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1

Puzzles and Challenges / Re: Menagerie-only: fast win with perfect shuffle luck

« on: October 23, 2021, 06:19:52 pm »

Using only two landscapes, at most one of which is a Way, you can buy 8xProvince on turn 4. (Such kingdoms conform to the Menagerie rule book's randomization recommendations.)

SPOILER WARNING: there are no spoiler tags

Shuffle luck required:

• Open 4/3 or 3/4
• Your third hand is 1st buy, 2nd buy, 2xCopper and at most one Estate (in retrospect, this can be relaxed to "hit $5 except in a particularly bad way")
• One very friendly shuffle near the end

The key ideas:

• Use Stockpile/Gamble to get a good chunk of money
• Use Cavalry/10xDestrier to play 10xStockpile for $30 instead of gambling them for $10.
• I think this can get to $56 and enough buys for 7xProvince and a 3-pile, with merely quite good shuffle luck.
• Use Animal Fair with Gamble to turn actions in hand into net +$2 per card trashed (and gaining buys)
• Use free Wayfarers as Animal Fair fodder.
• This gets to 8xProvince, using obscene shuffle luck.

The steps:

Open Stockpile plus Bounty Hunter.
Exile Estate with Bounty Hunter on turn 3, play Stockpile and buy Stockpile plus Stampede.
On turn 4, draw 2xEstate, 5xCopper and 3 random among {2xCopper, 2xStockpile, Bounty Hunter}

Play everything in your deck except 2xEstate, by buying 2xGamble.
That is, play 6xCopper, 2xStockpile and Bounty Hunter exiling Copper, for $(15 - 4) = $11 and 3 buys.
(If you have Bounty Hunter in hand: play it, exiling Copper, and all treasures, for enough to Gamble twice to play the last treasures. If you don't have Bounty Hunter in hand, reserve one Copper, play the other 4xCopper you were guaranteed to draw, plus all other treasures, with enough money to Gamble the rest into play. Either way you play your entire deck minus the exiled Copper and minus 2xEstate, and have 1 or 2 actions left depending on whether you gambled Bounty Hunter or not.)

(Your turn three hand can also be Bounty Hunter, Stockpile, 3xCopper; exile a Copper in turn 3 and an Estate in turn 4 instead. That exiles the same two cards, for +$3 each time, and you're guaranteed to have all Estates in hand so they don't interfere with Gamble. TL;DR: it's the same, it doesn't matter)

Buy Stockpile, gamble NxStockpile for net +$0 and +2 buys (N=3 initially). Repeat this a total of 7 times, leaving one Stockpile in the supply.
This nets you $(0 + ... + 6) = +$21 and +(2 + ... + 8) = +35 buys. You have $32 and 38 buys. [You can win now by 4-piling Estate, Stockpile, Destrier, Wayfarer, even if there are 12 Estates.]

Buy Stockpile (discarding 9xStockpile), 10xDestrier, 8xWayfarer, Cavalry. You have $25 and 18 buys. Draw 2xDestrier off Cavalry's on-gain. [If I cheat-shuffle, the deck is Destriers then Stockpiles then Cavalry then Wayfarers. Less rigid shuffles will do, but not by much. This is where the obscene shuffle luck happens.]

Play 10xDestrier for a hand of 10xStockpile, Cavalry, Wayfarer. Play Wayfarer drawing 3xWayfarer.
Play 10xStockpile. Have $55 and 28 buys.
[You could have $56 if you had bought a Copper and no Wayfarers, with only very good shuffle luck. This buys 7xProvince which is majority VP if you don't put cursers in the kingdom, and you can also three-pile Stockpile, Destrier, Wayfarer on top of this.]
Gamble a Wayfarer into a hand of Cavalry+6xWayfarer, and $53.
Buy 7xAnimal Fair by trashing your hand (you have 21 buys).
Gamble all of them, to hit $67 (each is net +$2, total +$14) and at least 21 buys.

Buy 8xProvince. Optionally buy Estate and the Curse pile.

Cards used: Bounty Hunter, Stockpile, Destrier, Wayfarer, Cavalry, Animal Fair // Gamble, Stampede

Come to think of it, you probably don't need Bounty Hunter. Just open 2xStockpile, buy Stampede in turn 3 and draw deck on turn 4. You need a bit of shuffle luck to draw 3xEstate and not have them interfere with your gambling, and you need to spend at most one Stockpile when you buy Stampede since you need 2 buys to kick off. If you spend one Stockpile on turn 3, you have an 11-card deck with $10 in it, out of which you need to spend $2 on a Gamble. So you start with $8 instead of my $11, and end with $64 instead of $67.

You can also wiggle the Wayfarer business a bit: the terminal one can draw 3xCopper instead of 3xWayfarer, and you can gamble twice instead of once if you buy 9xWayfarer. This transformation nets $1. If you gambled the turn 4 Bounty Hunter you have 2 actions and not just 1, so you can draw 6xCopper with 2xWayfarer, gamble twice and draw the remaining 6xWayfarer dead. This nets an additional $3 on top of the $1. So I think you can hit $71, and also empty three piles before playing Animal Fair (spending an additional 8 buys gross, 1 buy net).

2

Puzzles and Challenges / Re: The Ultimate Legal Fairground

« on: October 10, 2021, 12:24:25 pm »

I'm thinking that it may be fun calculating the values of the Ultimate Gardens

Long ago I came up with the puzzle of setting up the longest sequence of known top-decked cards, see http://forum.dominionstrategy.com/index.php?topic=17923.0. It turned out to be an exercise mainly in maximizing how many cards were in the game. The solution is probably outdated, given e.g. Horse.

Maximizing Gardens probably amounts to the same thing: maximizing how many cards are in the game (given that at least one of them is Gardens). Is it OK if you buy Gardens in the Black Market? That way, you can have a 10- rather than 8-card pile in 2-player games.

3

Dominion General Discussion / Re: Cards essential to infinite loops

« on: October 10, 2021, 11:40:44 am »

Maybe I can make the question in a different way. Which are the features of the cards that make possible to them create an infinite loop?

For a lot of loops, the key is being able to remove things from play, such as with Mandarin or Bonfire, so that they can be played again.

Your categorized lists earlier in this thread are very nice, I'll have to bookmark this thread. Even so, I feel like answering your original question in my own words, in the hope it's helpful to someone (who might be me, if I invite corrections).

There are a lot of quantities in Dominion which typically only move in one direction:

• Number of actions
• Amount of money you have to spend
• Your number of buys
• The number of cards in play
• The number of cards in the trash
• The number of cards in the supply
• How far you have progressed along the phase trajectory (action -> buy -> night -> cleanup)
• I'm sure you can think of more quantities here

The most interesting quantities are those tied into your ability to change the game state—most often by playing a card, but sometimes by triggering on-buy, on-gain and on-trash abilities (and triggering reactions, but they're typically not powerful enough to be useful).

There are many effects which give you +2 actions, +(1-5) cards, +$1, etc.; those are not so interesting. Effects that take cards out of play, or out of the trash, or return them to the supply, and so on, are rare; much rarer than vanilla bonuses. It makes good sense to make an inventory of those effects, as you have done, since if you can use one of them to overcome a limitation, you can usually think of vanilla cards that fill in whatever the gaps are. The rarest effects are, in some sense, those that are most responsible for enabling loops. [For example, give each card a point for every valid kingdom with a loop it occurs in; your lists will likely contain all the high-scoring cards: the more substitutes a card has, the less of the point mass will be dedicated exclusively to it.]

There are some other effects that may sometimes be useful, such as repeatably stealing a card from your opponent's hand via Masquerade, Cutpurse, Pirate Ship and Treasurer (or Thief), as I did here: http://forum.dominionstrategy.com/index.php?topic=15366.msg697190#msg697190. This was necessary as a side effect of using Ambassador to return Villa to the supply; these days, with Way of the Horse, those shenanigans are likely not necessary, but it may be useful to know techniques and combinations for achieving various tasks such as this. All of these are unique (IIRC) tools for taking a card out an opponent's hand without making them discard, repeatably forcing a discard (without gaining treasures to your discard pile), trashing a Copper in your opponent's discard pile and gaining Copper from the trash. None of them are obvious loop enablers, and maybe Pillage is better, but they do work around a limitation of Ambassador which is a (more obvious) loop component.

The tokens from Peasant/Teacher are also often helpful, see e.g. http://forum.dominionstrategy.com/index.php?topic=20927.0. They don't circumvent any of the unidirectionalities I outlined above, but they often help a loop be net neutral or positive on some resource, such as buys in the linked example (or money, if you use Highway instead of Merchant Guild). Resource conversions are also useful to know about: money into buys via Travelling Fair, trashes into money with previously played Priests, and buys into trashes via Advance, for example.

4

Puzzles and Challenges / My kingdom for a Horse: a minimalistic (but slow) loop

« on: October 10, 2021, 07:05:33 am »

Here's a loop:

• Draw your deck
• Play 5xMerchant Guild
• Buy a Cavalry (gaining 5 coffers)
• Draw the Cavalry from its own on-gain
• Play the Cavalry using Way of the Horse
• Spend 4 coffers
• Go to step 3

This nets you 1 coffer per iteration. Add Travelling Fair or a +buy token from Teacher to buy the whole kingdom for a horse. Putting a +action token from Teacher on Merchant Guild saves you from needing a village.

Merchant Guild is convenient and unique in that it effectively reduces the cost of Cavalry below zero. You can use other cost reducers instead (e.g. Highway) if you net money via some other channel (e.g. a +$1 token). You can also use Villa instead of Cavalry, but then you need to come up with a buy somehow. You can't do both substitutions unless there's something I've missed.

If you play the following kingdom, there's a slow but guaranteed way of going off:



Here's how to go off (slowly, and probably without many surprises):

• Get to Merchant Guild plus Soldier
• Do the Teacher business
• Get to 5xMerchant Guild
• Gain the Horse pile
• Draw your deck and go off

To get to Merchant Guild plus Soldier: either open Merchant Guild + Peasant and promote the Peasant, or open Peasant + Peasant, promote the Peasant to Soldier, pass until you reshuffle, then play Peasant using Way of the Horse the first time you draw it. That divides the $9 of your deck across exactly two hands; buy Merchant Guild on the hand that hits $5. (You play Peasant either on the first or second hand of your shuffle, or the first hand of the next shuffle if it misses.)

To do the Teacher business: promote your Soldier to Teacher (passing while you wait to draw a Traveller), then play and call Teacher repeatedly to place the tokens, then leave Teacher on the mat. (You may optionally put +$1 on the Peasant pile, if you think it speeds up the next step.)

To get to 5xMerchant Guild: buy Merchant Guild whenever you can. Play Merchant Guild whenever you can. If you can't buy Merchant Guild on the turns where you play Merchant Guild, instead buy a Peasant (gaining a coffer). Play the Peasant using Way of the Horse whenever your draw it. (You can interleave this step with the previous; if you prioritize the Teacher terminals the previous step is guaranteed to eventually complete.)

To gain the Horse pile: with 5xMerchant Guild plus your starting cards, you're guaranteed to hit $4 eventually (you can't spread 3xEstate across three hands such that there's at least two estates in each, and your non-estates are each worth $1). Buy a Cavalry. Play it every time you draw it, until you've gained the Horse pile. You can speed this up by buying more than one Cavalry (so you can play them more often) and by buying arbitrary actions (e.g. Peasant) which serve as Horses (by the Way).

To draw your deck: hold your horses until you reshuffle. Then play a Horse whenever you have one (including Cavalry using Way of the Horse). Pass if you haven't drawn your entire deck. Eventually (in at most four turns) you will. In detail: you have 15 stop cards, so playing 11xHorse will get you to a hand size greater than the number of stop cards; at that point you will draw your deck. That means you can burn 20 horses and still have enough (by "burn" I mean play a Horse on a turn where you don't draw your deck). But you can burn at most 10 horses: every Horse you burn gets you past a stop card; eventually you will have drawn past all of them, or rather enough.

Formally, after discarding but before drawing your hand in the clean-up phase, the number of horses in your deck exceeds the number of stop cards in your hand by at least 11:

• when you first reshuffle it's 31 vs. 15 (and 31-15 = 16 > 11)
• after discarding once it's 31-X vs. 15-5-X where X is the number of burned horses, and 31-X - (15-5-X) = 31 - 10 = 21 > 11
• after discarding twice it's 31-X-Y - (15-5-X-5-Y) = 31 - 5 = 26 > 11
• after discarding three times it's 31-X-Y-Z - (15-5-X-5-Y-5-Z) = 31 - 0 = 31 > 11
• eventually there will be zero stop cards left in your deck, along with 11 or more horses
• (this analysis generalizes to any positive initial hand size, though for a hand size of 1 you'll need 15 horses)

Technically you'll only need to play 10xHorse (with a hand size of 5): that draws all your stop cards. During the first loop iteration you'll draw two more horses off of Cavalry's on-gain. Play Horse until you draw the Cavalry you gained, then resume the loop.

If my math is wrong and you need way more horses than I think: gain an unbounded number of coffers the slow way, by repeatedly buying (and later returning) Peasant. Then buy 9 cards from every pile of actions cards, and put the entire Peasant line into your deck (30 cards). Then gain the Horse pile. That ought to be enough.

5

Variants and Fan Cards / Re: Really bad card ideas

« on: September 17, 2021, 07:27:55 pm »

Inflation
Project
$0
Every fifth time a player plays a treasure, they gain a Ruin.
When you buy Inflation, +1 buy and +

-----------------

[The ruination is quadratic in the number of players. One of several reasons this is a bad idea.]

6

Dominion General Discussion / Re: Homage to the Best Card

« on: October 24, 2020, 03:07:37 am »

When a bunch of goons are disturbing your study time

7

Dominion Articles / Re: Sometimes you don't need to trash right away

« on: September 16, 2020, 05:48:12 pm »

I think "tempo loss" can be broken down into two parts: one is, you can start drawing large chunks of your deck even with light trashing and getting the trasher is a turn spent not getting more draw. Another is where trashing interferes with your economy in a way that detracts from building. That is, the decrease in draw is not (only) from not buying draw on the turn where you buy the trasher, but (also and primarily) from not buying draw on later turns.

I've recently played on this kingdom:



(Estates and Provinces, no landscapes)

I want to draw my deck with Festival and Library, to do it I want to trash, I want to be very treasure-light and I would like to get an Artisan to help me get Festival and Library if I can find time to do it. How should I open? Thinning is winning so I get Silver and Moneylender, and my first $5 is Sentry, yes? Or maybe even Moneylender/Cellar to play Moneylender more often?

Maybe, it looks plausible but I'm not super duper certain: opening Silver plus terminal silver gets your money to $11 in 12 cards or slightly less than $1/card (= $5/hand on average). Moneylender only trashes Copper and Sentry only increases your money density on average if you either selectively trash estates or your money density is already at least $1/card or you look at Copper+Estate. How do you hit the next $5? A second silver is unattractive in your eventual Festival/Library deck, Militia fights with Moneylender for terminal space (as does Vassal early), so Poacher? A fine card that you're happy to have, but are you happy with that plan for hitting $5?

Getting a Festival as your first $5 helps your economy while also making it more attractive to add a second terminal silver. You might want to delay trashing until your economy is at the point where trashing actively improves your economy (i.e., on this board, your chance of hitting $5). So maybe Moneylender/Silver, Festival as your first $5 and Sentry as the second $5, then more Festivals?

... or did I just get burned by a bad experience that was due more to variance and bad luck than the fundamentals I'm trying to point to, and I'm rationalizing it post-hoc? I had a hard time hitting $5 opening Moneylender/Silver.

In any case, I think the general pattern I'm talking about is clear: missing a key price point really hurts and the particular trashing on the board hurts your chances of hitting that price point until you build for a little while, yet you also want to trash. (And the trashing is on the slow side, maybe.) On those boards I think it makes sense to delay trashing. Identifying those boards seems non-obvious. Perhaps non-obvious enough that I failed

8

Dominion Articles / Re: Mandarin-Scepter Loops

« on: September 16, 2020, 05:03:30 pm »

• An Action that will gain a $5 cost Action on-play, while staying in play. Without cost reduction, this basically means Artisan or Altar, although Altar requires having things to trash.

Don't forget University.

I think the OG loop (one of them) was Lurker + Watchtower + Mandarin + Overlord-as-Crown with a self-trasher (e.g. Raze). Overlord has been changed, but Scepter-as-Lurker can still gain Mandarin from the trash, Watchtower in hand can put the Mandarin back where it does the most good for you, and a Scepter'd Watchtower can draw you more Scepters.

Lurker gaining all the actions you can eat (topdecked with Watchtower if you want) is also a very nice and flexible payload of such a loop, if you can play them after a Scepter. Villa is helpful here.

9

Dominion General Discussion / Re: Feedback wanted on my "make rebuild interesting" Dark Ages designed kingdom

« on: September 16, 2020, 04:17:12 pm »

[analysis of Feodum stuff and the moneyish strategy]
If you replace Marauder with Jack, I would expect the Rebuild vs money matchup to be more even, possibly in the money player's favor.

Noted, thank you for the suggestion.

I was considering adding Hermit, which trashes shelters and gains silver about on par with Jack; the draw and self-spy effect is less strong with Hermit. If Hermit going in is not kicking out Market Square I think I'm no longer going for Rebuild. Hermit instead of Market Square is probably not as good for money as Jack instead of Marauder. How do you think Madman impacts Rebuild vs. other strategies?

My super duper hot take: the biggest effect of Madman is to draw your broadly-understood gainers (Rebuild, Rogue, Squire/Forager/Feodum), so it amplifies the difference between the gainer-oriented strategies—whichever was stronger becomes stronger still. Madman in big money to me feels... you know, nice but not earth-shattering. Most likely 8 cards is not going to get you a double province turn—a money density of $2/card with a +buy probably means you overbuilt.

10

Dominion General Discussion / Re: Feedback wanted on my "make rebuild interesting" Dark Ages designed kingdom

« on: September 16, 2020, 03:55:54 pm »

That's kind of the thing about Rebuild. It's [everything or nothing]. There's no sprinkling in Rebuild into the middle of a normal game, [and when Rebuild dominates] there's no board interaction or meaningful build decisions or what have you [...].

I haven't played a lot with Rebuild but I've seen it played on video. Most random rebuild games look a lot like this: get a few silvers, get two rebuilds, try to win the duchy split, and on $0-$4 hands you consider whether you want more silver or more whatever-the-only-support-card-is. (Assuming you do go for Rebuild.) That agrees with what you're saying 100%.

I tried building a kingdom where that is not true. Did you mean to say that in your eyes I failed? If so I would love to learn where I went wrong. I can believe that even though Rebuild interacts more with this board than with random Rebuild boards, the build decisions are straightforward and thus uninteresting. Do you find that to be the case?

Alternatively, are you saying you don't go for Rebuild on this board? If so, what would you go for, and why do you think it's stronger than Rebuild?

... or am I reading to much into your comment?

11

Dominion General Discussion / Re: Feedback wanted on my "make rebuild interesting" Dark Ages designed kingdom

« on: September 15, 2020, 03:33:10 pm »

It has some cards in it that are good cards, but it doesn't mean there is a strong non-Rebuild strategy available. And there isn't.

I'm interested in this point. What's the strongest one or two non-Rebuild strategies you see here, and why do you think they're too weak? Are there moderate tweaks that could be made to make them approximately competitive?

I see something moneyish with Squire, Forager, Market Square and maybe a Rogue or two to steal Duchies. I also see Squire/Feodum, again with an opportunistic Rogue or two thrown in. I have a hard time evaluating them, but they at least seem coherent and potentially good.

How would you play Rebuild against them, and why would they fail?

12

Rules Questions / Re: Obscure ruling for single-players / play-removers / durations

« on: September 14, 2020, 04:38:02 pm »

I have to make a ruling for, in what circumstances is a card no longer "that card." I need this because we can actually lose a card while still caring if it's "that card." In particular if it's shuffled into a deck we've lost it; so, a card shuffled into a deck is no longer "that card."
[...]
In practice we can totally know if we have the right card; and if we aren't sure which physical card is which that doesn't matter, I can say, "I take the one that's the same one" or "I take a different one." In these situations that never come up. But, shuffle it into a deck and man, we don't know and there's no way out (except now this ruling).

I love edge cases. I think this one says the decision you went with later is a good one, and the "it's no longer 'that card' when you shuffle" is incomplete. Here's the edge case:

I play a duration card, let's say Fishing Village. I take it out of play and put it back into hand. Using Secret Passage I put the Fishing Village somewhere in the middle of my deck without counting. Then I play Scrying Pool, drawing cards up until roughly about where I put the Fishing Village. I play Vassal, hitting a Fishing Village.

Is it "that card"? Who the knows...

The duct-tapiest workaround ever is to say that you either count where you put the Secret Passage card, or else what you're doing is a very limited form of shuffling, and so it's no longer "that card". What does that do to Stash? 

Like I said, I like your later decision.

13

Dominion General Discussion / Feedback wanted on my Dark Ages kingdom designed to make Rebuild interesting

« on: September 14, 2020, 02:44:31 pm »

I tried designing a kingdom with Rebuild and 9 other Dark Ages cards that would be interesting. This is my first revision:




(Shelters and Provinces, no landscapes)

Would you consider this kingdom interesting to play (and also: fun)? If an interesting Rebuild kingdom (100% Dark Ages) is something that exists in your world, could this be made more interesting, and if so how?

My design process is not particularly sophisticated: pick Rebuild, then pick all the cards that interact with how a normal Rebuild game plays out.

Trashing non-Rebuild cards increases your Rebuild density and trashing your money density up to $1 increases your Rebuild and Duchy gain rate. Junking un-trashes your opponent. Scavenger and Pillage do card (de-)selection, Market Square and Rogue interact with the trash(ing). You know, "+$2, gain a Duchy" is great. Feodum gives Overgrown Estate two paths along which it can be promoted into Duchy, and Squire lets you gain the expensive attacks without Rebuild or Duchy being part of the opportunity cost. Death Cart might give you Province money, and if 2xMarauder pile the ruins it's nice to gain. Squire/Feodum with Rogue support might let Rebuild play a non-mirror for once. Is Rebuild/Feodum a thing?

The missus and I had fun playing the kingdom and I found it interesting, so mission success, mostly. I have been underwhelmed by Marauder and Death Cart; everything else played roughly how I expected. Maybe I'm underestimating Marauder, though? Forager is happy to trash the ruins, but making $1 off of two cards makes it hard(er) to hit $5.

The card selection effect of Scavenger is very overt. Sage and Wandering Minstrel are more indirect in their Rebuild-finding effects, and maybe more interesting but perhaps also clumsy enough that they won't see play? Sage will find a lot of non-Rebuild cards and Wandering Minstrel will help your terminals collide. Maybe making them work is an interesting challenge? I think not, but it seems worth experimenting with.

I think Poor House might be a worthwhile Death Cart replacement in v2 of the kingdom. It'll help you hit $5 with support (Silver, Forager, Squire), but at the cost of terminal space; it might be easy to pick up off a spare Forager buy.

Anyways, I've rambled enough. Would you find the kingdom interesting and fun to play?

14

Variants and Fan Cards / Re: Really bad card ideas

« on: September 14, 2020, 01:39:50 pm »

Scout(n) - Action - $(4+n)
[...]
Infiniscout
[...]
MegaScout

NegaScout — Action - Scout — $4
+1 Action
Look at the top four cards of every other player's deck. Trash all revealed scouts and put the rest back in any order you choose.

(See also https://en.wikipedia.org/wiki/Principal_variation_search)

15

Variants and Fan Cards / Re: Really bad card ideas

« on: September 14, 2020, 01:28:27 pm »

Look at the top four cards of your deck. Put the rest back in any order.

Synergies: Pearl Diver and Secret Passage.

16

Dominion General Discussion / Re: Help me understand missing the shuffle

« on: September 14, 2020, 01:20:04 pm »

TL;DR: yes, it sounds like you've understood the idea.

The long version, just to be on the safe side:

The basic idea of "missing the reshuffle" is that you'll be able to play the cards at the bottom of your deck less often than the rest.

Let's go over an example. Let's saying you're playing the "first game" recommended kingdom from the base set, and your first two buys are Workshop and Remodel. At the end of turn 2, you shuffle.

Scenario 1: your cards, in order, are ccceW cceeR cc (c=Copper, e=Estate, W=Workshop, R=Remodel). You play Workshop on turn 3, you play Remodel on turn 4, then you shuffle again. Let's say you gained a Village, bought a Village, remodeled Estate into Smithy and bought a Cellar. You shuffle again. The cards in your deck, in order, are cc-eeW ccccR and more stuff. The two coppers before the dash are the ones that were at the bottom of your deck after your turn-2 shuffle, the rest are the cards that go below them after shuffling. On turns 5 and 6 you can play your Workshop and Remodel again.

Scenario 2: your cards after the turn 2 shuffle are ccceW cccee cR. You gain a Village and buy a Village on turn 3, buy a Village on turn 4 (perhaps not the best idea), then reshuffle. Your cards at the start of turn 5 are, in order, cR-cce, cccWe and then some more. On turn 5 you play Remodel, on turn 6 you play Workshop, and so on.

Note that in scenario 2, by turn 6 you had played Workshop twice and Remodel only once. Compare this to scenario 1 where you played both of them twice. That's the essence of missing the shuffle.

If you like, you can think of "a shuffle" as a set of cards: the cards you will have in hand and be able to draw before the next time you shuffle. In scenario 1 those are 5xc, 3xe, W, R. In scenario 2, they are 6xc, 3xe, W (but not R). In scenario 1 you have 2xc miss the shuffle; in scenario 2, cR miss the shuffle: you won't get to play them before you reshuffle (which is usually a while if you don't see all your cards every turn).

Let me work over an example with Minion.

Let's say your starting hand is Minion and 4xEstate and you have an empty discard pile. You play Minion for cards and draw Minion with 3xEstate; now 4xEstate are in your discard pile. You play Minion for cards again, you get Minion with 3xEstate again, you Minion for cards again (10 Estates in the discard), you 4xMinion and your deck is now empty. You play 3xMinion for money. If you play the last Minion for cards, you'll shuffle your 10 Estates and draw 4, leaving 6 on the deck. Then, after having bought something, you discard your 7 Minions and draw a hand for next turn. That hand will be 5xEstate. You'll have one Estate on your deck, and your discard pile will be 7xMinion plus the card you bought ("and for $6... the last estate"). You'll have made all your Minions miss the shuffle.

Obviously a hand with 5xEstate is super duper bad; you'll do nothing for that turn.

Okay, so that's a highly contrived example: misplaying the last Minion set you up for the worst turn possible. If instead of discarding Estate you had discarded, I dunno, Steward and a Silver and some other cards which are fine and decent cards but which won't help you find your Minions, you won't be seeing all your cards on the next turn, and thus you'll (most likely) have a less powerful turn than if you had more Minions in your draw pile.

I hope this helped.

17

Puzzles and Challenges / Re: Villa: To Infinity and Beyond

« on: September 13, 2020, 03:53:33 pm »

I'm not sure my 9-card loop was ever that useful, but I like it and I have an update I want to share: it can be done using only second edition cards, i.e. without Thief. In particular, Treasurer can get back the copper you send. Also, as an optimization, by alternating Pirate Ship and Treasurer as kinging targets, you need one less Lurker.

Here's the kingdom:




The setup is still equally ridiculous: empty their deck and get enough tokens on Pirate Ship. Have no non-actions in your deck, i.e. Masquerade your estates and either Bonfire your potion or gain Scrying Pool with Lurker. Have at least 3xCopper in the trash.

To kick off, play Scrying Pool to draw your deck, then King's Court on King's Court, kinging Treasurer for 3xCopper from the trash, Ambassador to also give your opponent three coppers, and a third (kinged) King's Court which begins the loop.

The loop is:
King a King's Court which kings a King's Court (yo dawg), kinging 4xLurker and a payload card.
Ambassador returning 2xVilla
Masquerade giving Copper and receiving Villa.
Cutpurse to make them discard the copper
Bonfire all the cards, using Travelling Fair to get enough buys
Buy back the second Villa
Scrying Pool to draw the second set of cards you gained with all the Lurker plays.

Cards played: 3xKC, 4xLurker, Payload, Ambassador, Masquerade, Cutpurse, Scrying Pool; 12 in total, which is how I cut out a Lurker.

The payload is initially a Pirate Ship large enough to afford three iterations of the loop when kinged (i.e. a single play affords a single iteration), then Pirate Ship for the trashing attack on the second iteration (putting 3xCopper in the trash), then Treasurer gaining 3xCopper from the trash.

The three-phased nature of the loop is why you gave them 3xCopper with Ambassador: that way the Pirate Ship attack trashes 3xCopper, the Treasurer gains 3xCopper and your Masquerade gives them 3xCopper.

Over the course of three loops, Pirate Ship gets an additional three tokens. It eventually becomes big enough to afford two/six iterations of the loop. Once that happens, on every third iteration you can alternate between playing Pirate Ship for the money and some other payload card. As before, you can omit the payload card to effectively payload a Lurker.

Alternatively you can add a fifth Lurker and play Treasurer and a second Pirate Ship every iteration. Then the Pirate Ship for money can get away with about a third of the tokens.

With the 12-card loop, you need $4 for Villa plus $18 for 6xBonfire plus $14 for 7xTravelling Fair, i.e. $36, so that's how big your Pirate Ship needs to be (except Cutpurse chips in $2 and Treasurer chips in $3).

Also, by my count you need 4 King's Courts to kick off and 3 on every iteration, which you Bonfire. That leaves one in play. If you played an odd number of cards (to payload Lurker), Bonfire the extra King's Court. The next time you play an odd number of cards, leave a King's Court in play and gain the extra King's Court from the trash. That is, you can alternate between trashing one card more and one card less than you played.

Note the beautifully interlocking gears of circular card flow:

• 2xVilla in your hand -> 1 in supply, 1 in opponent's hand -> 1 in supply, 1 in your hand -> 2 in your hand.
• 3xCopper in your hand -> opponent's hand -> opponent's discard -> trash -> your hand. Coppers leave your hand and your opponent's hand one by one, then go from discard to trash to your hand in batches of 3.
• One set of action cards in play, one in the trash -> 1 in play, 1 in discard -> 1 in trash, 1 in discard -> 1 in hand, 1 in trash -> 1 in play, 1 in trash.

The Monument is there just because I like it as a payload card.

18

Solo Challenges / Re: Copper Rush: Drain the Copper pile as fast as possible

« on: September 13, 2020, 09:16:18 am »

I need only 3 turns and an old old card I like.

Kingdom: Lurker, Develop, Watchtower, Coppersmith, Fortress, Villa, Band of Misfits, Counting House, Border Village, King's Court
Events: Advance, Travelling Fair

[...]

buy 25 Coppers, 8 Provinces, 8 Duchies, 8 Estates

Nice finish. You didn't trash any coppers so this is hard mode.

As far as I can tell you can't go infinite: you can never take cards out of play, you can never make money without playing a card and you never get more buys without either playing a card or spending money (on Traveling Fair). So when all the cards are in play, all the money is spent and you have used all your buys you can do nothing more, and every move gets you closer to that endpoint. So there's a finite upper limit on how many cards you play, how much money you make and how many buys you have, and you can't gain Copper without either playing a card or spending a buy. (You can gain a Copper with your Border Village, but you can only gain Border Village by buying it or playing Lurker or Develop.)

So the best known solution in the category 1st-edition-cards/hard/bonus is 3 turns. Well done.

(Also, hi, I'm back from my f.ds hiatus.)

nasmith99 and qvist, since I don't have a ShuffleIT subscription, would you mind sharing the general idea of your solutions?

19

Dominion Articles / Re: Occasionally Relevent Rule Edge-Cases

« on: September 11, 2020, 07:39:42 pm »

Playing Treasures During the Action Phase
So far, you can do this with Black Market and Storyteller.

In a wholly unsurprising turn of events, with Capitalism you can play your actions in your action phase as usual, but some of them will be treasures.

I don't think that's how you use Capitalism optimally.

You can also Crown a Smithy in your action phase, that's playing an (Action —) Treasure in your action phase.

With capitalism you can use a Black Market to play any number of action-treasure Black Markets and Storytellers. I would recommend you apply v2 of the "lose track" rule: if you deliberately make your opponents lose track of what the fuck is going on, game night is over.

Black Market and Storyteller are the only ways of playing non-action treasures in your action phase I know of.

20

Puzzles and Challenges / Re: Most Potions in 1 turn?

« on: July 29, 2019, 06:25:27 am »

I think with Scepter and/or Capitalism there are many more loops.

For example:

In play: Lurker and Smithy
In hand: Watchtower, 2xScepter, Potion
On deck: 2xScepter, Potion
In trash: Mandarin

Loop: play Potion, Scepter as Smithy (drawing 2xScepter plus Potion), Scepter as Lurker gaining Mandarin, topdecking 2xScepter and Potion, revealing Watchtower to put the Mandarin back in the trash. Now you're back at the starting position, except one potion richer.

Use Hunting Grounds instead of Smithy if you want to draw your deck. Use Council Room if you also like buying things, and use a Copper or an extra Scepter for money instead of Potion every now and again if you want to buy nice things not named Vineyard.

Lurker, Hireling and Bonfire can set up almost any situation fairly easily if you're a stickler for guarantees (against passive cooperation).

21

Puzzles and Challenges / Re: Maximum Wishes gained in a turn?

« on: July 29, 2019, 06:02:48 am »

I feel like we've reached the point in Dominion where the answer to all puzzles in the form of "what's the most ______" can by answered by "unbounded, here's the infinite loop".

You can design challenges that are inherently bounded above by the number of cards in the game.

For example, the poor house challenge (which I stole from Adam Horton), what's the most money you can lose by playing a Poor House—this is obviously bounded above by (approximately) the number of treasure cards in the game.

Or the top decking challenge: maximize the number of known cards on top of your deck. Mandarin gives you an easy score of 1, cartographer gives you an easy 4, etc.; obviously bounded by the number of cards in the game.

However, it feels like the puzzle design space around number-of-card bounds is at least 20% and maybe as much as 80% exhausted just by those two puzzles.

You could perhaps try "how many different [something]", though I suspect the answer will very often be "Black Market". There's also "how fast can you [something]", but without ruling out loops the answer is probably often "turn 1".

So I 80% agree: if you allow loops then either the design space is small or the answer is often trivial and easy.

22

Puzzles and Challenges / Re: Turing Machine from Dominion Cards and Mechanics

« on: July 27, 2019, 07:06:08 pm »

In Robert Hearn's thesis (https://erikdemaine.org/theses/bhearn.pdf), he describes a game where the game state itself is finite, yet deciding who wins at optimal play is undecidable. I'd start reading on page 69, "undecidability".

Erik Demaine has taught a course on computational complexity in relation to puzzles and games; I think he covers the particular game in

The basic idea is that you make the players simulate a turing machine but essentially shunt off the unbounded memory into the player's heads.

I don't know if it's useful here, but it sounds potentially relevant.

23

Puzzles and Challenges / Re: Give your opponent infinitely many points

« on: July 27, 2019, 06:07:51 pm »

I suspect there's some solution involving Tomb and Thief (or maybe Pirate Ship and Treasurer). That sure seems like the easiest way of giving them points.

24

Puzzles and Challenges / Re: RNG vs decisions

« on: July 27, 2019, 06:00:40 pm »

This is also a fun thought experiment on other games

For sure. One I've enjoyed doing: instead of doing the random thing, the player doing the random thing chooses the outcome (e.g. orders the cards that would be shuffled, selects the dice roll). Who wins?

For some Magic: The Gathering decks used at the world championship throughout 1998 to 2004 (or rather pairwise matches), this becomes solvable. I imagine player 1 wins at Machi Koro due to first player advantage, they can do everything player 2 can do but earlier. It's not fully coherent who decides the ordering of a shared deck. If the player receiving the card chooses which card to get, then player 1 wins Love Letter: take Princess and then Baron, play Baron.

Who replenishes the market when plants are scrapped in Power Grid? Who selects the plantation tiles in Puerto Rico? Who does the random setup in Terra Mystica? This notion is not always completely coherent, but when it is coherent it often generates interesting puzzles.

For example, the RNG player wins Monopoly.

Is there a simple argument for why this is the case? Like, the deck of random events is cashflow net negative and RNG can make decider hit it arbitrarily often while not landing on any property? Or going through a revolving door in and out of jail?

Let's do a few more.

Love Letter: if RNG plays first, RNG holds double Baron vs. Priest. If RNG player plays second, decider holds double priest, then faces double Baron. RNG wins!

Machi Koro: RNG rolls a 2 on their own turn and a 6 on decider's turn. Decider never lets RNG buy any building with their ever increasing fortune, and decider never goes above $3 and so cannot buy any victory buildings. Stalemate!

Star Realms: RNG cannot prevent decider from playing Viper 50 times, decider makes RNG never play anything. Decider wins.

Terra Mystica: Decider builds Temple, takes... IIRC FAV11, the one that gives 2 VP for building a dwelling. Then decider digs somewhere and builds a dwelling. RNG player never scores any VP. Decider out-earns RNG on the cult tracks, scoring 8 vs. 0-or-2 on each track. This easily outweighs the end-of-game resource conversion on the part of the RNG player. Have each player select the same bonus tiles in a cyclic pattern, and have the RNG player wast their power on e.g. digs or an unspent priest if they need to take an action to make decider quit first.

Puerto Rico: Decider buys a plant matching their crop type, if applicable, and mayors once, then the role selections are Craftsman, Captain, Trader for decider and Prospector, Builder, Settler for the RNG player. The VP earnings are 2 vs. 1 every Captain, for an easy win.

Twilight Struggle: load your opponent up with enough Defcon suicide cards at once I guess? OTOH, I guess a decider can always keep the defcon high enough to survive, then just take control Europe and score it for the win.

Food Chain Magnate: decider hires a Waitress on turn 1 and sends her to work every later turn; the RNG player never hires anyone. Decider wins.

Power Grid: Decider buys plant 4, RNG buys plant 5. Nobody buys any fuel or builds any houses for an awfully large number of turns, then decider buys two coal, builds 21 houses and powers one house for an easy win.

Power Grid: The Stock Companies (v1 and/or v2): decider invests in a company and runs it half-decently, it appreciates in value. In v2, it eventually builds 15 houses and powers one of them. The RNG player never invests. Play variant 3 as base Power Grid.

Splendor: decider has the RNG player only ever pick tokens, decider buys everything in deck 1, then deck 2, then deck 3, except decider will have already hit 15 VP before deck 3 is exhausted. To accomplish this, decider somehow accumulate two chips of every color to buy a card in deck 1, and has RNG player release any necessary chips by going over 10 (focused on other colors).

Coup: RNG always claims roles they don't have and decider calls the bluff. Or, RNG takes one coin per turn and decider steals two per turn. RNG is never forced to shoot decider, decider is forced to shoot RNG.

1846: decider buys any private company, then everybody passes on the second private to make the first private pay out, and repeats doing this until the bank breaks. Decider wins. (This works in several 18xx titles, but not all of them have randomness or 2p variants. I'm using the 2p rules from https://boardgamegeek.com/thread/1616729/draft-2-player-1846-rules-game-designer). It's noteworthy that you can win before your first "real" turn.

Warpgate: RNG player always spends their action cards drawing more cards. Decider draws cards on turns 1-3, and plays a movement card on turn 4, going towards a group of trade planets. Then, every later round, draw cards on turns 1-3, then play the trade action if you have it on turn 4. If you don't have it, move some ship not in the set of trade planets, and play the trade action on the next turn (they'll be the last two cards of the deck). Eventually get all the trade tokens. They're enough points to defeat an objective that's satisfied by default.

25

Puzzles and Challenges / Re: Make a Leprechaun give you a wish more than once in a turn

« on: July 27, 2019, 04:23:40 pm »

Use Majiponi's Overlord-as-Crown loop.

Play 4 Overlords as Crown, crowning the next Overlord. The 5th Overlord is played as a self-trasher and a Lurker which gains Mandarin (topdecking the four Overlords), revealing Watchtower to put Mandarin back in the trash.

The second play of the 4th Overlord is as Lurker, to regain the trashed Overlord (topdecked with Watchtower). The second play of the 3rd Overlord is any action costing up to $5, e.g. Leprechaun, and the second play of the 2nd Overlord is as Watchtower to draw all the Overlords you topdecked.

To make the Leprechaun give you a wish, have e.g. seven schemes already in play.