * N Priests. Let's just set U=N to simplify, so that we have N * 2^N Priest plays then N * 2^N Ironworks plays, giving us on the order of \$(N^2 * 4^N) and (N * 2^N) buys.
Every Masterpiece buy/trash multiplies the wealth by N * 2^N, so our total wealth before the end of the buy phase is on the order of
(N^2 * 4^N) * (N * 2^N)^(N* 2^N) ~ (N*2^N)^(N*2^N) < (2^N)^(2^N) < 2^(2^N).
So we can grow from N -> 2^(2^N) every turn. I'm a little confused where this puts us in growth rate at the moment.

---

So another thing I think we can do is add Squire and trash it for midturn Scrying Pool gains. Then our finiteness argument should be like

1. You cannot gain Universities mid-turn (or take them out of play).
2. Supposing you do not play any Universities, every card you play does not increase the number of available (Scrying Pool + Cultist + Squire + Priest + Ironworks) that you have.
3. Increasing your handsize strictly decreases this availability count.
4. Besides playing your single Scheme, Fortress, or Watchtower, every action you can do either strictly decreases your hand size or your total availability count (or both).

In this proposed loop, I'm going to ignore +Actions since we aren't using it as a limiting resource and could fix it with Academy or maybe Lost Arts on Ironworks. The loop should look like

Draw deck (with scrying pool)
inner loop start
Requirement: Hand has at least 1 Scrying Pool. If not the last loop before a University, hand has at least 2 Scrying Pools or 1 Scrying Pool, 1 Priest, 1 Squire.
Play all Ironworks, gaining either Ironworks, Priest, or Squire. (In most loops, almost every gain is for Ironworks. Replace with a Priest/Squire gain if needed to make the above condition satisfied.)
If not the last loop before a University:
If there is only 1 Scrying Pool in hand, first Priest to trash a Squire, gaining Scrying Pool. Either way, play a Scrying Pool.
If the last loop before a University (only 1 Scrying Pool in hand, and don't have Priest + Squire):
end inner loop

Outer loop
Do inner loop until it ends (note: in the inner loop for the last iteration of the outer loop (no Universities left), be sure to gain lots of Priests and play them too.)
Play University

Analysis for this:
To simplify, let's just say we have N each of Ironworks and Universities to start, and some negligible amount of Scrying Pools, Priests, and Squires. Once we have 1 Scrying Pool, 1 Priest, 1 Squire left, each inner loop will have to spend two gains on Squire and Priest, and the rest on Ironworks. So if we have X Ironworks to start, we'll end up with X-2 Ironworks on the next iteration. Iterating until the resources are exhausted, we'll have gained/played around X^2/2 Ironworks total. So every full outer loop takes our Ironworks from X->X^2/2. We will do this N times, once for each University.
N iterations of this starting from 1 gives us O(2^(2^N))) at the final iteration. Of course, we're starting at N, not 1, but this will not increase the asymptotics very much.
With 2^(2^N) Priest plays and 2^(2^N) buys, we will wind up with a N -> (2^(2^N))^(2^(2^N)) < 2^(2^(2^N)) growth per turn.

5
##### Variants and Fan Cards / Re: New Weekly Contest: Fan Card Mechanics
« on: February 04, 2021, 10:52:57 pm »

It'd be so funny to have a game where the scoring is this + Fortress + Tomb. Mwahahahaha

6
##### Variants and Fan Cards / Re: New Weekly Contest: Fan Card Mechanics
« on: February 02, 2021, 10:18:56 pm »
I think it would be approximately as strong, and still stronger than Chapel/Cathedral even if the Worshippers only trash the in play cards (like Bonfire). My analysis:
If you open Mendicant/Silver, you have 12 cards. If you see Mendicant in your first 10 out of 12 the next shuffle, you are going to go through all 12 cards exactly over the two turns. Assuming there is an Estate on the turn you play Mendicant (note that you see 6 out of the 11 other cards that turn), you can trash Estate and 2 Coppers that turn. Also assuming both these two things happen, you will have \$9 money over 2 turns and will be guaranteed to hit 5. I think the most likely split is \$5/\$4?

This already seems favorable to me compared to Chapel -- comparing the most common cases of either, you're trashing one fewer card (and not as many Estates perhaps), but you have a \$5 in your deck too over the Chapel open. Also the Estates don't seem obviously worse than Coppers to me -- finding one with a Mendicant means you can trash 2 Coppers that turn as well, after all.

7
##### Variants and Fan Cards / Re: New Weekly Contest: Fan Card Mechanics
« on: February 02, 2021, 07:32:52 pm »
Assuming I've interpreted the Worshippers rules correctly, I think that Mendicant is ridiculously strong. It's pretty likely that in a game where you open it and Silver, that by the end of your Turn 5, you've gotten to trash 2 Estates+4 Coppers or 3 Estates+3 Coppers, and hit \$5 once or twice. This seems better than Chapel or Cathedral in most games.

8
##### Variants and Fan Cards / Re: New Weekly Contest: Fan Card Mechanics
« on: February 02, 2021, 07:10:57 pm »
So for the rules of the Worshippers, do they work on cards that were in play that you would discard in cleanup, or cards that were left in your hand, or both?

EDIT: I guess from looking above, it's either? And the wording is to disallow trashing things like Durations that are supposed to stay out?

9
##### Puzzles and Challenges / Re: Best Asymptotic Point Scoring
« on: December 29, 2020, 05:17:31 pm »
Exciting stuff I'll try to take a closer look at the effect on liveries per golem played since that seems a little bit sketchy to me.

If I'm not mistaken, I believe the second row can be referred to as a double exponential function?

10
##### Puzzles and Challenges / Re: Best Asymptotic Point Scoring
« on: November 08, 2020, 06:48:42 pm »
I'm saying this on the basis that exchanging a card that is being gained from the Black Market deck shouldn't work, and you'll be forced to take the card you were originally gaining. So in our case, our Fairgrounds would get removed from the Black Market deck and we'd stop being able to buy it.

Though, I'm remembering that gaining Horse can be exchanged with Changeling, and that's not from a supply pile, so maybe it does work after all. I've yet to test this with the Black Market / Trader situation on the client.

11
##### Puzzles and Challenges / Re: Best Asymptotic Point Scoring
« on: November 01, 2020, 01:33:36 pm »
I believe that the latest Trader change kills the triple up arrow solution. It had a good run.

12
##### Non-Mafia Game Threads / Re: Zendo Questions 2
« on: July 10, 2020, 01:15:19 am »
Guessing time
brussels sprouts
cauliflower
donut

13
##### Non-Mafia Game Threads / Re: Zendo Questions 2
« on: July 10, 2020, 12:59:50 am »
Guess: Return yes iff. the sum of the ASCII values of all characters is even.

Aww, I was gonna guess that too, lol. I was pretty sure you were onto something with that first guess!

14
##### Non-Mafia Game Threads / Re: Zendo Questions 2
« on: July 09, 2020, 09:12:49 pm »
!
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\$
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^
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15
##### Non-Mafia Game Threads / Re: Zendo Questions 2
« on: July 09, 2020, 08:59:17 pm »
apple pie
c
cc
d
dd
e
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f
ff
g
gg
h
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16
##### Non-Mafia Game Threads / Re: Zendo Questions 2
« on: July 09, 2020, 06:15:09 pm »
b
bb
bbb
bbbb
bbbbb

bananabanana
bananabananabanana
bananabananabananabanana
bananabananabananabananabanana

cherrycherry
cherrycherrycherry
cherrycherrycherrycherry
cherrycherrycherrycherrycherry

apple pie apple pie
apple pie apple pie apple pie
apple pie apple pie apple pie apple pie
apple pie apple pie apple pie apple pie apple pie

17
##### Non-Mafia Game Threads / Re: Zendo Questions 2
« on: July 09, 2020, 01:36:17 pm »
aaaa
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aaaaaaa
aaaaaaaa
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appleapple
appleappleapple
appleappleappleapple

18
##### Non-Mafia Game Threads / Re: Zendo Questions 2
« on: July 09, 2020, 12:23:59 pm »
a
aa
aaa
apple
banana
cherry
two apples
three apples
the quick brown fox jumps over the lazy dog

19
##### Non-Mafia Game Threads / Re: Zendo Questions 2
« on: July 08, 2020, 11:03:58 pm »
bcd
bdc
cbd
cdb
dbc
dcb

cde
ced
dce
dec
ecd
edc

ace
aec
cae
cea
eac
eca

20
##### Non-Mafia Game Threads / Re: Zendo Questions 2
« on: June 25, 2020, 07:21:18 pm »
chose
hose
care
bare
dare
fare
hare
mare
ware
rare
tare
reality
veal
reel
ban cultist
seal
If not, I have.

21
##### Non-Mafia Game Threads / Re: Decrypto 4
« on: June 07, 2020, 02:49:48 am »
Intercept Guess: 4-2-3
Team guess: 4-1-3

Code was: 4-1-3

22
##### Non-Mafia Game Threads / Re: Decrypto 4
« on: June 05, 2020, 05:26:40 am »
Clue: Inn - Favorable - Water

23
##### Non-Mafia Game Threads / Re: Decrypto 4
« on: June 03, 2020, 02:05:24 pm »
Round 2 Intercept Guess: 2-4-3

24
##### Non-Mafia Game Threads / Re: Codenames X
« on: May 31, 2020, 05:08:51 pm »
Moon

25
##### Non-Mafia Game Threads / Re: Codenames X
« on: May 28, 2020, 03:21:46 pm »
Stock, Chick then pass if both are right.

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