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51

Dominion Articles / Re: Combo: Donate-market square.

« on: August 09, 2017, 11:49:42 pm »

i know i'm inviting pages of pedantic debate with this, but...can we safely call this the fastest big money strategy? top 3 would probably be:

1. Market Square/Donate
2. Gear/Inheritance
3. Jack/Donate (think this might move up a spot if Borrow is also in the game)
Honorable Mention: Jack/Bonfire (just barely worse than Donate)

Not sure exactly what classifies as a big money strategy, but dungeon/tunnel and courtyard/delve are pretty good. Travelling Fair/Counting House also if it counts (which clearly it does).

52

Dominion General Discussion / Re: What are everyone's favorite and least favorite cards?

« on: August 05, 2017, 01:38:03 am »

Least favorites:

Governor: Maybe I misplay it, but I often find myself in a point hole that I can't quite make up with the deck I have. I just hate how you pretty much always have to go for it, and it seems to work out for me less often than I'd like.

Minion: Nothing frustrates me more than repeatedly discarding 5 good cards for 4 bad cards.

Page: Too many things about it can make me want to ragequit. Warrioring a warrior is the notorious one, but sometimes it can be something like my Champion was in my bottom 3 cards, so I got the last few curses/ruins right before I played it.

Fools Gold: I mostly dislike it because I ignore it perhaps more often than I should, but it also sucks to get behind early on the split, like if you get a +buy card and it misses the shuffle or something.

Favorites:

City Quarter: I like how the timing works for this card. Sometimes I get it wrong, but it's really fun to get right.

Black Market: Pretty much always lets you at least try to do something interesting.

Encampment/Plunder: Another one that I sometimes play wrong, but it's really fun to get the majority of these and rack up points while drawing the deck.

Farmer's Market: Really fun in an engine game, where hitting the high payoffs and keeping the right number of these around keeps things interesting.

53

Dominion General Discussion / Re: Semi-Interesting Dominion Moments Thread

« on: July 28, 2017, 01:19:25 am »

Just played a semi-interesting game, will attempt to describe via limerick

Opponent bought sea hag to curse
Some upgrades I bought to trash curse
Oh no, look there's poor house
Wait, Obelisk'd poor house
3 piles with upgrade and curse

Rhyming a word with itself is generally frowned upon.

You literally did this on every line in the limerick.

I am now even happier that I chose to describe my game via limerick.

54

Dominion General Discussion / Re: Is it ever worthwhile to buy trashers on a Donate board?

« on: July 27, 2017, 01:28:25 am »

Against junk attacks, you want a trasher to avoid getting 8 debt on a regular basis.

Unless your payload is a bunch of goons and you buy coppers/curses + donate every turn.

55

Dominion General Discussion / Re: Semi-Interesting Dominion Moments Thread

« on: July 27, 2017, 01:06:42 am »

Just played a semi-interesting game, will attempt to describe via limerick

Opponent bought sea hag to curse
Some upgrades I bought to trash curse
Oh no, look there's poor house
Wait, Obelisk'd poor house
3 piles with upgrade and curse

56

Dominion General Discussion / Re: Neat card interactions that were useful in the game you found them in.

« on: July 22, 2017, 02:59:56 am »

Played a game the other day with University + Pillage. Pillage is known for being an underwhelming card, some of its drawbacks:

1. It's too slow. Once you buy pillage, you have to wait to draw and play it, and then you have to wait again until you draw the spoils to use the spoils it gives to generate actual economy from it.

2. The attack, while it can be good, sometimes doesn't do a whole lot.

3. It's usually not worth using a buy and 5 coins on.

University often helps address all of these. On a board with enough of an engine to draw the deck (not too hard to achieve with university), you can often play the pillage the same turn you gain it (and then maybe even play the spoils too if you have enough draw), speeding things up considerably (addressing point 1).

For the 2nd point, the attack can actually be quite powerful in this situation if you can use it to prevent your opponent from firing. If the engine consists of say university for actions and some sort of terminal draw, then unless your opponent has at least 2 of each of these in hand, a pillage play means your opponent probably won't be able to kick off. This is nice, especially if you're playing pillage every turn (easier to do because of point 1).

For the 3rd point, well, you're just going to gain pillage with University. Probably your 5 universities are giving you plenty of gains of action cards so this is a pretty low cost.

The game I played had these two cards along with chapel and patrol and no other villages or draw (as well as no other coin from action cards). Pretty much the ideal situation for pillage being good, though I suspect that pillage and university still work well together even in somewhat less favorable circumstances.

57

Puzzles and Challenges / Re: Best Asymptotic Point Scoring

« on: July 07, 2017, 11:12:28 pm »

So if we only play a p fraction of the kc's and stonemasons each iteration, we'll get a 2p size increase instead of a 2 factor increase each iteration. However, this means that we have a (1-p) fraction of those cards remaining in our hand. As a result, playing k=1-log₂(1-p) cq's should be sufficient to draw the deck each time.

This yields a total increase of (2p)^d/k-O(1) to the deck size. WolframAlpha says that the optimal value for p is about .829464, which yields about 1.153^d for d', which is somewhat better than 3^1/88, though still not very close to 2.

I want to say we can get rid of tfair and training by just adding candlestick maker and scheme to the kingdom and having the last iteration of gains be a bunch of candlestick makers and a few schemes to topdeck cq's. In any case, I think we need scheme to guarantee firing each turn.

I agree though that I don't care so much about the base and think that maybe it's possible to add another arrow (especially if we go to 2 player).

Okay a bunch of things with what I said are wrong:

1. Scheme is bad, pretend I didn't say that. We can have royal seal to topdeck the cq buys if we don't want tfair.
2. What I said doesn't give enough cq's. Instead of candlestick maker, we use forager and have lots of treasures in the trash (some from the black market deck).
3. I forgot that stonemason gives a factor of 4, not 2.  This means we want to optimize (4p)^d/k-O(1), where k=2-log₂(1-p). Optimizing now yields p ~= .715408, so 1.3175^d.

As an aside, (I believe) we don't have infinite vp in a turn because the only draw is cq and kc/fortress and we can't gain those mid turn (we would need to gain both kc and fortress mid turn to get draw out of it). On the other puzzle, we ensured bounded +actions, maybe we can try the same here, though then we can't have forager I guess.

58

Puzzles and Challenges / Re: Best Asymptotic Point Scoring

« on: July 07, 2017, 10:20:11 pm »

Alright, so mojiponi's solution (and Holger's addition) ends up on the rough order of 2^kn2 for any k.

I think what luser originally wrote works but tim's suggestion is more clear and is technically better (improves the base of the exponent, pretty much). A more explicit (but still not totally optimized) description of luser's solution with additions (it took me a bit of work to decipher exactly what was happening):

Kingdom:  KC, stonemason, city quarter, fortress, gardens, training, travelling fair, inheritance (3 events, oh well). Training on stonemason, inheritance on KC (okay add a cost-reducer to the kingdom). When our deck has size d: Deck has 1 gardens, 1 fortress, ~7d/22 estates, ~14d/22 Stonemasons, ~d/22 City Quarters where x = o(d).

Turn:
Play ~log₂(d) City Quarters to draw the deck
Play the estates as d/4 KC on d/2 stonemasons for 3d gains, make them d estates and 2d stonemasons.
We have d/4 cards left in hand, so play 4 city quarters to draw everything again.
Play 3d/4 estates on 3d/2 stonemasons for 9d gains, which are 3d estates and 6d stonemasons...
Repeat like before until we run out of city quarters. We now have over d' = 3^d/88d cards in our deck, and the number of stonemason plays a bit over half of that. From training we could buy d'/20 city quarters, but just buy d'/22 instead (using travelling fair for buys).

Each turn d' = (3^1/88)^d, so we end up with around 3^1/88 ↑↑ n points.

See, that wasn't optimal at all (the base is around 1.01), but I think it would take quite a bit of work to get it much higher than that. I rounded down numbers in several places which could let us improve a little, but I don't see the base getting close to 2 very easily, mostly because we don't have enough coins!

I wouldn't be surprised at all if three arrows is possible though... I'll think about it...

So if we only play a p fraction of the kc's and stonemasons each iteration, we'll get a 2p size increase instead of a 2 factor increase each iteration. However, this means that we have a (1-p) fraction of those cards remaining in our hand. As a result, playing k=1-log₂(1-p) cq's should be sufficient to draw the deck each time.

This yields a total increase of (2p)^d/k-O(1) to the deck size. WolframAlpha says that the optimal value for p is about .829464, which yields about 1.153^d for d', which is somewhat better than 3^1/88, though still not very close to 2.

I want to say we can get rid of tfair and training by just adding candlestick maker and scheme to the kingdom and having the last iteration of gains be a bunch of candlestick makers and a few schemes to topdeck cq's. In any case, I think we need scheme to guarantee firing each turn.

I agree though that I don't care so much about the base and think that maybe it's possible to add another arrow (especially if we go to 2 player).

59

Puzzles and Challenges / Re: Best Asymptotic Point Scoring

« on: July 07, 2017, 02:26:43 am »

I have better f(n)= 2^2^2^(O(n) times) kingdom kc, workshop, city quarter, training, tfair, bridge, gardens.  Deck contains starting cards one gardens, rest are action. Training on workshop

Turn starts by drawing deck with log(d) cq where d is deck size, play kc-bridge. Then you start multiplying workshops/kc. Assume that deck has k kc and k workshops. play k/2 kc on k/2 workshops to gain 3/4k workshops and 3/4k kc then play cq to draw these and repeat by number of cq in deck. If you start with 3 kc and 3 workshops and l cq you will end with 2^l workshops. Coins from training allow you to buy 2^l/10 cq which shows that f(n+1)>=2^f(n) and bound follows.

More or less. I guess you want to have k/3 kc and 2k/3 workshops to gain 2k/3 kc and 4k/3 workshops, giving you the factor of 2. But then you'd need more cq's to draw everything each iteration, giving you only sqrt(d) iterations. If you only play half of what you draw each iteration, you're not actually getting an exponential increase. Maybe I'm misunderstanding your suggestion though (or my math could be off).

You could also probably do a bit better with the factor by stonemasoning a fortress into stonemasons/workshops.

In any case, looks like we're into up arrow notation land.

I guess you could play like slightly fewer kc's and workshops each iteration so that you only need a constant number of cqs to redraw the deck, giving you f(n+1) ~= (2-c)^f(n) for some small constant c.

60

Puzzles and Challenges / Re: Best Asymptotic Point Scoring

« on: July 07, 2017, 02:21:28 am »

I have better f(n)= 2^2^2^(O(n) times) kingdom kc, workshop, city quarter, training, tfair, bridge, gardens.  Deck contains starting cards one gardens, rest are action. Training on workshop

Turn starts by drawing deck with log(d) cq where d is deck size, play kc-bridge. Then you start multiplying workshops/kc. Assume that deck has k kc and k workshops. play k/2 kc on k/2 workshops to gain 3/4k workshops and 3/4k kc then play cq to draw these and repeat by number of cq in deck. If you start with 3 kc and 3 workshops and l cq you will end with 2^l workshops. Coins from training allow you to buy 2^l/10 cq which shows that f(n+1)>=2^f(n) and bound follows.

More or less. I guess you want to have k/3 kc and 2k/3 workshops to gain 2k/3 kc and 4k/3 workshops, giving you the factor of 2. But then you'd need more cq's to draw everything each iteration, giving you only sqrt(d) iterations. If you only play half of what you draw each iteration, you're not actually getting an exponential increase. Maybe I'm misunderstanding your suggestion though (or my math could be off).

You could also probably do a bit better with the factor by stonemasoning a fortress into stonemasons/workshops.

In any case, looks like we're into up arrow notation land.

61

Puzzles and Challenges / Best Asymptotic Point Scoring

« on: July 06, 2017, 01:18:32 am »

Suppose you're playing a game of dominion where the kingdom piles are infinite instead of their usual size (and therefore the game never ends). The puzzle is to come up with a strategy that yields the best score as a function (f) of n, the number of turns played so far. Since I believe it's possible to score an unbounded number of points in a single turn on some boards, I want to restrict to only boards where the number of points that can be scored on the nth turn is bounded by a function of n (i.e. no infinite points in a single turn). Ideally, I'd like solutions to work regardless of shuffle luck.

To give a simple example, suppose you opened monument/donate, and then just played monument every turn for the rest of forever. On the nth turn, you would have n-2 points, so in this case f(n) = n-2 = O(n).

To do slightly better, suppose that you trashed down to a golden deck of bishop, silver, silver, gold, province, and trashed the province, buying a new one each turn. This would yield f(n) ~= 5n

It's not too hard to do better than linear in n, but I'm not sure quite how well you can do. I'll add the best that I've come up with so far after not too much thought in spoiler tags below, and leave it up to anyone interested to go crazy with this.

I was thinking about solo games, but feel free to try with 2 players if you think that would help (maybe you can do something with possession).

See also Busy Beaver amount of Coin and How high can you go for similar puzzles.

Function:

f(n) =O(n!)

Strategy: (I don't think this board allows infinite points in a turn, but I haven't thought it through enough to be fully confident.)

Have a vineyard on your island mat, and have a deck containing the following:

2 schemes
2 treasuries
2 scrying pools
potion
k ironworks

turn:

1. start with 2 treasuries, 2 scrying pools, and something else in hand
2. play scrying pools to draw the deck
3. play k ironworks to gain k ironworks
4. play treasuries
5. play schemes
6. play potion
7. buy scrying pool
8. Topdeck 2 pools with schemes, and 2 treasuries

You had roughly k actions at the beginning of the turn, now you have roughly 2k actions, for twice as many vineyard points. Next turn, you'll be able to play the 2k ironworks to gain 2k ironworks, and then play the extra scrying pool to play those 2k ironworks to gain another 2k, giving you roughly 6k ironworks in total (and buying another scrying pool). Doing this for n turns will yield O(n!*k) points, hence the value of f(n).


Perhaps one can do (asymptotically) better on this board, I just wanted to come up with something that did reasonably well. Feel free to come up with something better.

62

Puzzles and Challenges / Re: Infinite stalemate game

« on: June 30, 2017, 10:01:43 pm »

I was thinking about this the other day, turns out there is a thread on the forum from forever ago. A couple I had in mind:

1. You get down to KC KC Militia Masq, but your opponent already has more than half the VP islanded away (and can't empty any piles other than copper and curse). He can't end the game as long as you keep pinning him, and you don't want to end it because you can't win.

2. With tax, I think a scenario like the following might be reasonable:

The estates and some other pile are empty, and the only remaining VP are duchies and provinces. Scores are currently tied. There are two duchies left, and you hit 4 and 2 buys. Since you're afraid your opponent will hit 10 and 2 buys for the last 2 duchies, you tax the duchies twice. Your opponent hits 4 and 2 buys and does the same. This goes on until there's a huge pile of debt on the duchies. Eventually the same thing happens with the provinces when they get down to 2 left, and ultimately to every other pile in the game. The idea is that you never want to buy the 2nd to last of anything, because your opponent will almost certainly be able to afford the last one and a province (or duchy) before you can pay off the debt.

This feels like something that would only actually happen between two bots, but it seems like in the right situation it would arguably be the correct line of play.

63

Dominion General Discussion / Re: Best Uninteresting Moments in Dominion

« on: June 12, 2017, 11:40:04 pm »

I kept my hovel around so that I'd have something to reveal to my courtiers.

64

Dominion General Discussion / Re: What will the next Dominion expansion be???

« on: June 12, 2017, 11:14:21 pm »

One more rule that was broken: you can't play actions after you enter your buy phase (villa)

65

Puzzles and Challenges / Re: Most VP from 1 buy

« on: June 02, 2017, 11:11:04 pm »

I guess I viewed decreasing negatives from wall/wolf den as VP gain. Regardless, I think this is (roughly) the best I've been able to do:

Number of points: ~1500

Board:

Groundskeeper
Overlord
Haggler
Castles
Hunting Grounds
Market Square
Duplicate
Silk Road
Gardens
Black Market

Tower
Palace


Approach:

4 player game, 24 estates in the supply due to ambassador/moat/lighthouse/champion

Have the following in play:
10 groundskeepers
10 overlords as hagglers (you gained the last haggler mid turn after playing the overlords)
10 hagglers

Have 10 duplicates in reserve, watchtower + 10 market squares in hand, and the first 11 castles in your deck.  Also, you have 59 coppers, 39 silvers, 20 golds, 4 silk roads, most of the black market deck, and all the duchies, provinces, and colonies

Buy king's castle, gaining 20 cards from hagglers
Gain 8 hunting grounds, reveal watchtower to instead gain 24 estates
Discard 10 market squares to gain the last 10 golds
Gain the last copper
Gain the last silver
Gain 10 border villages, which also gain 8 silk roads and 2 gardens
Call 10 duplicates to gain 10 more gardens

Total points gained:
King's Castle is worth 24, and it increases the other King's castle by 2 and the 2 humble castles by 1 each
24 estates are worth 24
10 Groundskeepers gain 450 points in total
Gaining 8 silk roads each worth 24 points: 192 points
Gaining 12 gardens each worth ~50 points: 600 points
Gaining 45 victory cards increases your 4 existing silk roads by 12 points each: 48 points
Gaining the last 10 golds gives you 30 more palace points
Gaining the last copper, silver, gold, and border village gives you 140 palace points


Disclaimers:

1. I haven't verified that you can get to this game state (i.e. gaining all the last cards of the other piles and getting everything into your hand/where it needs to be), but it seems like it should be possible with the entire black market deck.

2. I'm not sure if anything in this allows unbounded VP gain with one buy. We can obviously leave offenders out of the black market deck, but I haven't fully thought through whether anything in the kingdom itself allows unbounded VP.


Feel free to comment if you spot any issues or anything.

66

Puzzles and Challenges / Re: Most VP from 1 buy

« on: May 31, 2017, 10:58:27 pm »

Do you need to buy a card, or is an Event possible?

(suggestion: do not allow Events; Triumph goes crazy.)

Events are not allowed (as the thing to buy).

67

Puzzles and Challenges / Most VP from 1 buy

« on: May 28, 2017, 10:28:00 pm »

Suppose you buy one card (resolving the buy and any effects triggered by that buy). What is the largest number of VP you can gain from that process? Here are the rules/constraints I'm imposing:

1. (at most) 4 player game following standard set up procedures (at most 2 events/landmarks, etc)
2. You can choose the game state as long as it's legal (i.e. the game hasn't ended before your turn, it's possible to reach that state from a standard start state, etc)
3. On some boards, the number of VP you can gain might be unbounded (e.g. Temple). I want to restrict to setups where this is not the case.

Not sure if I'm forgetting anything, if you think something is amiss, feel free to comment.

68

Dominion General Discussion / Re: Best Uninteresting Moments in Dominion

« on: May 25, 2017, 01:00:12 am »

Opened plan + swindler. My opponent ignored plan, which ended up being a good choice, as my first 3 swindler plays hit his 3 shelters.

69

Dominion General Discussion / Re: Forced Wins Training Sessions

« on: May 21, 2017, 10:42:08 pm »

How do you know he won't react to the mountebank by discarding a curse?

Procession: Butcher. Trash Butcher+ 3 coin tokens for province. Trash Loan + 3 coin tokens into hunting grounds.  Trash the played butcher and gain hunting grounds. 2 piles empty, 26 - 20.  Play Mountebank, curses empty.  Buy province, 26-25 win.

70

Puzzles and Challenges / Re: Busy Beaver amount of Coin

« on: April 28, 2017, 11:47:50 pm »

For those interested, I'll outline my best idea with spoiler tags. The first tag contains the board. The second tag contains my approach and result.

Board contains:

Hermit
Bank
Villa
Counterfeit (or whatever nonterminal that gives at least 1 coin and +buy that you want)
Raid



Start your turn with a hand of \Theta(n) madmen, n/4 banks, n/2 silvers, and \Theta(n) counterfeits in hand.

1. Play silvers and counterfeits to get \Theta(n) buys and coins
2. Buy raid to gain n/2 silvers
3. Buy and play villa
4. Play 2 madmen to draw n/2 silvers
5. Play n/2 silvers
6. Buy raid to gain n silvers
7. Buy and play villa
8. Play 3 madmen to draw n silvers
9. Play n silvers
10. Buy raid to gain 2n silvers
11. Buy and play villa
12. Play 4 madmen to draw 2n silvers
...
Keep doing this until you run out of madmen, which will happen after \Theta(\sqrt(n)) iterations.  In total, your madmen
drew \Theta(n*2^(\sqrt(n))) silvers.

After playing all the silvers, play your n/4 banks, each worth \Theta(n*2^(\sqrt(n))) coins apiece.

This yields \Theta(n^2 * 2^(\sqrt(n))) coins overall.

I believe my analysis is correct. If you spot any mistakes, or think there's a way to generate an unbounded amount of coin on this board, feel free to comment. Also, of course feel free to expand on my idea to do better.

71

Puzzles and Challenges / Busy Beaver amount of Coin

« on: April 28, 2017, 09:41:30 pm »

Consider a modification of (1 player) dominion, where supply piles are infinite (or if you don't believe in infinity, arbitrarily large). Suppose also that you start your turn with an n card deck, and all of those n cards are in your hand.

On certain boards, it is possible to construct such a scenario where you are able to generate arbitrarily many coins on your turn (e.g. a board with highway and villa (and n >=4), since you can play 4 highways and then buy and play arbitrarily many villas).

I want to only consider boards on which, for any positive n, the number of coins you can generate is bounded by some (finite) function of n (call it f(n)).

What's the largest achievable f(n)? Clearly you can get at least f(n)=5n (just have a hand with n platinums). However, you can certainly do much better than this. I'll break this up into 2 parts:

1. What's the best O() complexity achievable? Is it O(n^2), O(2^n), O(2^2^n)?

2. Can we also figure out the optimal constant?

I have some thoughts on 1, but probably one can do better than the best I've come up with. Feel free to let me know if you find any issues with my formulation.

72

Dominion Articles / Re: Golden Decks

« on: April 14, 2017, 07:53:58 pm »

Crossroads, Butcher, Mint, Distant Lands, Beggar

73

Dominion General Discussion / Re: Neat card interactions that were useful in the game you found them in.

« on: February 18, 2017, 05:35:05 am »

Transmogrify + Catapult/Rocks

Transmogrify helps turn estates into catapults to help get to the rocks.  Once rocks are uncovered, you probably have mostly coppers and a bunch of catapults, which ends up working out quite well.  Say for example you have a transmogrify on your tavern mat and a hand of 2x catapult, 3x copper.  Call tmog to turn a catapult into a rocks, gaining a silver to hand.  Play the other catapult to trash the rocks, gaining a silver to hand.  Now you have 8 for a province, and you curse+discard attacked your opponent.

I saw this in a game a couple days ago, where it won handily.  Squire helped somewhat, but it was clear that this was the main interaction.

74

Rules Questions / Re: Type of Pile

« on: February 09, 2017, 09:18:41 pm »

The randomizer. So Encampent can take any token, even when Plunder is top. Castles can take no token even if Small Castle is on top.

This is sad.  I want to be able to ferry small castle, ambassador back my two humble castles (opponents reveal trader), and then stonemason a squire into two humble castles and dame josephine with groundskeepers in play.

75

Dominion General Discussion / Re: Neat and potentially useful card interactions

« on: December 30, 2016, 07:17:07 pm »

Vault + Scrying Pool

Draw your deck with scrying pool and a couple villages, then play a vault and discard all your action cards for coin and use a scrying pool to draw them all back.  It needs villages, +buy, and maybe some trashing to really work optimally, but can be a huge source of payload when it works.  The fact that you can discard specifically your actions for coin to guarantee that you can draw them back with scrying pool and repeat several times makes it more than just the "vault likes big hands, scrying pool likes payload actions" generic synergy.