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301

Dominion General Discussion / Re: Any joy in putting Player tokens on 1E cards?

« on: October 15, 2017, 07:21:02 am »

Would that make Cape a specific category of card, the way Trasher and Village Splitter Bunch-of-Actions-Thingy are?

Yes! Bandit is also a Cape.

302

Dominion Articles / Re: Dominion 101: What is an engine?

« on: October 15, 2017, 04:21:32 am »

Regarding deck taxonomy, I think maybe a key distinction is this: if you were to replace each card in your deck with n copies of itself (for n=2 the starting deck becomes 14xCopper, 6xEstate), would you typically be drawing the same number of cards each turn, or the same proportion of your deck?

I haven't done the math, but I would assume that Smithy/BM draws the same 5-sometimes-8 cards if you double/triple/etc. the deck, and most conventional (village+smithy) engines continue drawing 100% of the deck when you double it, since drawing deck is a function of total +cards, having enough +actions to support that, and drawing those in the right order, all of which stay the same when you add more of everything while preserving proportions (I gut-sense). [hand-wavy justification-ish: sampling with and without replacement converge to the same limit when the thing sampled from grows to infinity. Variance decreases as n increases—the sum of more dice looks more bell-shaped and less flat.]

So my distinguishing criterion seems to do the right thing for typical BM and typical engine decks. Probably it also works for engines that draw 70-90% of the deck, e.g. 10xCity plus starting deck plus some Bridges—though I definitely would want to do the math here and verify that nothing weird happens when you double all the things.

The impact of drawing O(1) cards vs. Ω(n) cards is of course that your output on a typical turn is proportional to the average/total per-card output, respectively, and that changes how you build your deck. So even though I'm not running the deck-doubling thought experiment when analyzing a board, I probably am thinking through the implications of that math.

One open question: are there in-betweens? Are there decks where you draw something like Θ(sqrt n) or Θ(log n) as you double/triple/n-plicate your deck? What do they look like?

MQ raises both the trivial point that decks are not static over time (duh) and the non-trivial point that this makes "draws the deck" undefined unless we're talking about one or more points in time. For my O(1)-vs.-Ω(n)-criterion, "when you start greening" sounds like a good point in time, or else "at the maximum" (and please don't tell anyone that O(...) is a partial ordering)—these seem roughly to be what we mean when we try to distinguish between engines and non-engines. (I also read MQ's post as saying "there's quite a bit of gray area". I'm not addressing that here.)

303

Dominion General Discussion / Re: How to play this Empires board: C/R,ChR,G/F,Cstl,Tmpl,Ar,Lg,WH,Ov,RB + Pal,Rit?

« on: October 14, 2017, 03:31:27 pm »

I'd say use Temple+Catapult to trash down quickly, get a bunch of Archive/Chariot Race, a single Gladiator, try to get Fortune when you can, and pursue Castles - Archive lets you get decently big hands, so get Opulent Castle when you can. Ignore Palace, it's more important to be thin. I'd tentatively ignore Legionary, as Catapult's attack is stronger here and you want one anyway.

Thanks for the response.

Catapult's attack is stronger than Legionary: Assuming we can rank card goodness linearly, they would discard their two worst cards to Catapult, and do the same to Legionary but also cycle their median card. Probably the median card is average, so it's as good as what they'll draw—but it's harder to plan what to do when you have two chosen cards and a random vs. three chosen cards. I think this slightly favors Legionary. Also, eventually you will have trashed all the treasures you want to trash, and Legionary doesn't require any fuel, so maybe you transition to Legionary in the late game—after trashing and getting a Fortune? I have a hard time seeing cursing as relevant, since there is plenty of trashing. I mean sure, it takes up terminal space, but it eats your Silver. I guess maybe, if you have $3 spare above your main buy... ?

Ignore palace because it's more important to be thin: each use of palace is card-count neutral, but adding cards to be ritual'ed isn't, and staying on top of trashing is at the expense of attacking with Catapult (or digging with Gladiator). I take it this is what you have in mind, approximately? I was tired when I wrote this, I read "Palace" and thought "Ritual". Pedantic nitpicking: I think the goodness of being thin is non-independent of what else you're doing, so "being thin is more important" should probably be recast as "The palace-focused strategy is weaker than some other strategy which performs best when your deck is thin, hence you should thin down, ignore Palace, and do that other strategy", with which I agree. (On some boards Gardens rush beats Palace BM/slog, so thinness is not always good and is not the only argument against Palace.)

Get a bunch of Archive/Chariot Race: do you get as many Archives as you can here, or is a small handful enough? In my experience, decks similar to what you describe work ok-ish with 3-4 Archives; they would probably work better with 1 or 2 more, but the opportunity cost is often a Gold, so you're drawing a bigger proportion of a smaller total payload. Eh, if I replay this board I should probably try with more Archives just to compare. How big a deal is Chariot Race? It looks to me like it can safely be skipped in favor of more Silver.

I take it Wild Hunt and Royal Blacksmith are out of question in this deck: you have plenty of actions and few terminals, so there'll be a lot of dead draw and the cards will prove not worthwhile. Maybe Overlord could play here? It can trash your Catapult/Temple/Gladiator once you don't need those, then become a spare Archive or Legionary? (Or maybe Catapult if that's better.) The cost looks non-trivial, though.

How big a deal is Fortune? Clearly Fortune is a good card—but you can get it if your opponent goes for Gladiator even if you don't. If you pick up a Gladiator and your opponent doesn't, your advantage is a cheap terminal sometimes-Gold (esp. if paired with a Castle in a 2p game), you gain a Gold when you buy your Fortune, and you likely get to play yours first (assuming you have $8 when you uncover it). The cost of this is a large amount of terminal space used on playing Gladiator that could be spent either trashing or attacking with Legionary. Is that worth it?  Maybe the right timing of Fortune (if you have the only Gladiator) is such that you're likely to drain the last two provinces from the supply on your first Fortune turn—that way you try to maximize the value of the asymmetric benefits of uncovering Fortune.

I think you want to do the catapult thing.

Boss the Catapult split, pelt them with Rocks, then pelt them with a few Catapults once you have completed the bombardment?

304

Dominion General Discussion / How to play this Empires board: C/R,ChR,G/F,Cstl,Tmpl,Ar,Lg,WH,Ov,RB + Pal,Rit?

« on: October 14, 2017, 01:01:26 pm »

Recently I had the following 2p kingdom come up. How would you play it? Catapult/Rocks, Chariot Race, Gladiator/Fortune, Castles, Temple, Archive, Legionary, Wild Hunt, Overlord, Royal Blacksmith — Palace, Ritual.





No villages, the only +buy is Fortune, the only non-terminals are Archive and Chariot Race. That makes the board rather slow.

Here are some strategies:

• BMU: buy the most expensive of [Province, Gold, Silver] that you can afford until you run out the provinces (tactically bump up Palace points near the endgame, and/or buy Duchy, maybe). Has a hard time with Legionary (I guess); maybe Archive can help a little? But this deck gets thick very quickly (whatever "quickly" means on this board), so you won't have Archive often, or many of them simultaneously, unless you delay ramping up Palace points.
• BM+Archive+Legionary: trash a bit, get some Archives, get a Legionary and a few Golds, attack a lot, buy Provinces and maybe sprinkle in some Rituals. Perhaps Overlord plays here?
• Ritual golden(ish) deck: trash down, get some Archives, get a Fortune, repeatedly trash Curse, trash a Gold for VP, buy a replacement Gold. Transition into Provinces when the Curses are out.
• Jam your deck full of Chariot Races and expensive cards (Gold and Province seems good), some Archives maybe, milk CR for VP. Sounds not terribly awful, but in my experience with Chariot Race it has been... lackluster.
• Play one Wild Hunt per turn, gain 40 VP and an estate around turn 45 sounds terrible, quite easy to contest, at which point... question mark?

I think Castles can fit into BM/Archive/Legionary, maybe in Ritual/golden if you have the time once the Curses run out. I haven't tried putting them into BMU, but I think it likes Province better; BMU's VP/turn rate drops off pretty sharply once it hits 7 Gold/Silver/Copper triples. But in general they seem like an expensive and slow VP supplement, probably not worth going for unless you put effort into getting the two scaling ones ($3 Humble and $10 King's).

I lean towards thinking BM/Archive/Legionary is strongest. The draw is limited, so the discard attack is strong, it can green reasonably soon and use Archive as temporary pseudo-thinning of green cards, so it should be possible to build to a stage where in can semi-almost-reliably attack and buy Province for a small handful of turns. My very lovely opponent never bought Legionary (we played ~5 games on this board) which I think helped me a lot; she swore a bit when I played mine

What do you guys think? What's best here? Which cards never play?

305

Dominion General Discussion / Re: Any joy in putting Player tokens on 1E cards?

« on: October 14, 2017, 10:26:21 am »

2 Platinums, 1 Copper, 1 or 2 Adventurers 2.0 and perhaps a sifter and you will get a Colony each turn.

Is that not also true of Adventurer1.0, except slightly less so? Throw in a Peddler, or one of your treasures in your starting hand, or Scheme a Warehouse, or [...].

Of course, "3" is the magic number at which you can't buy the biggest green card with a smaller number of basic treasures, so Adv2.0 is a one-card combo in a way that Adv1.0 isn't, but... my guess is that a deck built around abusing Adv1.0 only performs slightly worse than one built around abusing Adv2.0, and not massively worse. Agree/disagree?

Adventurer is incredibly weak but digging for 3 Treasures would be too strong (and boring).

Let's hijack this thread into "how to designed a better but well-balanced Adventurer2.0" until someone tells us to stop

If 2 treasures is too weak and 3 is too strong, how about 2.5? i.e. "dig for 3 treasures, choose 2, put them in hand and discard the other cards".

Initially it's a terminal silver. It quickly(?) becomes a terminal gold, with potential to become more than that if you put in some effort.

Also, hey, Moneylender/Adventurer synergy I hadn't yet noticed. ML makes you see Adv more often, and makes it worth more when you do. Adv cycles past ML or picks up the coppers you want to trash. [Uh, ok, ignore the last part.]

306

Dominion General Discussion / Re: Annoying and potentially harmful card anti-synergies

« on: October 14, 2017, 09:13:29 am »

Throne Herald, hit Counting House, draw all the Coppers, and then hit Royal Blacksmith with the second play.

Here, have a penguin

307

Dominion General Discussion / Re: Any joy in putting Player tokens on 1E cards?

« on: October 14, 2017, 03:48:21 am »

Adventurer should give 3 cards instead of 2 and cost 5, making it a BM focused Smithy variant.

That's an interesting idea. Let's compare terminal Golds (Qvist rankings in parentheses):

• Better-Adventurer cycles you quite a bit, and sometimes gives $4+
• (20) Count alternatively trashes and gains Duchies
• (31) Legionary sometimes does a strong attack
• (??) Courtier can be non-terminal, gain gold, +1 buy (but that's not typical in BM/Courtier)
• (86) Tribute gives $2-4 or cards, meh.
• (90) Mandarin, meh, anti-cycles you, topdecks some or all of your treasures when you buy it, meh?
• (96) Harvest gives you $0-4

Maybe Better-Adventurer is somewhere around Courtier? B-A is better for BM, Courtier is better in engines?

Some more numbers: if you add 7 Silver to your starting deck, Better-Adventurer on average gives $4.5, which means that the money density among the other four cards in you hand needs to be at least X where X is slightly less than 1, in order to hit province. With only 3 Silver, you have $13 in 10 treasure cards (+ 3 Estates), or $1.3 per treasure card, for an average value of $3.9, so you need slightly above $1/card in your other four cards in hand (and you already have $13 in 13 cards).

That makes it sound quite strong to me.

308

Variants and Fan Cards / Re: Really bad card ideas

« on: October 11, 2017, 02:02:25 pm »

Henchman
$4 — Action — Attack
+1 Action
+$2

Lackey
$4 — Action — Attack
+1 Action
Every player discards their hand, then draws 4 cards.

Overseer
$2 — Action
+$2

Custodian
$2 — Action
+2 Cards

Caretaker
$2 — Action
Trash 2 cards from your hand.

Aristocrat
$5 — Action — Victory
+2 Actions
Worth 2 VP

Lord
$5 — Action — Victory
+3 Cards
Worth 2 VP

Also Indigenous/Aboriginal Village, Resource Extracting Village (action costing $3: +2A/+1C/+$2, trash this) vs. (plain old) Village, Sea Robber vs. Loot Spender, Sibyl/Augur (Oracle), Saffron Seller and Vanilla Vendor, Hoarder/Spendthrift (Miser).

Grand Pawn
$6 — Action
Choose any three: +1 card, +1 action, +$1, +1 buy. The choices don't have to be different.

(seems pricey at $6 and strictly better than Laboratory at any lower price.)

Scoutpost might actually be almost ok.

Given that this in RBCI, I take that as criticism of my work. What could I have done better?

309

Variants and Fan Cards / Re: Really bad card ideas

« on: October 10, 2017, 07:18:45 pm »

Scoutpost
$5 — Action
+1 Action
If this is the first time you played a Scoutpost this turn, and the previous turn wasn't yours, then take an extra turn after this one.
For your next hand, reveal the top 4 cards of your deck. Put the revealed Victory cards into your hand. Put the other cards on top of your deck in any order.

Mote
$0 — Action — Reaction
When another player plays an Attack card, you may reveal this from your hand.

Knights Templar
$5 — Action — Attack — Knight
Each other player reveals the top 2 cards of his deck, trashes 1 to 3 differently named among those which cost from $3 to $6, and discards the rest.

Oracle
$3 — Action
Reveal your hand. Play all your treasures. Pay all your $. SELECT a card from your hand, DROP it onto the TABLE and play it. Gain an UPGRADE.

Steal
<8> — Event
Gain any number of cards from the trash.

The IRS
$4 — Action — Attack
Trash a copper from your hand.
Gain a Silver onto your deck.
Each opponent discards a Copper (or reveals a hand with no Copper).
Each opponent puts a victory card from their hand onto their deck (or reveals a hand with no victory cards).
Put <2> on a supply pile.

Illiterate
$3 — Action
+1 Action
Reveal cards from the top of your deck until you reveal one costing 2 or less. Put that card into your hand and discard the rest.

Mirage
$3 — Action
+1 Action
+1 Card
Discard a card

Royal Miscarriage
$5 — Action — Reserve
+1 Action
Put this on your Tavern mat.

Bridge to Nowhere
$4 — Action
-$1
+1 buy
Cards cost $1 more this turn.

Port Wine Merchant
$7 — Action
+2 actions
+1 card
+$4
+1 buy
Put this on your tavern mat.
---
At the end of your Buy phase, if you have at least $2 unspent, you may discard this from your Tavern mat.
When you buy this, gain a Port Wine Merchant.
You can't buy this if you have any Copper in play.

310

Variants and Fan Cards / Re: Really bad card ideas

« on: October 10, 2017, 05:49:35 pm »

The idea of Brutal Events is to take the situationally good events that can often be harmful instead and force them on your opponent.

Huh, it looked to me like the idea was to take events that are almost exclusively good (though not always worth the opportunity cost) and turn them into attacks by making the affected players "make" bad choices.

Some ideas on Brutal Event balance. Let the other players make the choices.

But... but... but this is RBCI

More seriously, I like the idea of having attacks that are identical to beneficial effects, except for who makes the choices. They are probably hard to balance when they have the form I like, though. Brutal Ritual on Overlord seems pretty harsh. Brutal Trade seems bonkers mad. Brutal Quest, choosing "discard six cards" and typically not giving a gold. Brutal Donate. Less bonkers, Brutal <token-placing-event>, letting you place anyone's token (including your own). Though I suspect moving people's +action token around can break their Smithy engine pretty badly. Also, with Brutal Inheritance I guess your Estates become Scouts while mine become Throne Rooms

Maybe Brutal Borrow, Brutal Save and Brutal Alms could be balanced, although having to pay $1 for Brutal Alms with no treasures limits it somewhat.

Also, I very much like the incoherently overlapping possessions created by Brutal Summon! Here I thought Storyteller/Crown was a rules question goldmine ;-)

311

Variants and Fan Cards / Re: Really bad card ideas

« on: October 10, 2017, 05:22:42 pm »

Jack, master salvager
$4 — Action
Trash any number of non-treasure cards from your hand.

Jack, master scavenger
$4 — Action
Look at the top card of your deck. You may discard it. You may repeat this any number of times.

Jack, master minter
$4 — Action
Gain any number of silvers.

Jack, master librarian
$4 — Action
Draw cards until you have 5 cards in hand. Repeat this any number of times.

312

Variants and Fan Cards / Re: Really bad card ideas

« on: October 08, 2017, 06:49:25 pm »

I like the idea behind the brutal events. I think they might have some balancing and rules issues.

Brutal Ritual
Event - Brutal - $5
All other players gain a Curse. If they do, they reveal their hand, and trash a card from their hand that you choose. Each player who did gain +1VP per $1 it cost.

Cool, I get to Cutpurse you, then turn the Copper into a Curse. Or I can sabotage your deck but give you a non-trivial amount of VP in compensation. I guess if I'm happy to swindle your 5'ers into Duchies, I might be happy turning them into 4-point duchies as well, given that I get to also Pillage your hand.

I think "if they do" should be "Each player who does reveals their hand [...]", unless of course it's intentional that I deal out the last n-1 curses to each player except the one on my right, without trashing anything.

Brutal Advance
Event - Brutal - $1
All other players reveal their hand, and trash an Action card from their hand that you choose. Each player who did gains an Action card costing up to $6 that you choose

For $1 I get to turn your King's Court into a Scout? That's crazy

I guess we're playing Big Money this game.

Brutal Delve
Event - Brutal -  $3
+Buy
All other players gain a Silver

Seems quite strong with Bandit Fort and maybe Wall, but rather meh otherwise.

Brutal Banquet
Event - Brutal - $4
All other players gain two Coppers and a Non-Victory card costing up to $5 that you choose.

Mountebank costs $5 to buy and gives +$2 when played. This costs $4 and a buy per "play", can't be blocked and gives out an extra Copper. And Mountebank is already very strong. This seems br0ken.

Brutal Wedding
Event - Brutal - $5
All other players gain a Gold, +1VP, and take 3 debt

Could debt-pinning someone work?

I could see buying this when I make an otherwise-PPR play. Once again, nice with Bandit Fort.

Outside of a few niche situations, meh, I'm not sure I would buy this.

Brutal Dominate
Event - Brutal - $15
Gain a Province. If you do, +9VP. Perform the instructions of a random Brutal effect (including those not in the kingdom).

You should probably specify that the random effect is chosen with a uniform distribution.

Brutal Torturer
Action - Attack - $6
+3 Cards
All other players choose a Brutal Event whose instructions you perform (Brutal events not in in the kingdom can be chosen).

Do they choose one each? In a 4p game, each opponent gains 3 silver (for example)? Do they vote for a single event?!?

Anyways, free silver doesn't seem like a too oppressive "attack". I think I prefer Smithy.

Brutal Summon
Event - Brutal - $6
All other players gain an Action card costing up to $4 that you choose (choose once for all players). At the start of their next turn, they play the set aside card. Until it finishes resolving, you can see all cards they can and make all decisions for them.

Brutal Summon a Steward, on your turn I call your Ratcatcher to trash one of your Provinces, then Guide your hand, use your duration Dungeon to make it hard for you to kick off, then Steward-trash two provinces. (All of this happens at the start of your turn, and I decide on your behalf which one you do next.)

Suppose Alice buys Brutal Summon on her turn and Bob buys it on his turn, then on Carol's turn both Alice and Bob decide which start-of-turn event to activate next, until either Alice's or Bob's summon has been resolved (in which case the other person unilaterally decides). Suppose Alice and Bob disagree, what happens?

If I Brutal Summon a Steward and Alice gains the last one, do I make all of Bob's decisions until the Steward he didn't gain resolves, i.e. forever? I think there should be words limiting the Posession-effect to those who gained a copy of the card. Maybe you should also copy Posession's trash-becomes-set-aside clause?

This looks like it has some rules issues left to work out.

313

Dominion General Discussion / Re: Dominion Confessions

« on: October 08, 2017, 10:53:04 am »

I once tried building an engine payloading mass Bridge off of Shanty Town and Patrol.

The math: playing Shanty Town plus Patrol nets one card. To play n Bridges I need to play n-1 villages; for n=5 I need to draw 4 cards, for which I need 4xShanty+4xPatrol (and I need to not draw whatever trasher is stuck in my deck). Note that n=6 requires 5xShanty for the payload and 6xShanty to draw all that with Patrol; only cheaters buy 11xShanty.

So that's a deck of 8xShanty, 4xPatrol, 5xBridge, a trasher, and probably an extra Shanty/Patrol pair to draw past the trasher, which is obviously super fast to build. Note that this is enough to single Province. I can probably add in a Gold if I add an extra Shanty/Patrol pair to draw it, to double Province.

Of course, you should continue adding Shanty/Patrol pairs as you green to draw past your green cards.

That was an unmitigated disaster, but it's great fun retrospectively

314

Dominion General Discussion / Re: Masquerade

« on: October 08, 2017, 09:27:46 am »

Here's a game between Adam Horton and Qvist which showcases several features of Masquerade very well: https://www.youtube.com/watch?v=JkogD_WLqG8&index=17&list=PL7MIC-UQuoeSnDnNa2HoWR85tod7J7Tqj. I recommend watching it, to see how some of your concerns play out in practice—or at least one way they can play out.

The constant threat of being forced to pass your opponent a good card in exchange for junk just screws over so many other aspects of the game. It feels like Possession in that you have to keep your deck crummy so that your opponent can't take advantage of it.

They're not quite comparable; an awesome deck with 20% bad cards passes bad cards to Masquerade but gives good turns to Possession.

Also, as you see in the linked game, even when forced to pass a good card, it looks like it's not a huge deal. Maybe Qvist could have played some more Monuments if he had passed fewer Mining Villages, and maybe Adam could have bought more green cards if he had passed less Silver, but on the whole it looks to me like it was much closer to having a mild impact on the game than causing huge swings.

-Should you not even bother with other trashers when it's on the board, simply because trashing down too fast will just give good cards to your opponent?

Trashing down fast with Chapel seemed to work out perfectly fine for Qvist in that game. Keeping a few bad cards around to pass to Masquerade makes sense when trashing down fast. Obviously the larger your deck, the more bad cards you need to have a high probability of having one in your opening hand.

-Are there any times it can be ignored? The only situation I can think of is Ambassador, which is a great counter because it's also a card that can thin and junk at the same time. Are there any other situations?

I would think any engine that draws deck and has some vaguely decent trashing makes mid-game Masquerade a complete non-threat. Upgrade, Forager, Junk Dealer all do a fine job. Steward and Chapel both do the job very well.

Given the choice I probably want Masquerade over Forager in the early game, due to the +2 cards, but I pick Chapel over Masquerade any day. I'm not sure between Steward and Masquerade: Steward trashes faster but also gimps your turns. (Chapel of course totally gimps your turn, but it gimps a smaller number of turns, and gives you really big turns faster.)

Note also a reason to not ignore Masquerade: when it's the only draw. I think Qvist's deck would've rather used Moat for draw if available, though. The presence of +buy/gain might swing a decision between Masquerade and Witch for draw—which is a choice you almost never have to make, so whatever :-)

-What about other junking attacks? Should you not bother with them because your opponent can just fling the junk back at you? It seems to me that Mountebank and Cultist are fast enough to bury an opponent who's relying solely on Masquerade, but the other junkers I'm not sure.

I wouldn't worry about getting junk returned. I think the real concern is whether the trashing speed of Masquerade makes the junking worthwhile or not. When the junking is faster than the trashing it seems great to go for. When it's equal, meh, I don't think I can give generalized advice. One general true statement, though: when trashing the junk you're given, it's (often) at the expense of trashing the junk you're starting with. Delaying your opponent's thinning may be worth it.

-Is buying more than one of them ever a good idea?

Qvist does it in the linked game, and it seems perfectly sensible to me; though he does it for the draw.

If playing Masquerade/BM, getting 2xMasquerade makes sense to me. The earliest you'll get rid of your starting cards is turn 12, Smithy/BM gets 4 provinces by turn ~14, and http://forum.dominionstrategy.com/index.php?topic=2532.0 ranks Masquerade/BM as stronger than Smithy/BM.

-Is passing good cards to your opponent just not that big a deal sometimes? Can you trash all the way down and build an engine so good that it can shrug off all of Masquerade's mischief?

I think Qvist succeeds in doing just that. The effect of Adam's Masquerade is not nothing, but it's also not a big deal.

(DG says "One player might want only actions cards and the other only treasures."; the linked game is an example of this.)

Any help on dealing with this insane card would be much appreciated. Thanks.

I think you overestimate how strong the attack part of Masquerade is. Passing a good card feels frustrating, but the intensity of the feeling and the impact on the game are not always proportional. Here's a random suggestion: on the next kingdom where Masquerade shows up, get one or two, but don't go out of your way to play around the risk of getting junk or having to pass good cards. After the game, estimate how much of the game outcome is due to Masquerade-junking or good passes.

315

Puzzles and Challenges / Re: Best Asymptotic Point Scoring

« on: October 01, 2017, 01:06:07 pm »

Claim 2: You can pretty much always get a specific n-card deck within ~n turns.

This is really easy. Just buy the cards you want and trash the rest.

Your suggested method is incomplete: If I want 7xCopper, 3xEstate and a single 5-cost card, I might get 3/4 on an arbitrary number of shuffles before I hit $5. If I want a $6+ card I also have to buy treasures which (let's stipulate) I don't want.

Here's a fool-proof way: open 2xLurker, then Donate. Gain 2 more Lurkers and 1 Hireling, then repeatedly play the following turn: play 4xLurker, gaining a desired action card and a Hireling, then play 1 Hireling. (That way you keep drawing your deck, making that turn golden.)

If you want any non-action cards, buy enough treasures to buy them, while gaining and playing enough Hireling that you keep drawing your deck.

Once you have all the cards in your deck that you want, plus at least one Copper and one Silver, buy Bonfire to trash the Hirelings you've played if you don't want them in your deck at the end of the game. Donate to get rid of any other excess cards (e.g. Lurker), except for the Copper/Silver pair. Use those to pay off your debt. Then Bonfire them.

Now you have exactly the deck you want, and no debt, with some number of Hirelings having been played.

This takes one turn per action card you want to gain plus one turn per non-action card you want to gain, plus a constant number of turns for setup and cleanup (and optionally a constant number of turns buying treasures).

I'm pretty sure you can gain cards at a higher rate, and you can increase that rate proportionally to how many Lurkers you already have, so I would guess you can obtain any n-card deck you want in O(log n) turns. (idea: as fast as you can, gain enough Lurkers that you can gain your desired n action cards in a single turn, buying non-action cards one per turn while you ramp up.)

If you object to Hireling'ing yourself, then here's an observation: 2xGold is enough to afford Travelling Fair plus Expedition (enough to draw those 2xGold) with one coin to spare.  Plan: get enough Gold that you can keep drawing your deck while adding one desired card per turn in a sustainable way. Once you have assembled your desired deck (plus a ****ton of Gold), Donate all the undesired Gold except one, pay off your debt, then Bonfire that Gold.

316

Game Reports / Re: Funny in a sad, WTH way

« on: June 15, 2017, 03:58:48 am »

With time expansion games moved more and more towards engines [...] I feel like Adventures, Empires and 2nd editions are responsible for the big push, though.

I'm willing to believe that engine frequency went up with (almost?) every new expansion, and that it went up more than usual with Adventures and/or Empires. I'm skeptical that it's a big jump, and I'm skeptical that second edition Base/Intrigue did a whole lot. Here are my arguments:

I can definitely see how Champion and +1 action tokens can make engine boards out of otherwise non-engine boards, and Storyteller can do interesting things. Empires, uh, has villages and terminal draw and trashing which increases the likelihood of those features being on a random board [I'm not too familiar with Empires].

I'm less sure about second editions. Base game adds Artisan, Bandit, Harbinger, Merchant, Poacher, Sentry, Vassal. I see two gainers (one is Gold-only), three virtual money cards (two peddler variants, one Conspirator/Herald hybrid), a Lookout/Cartographer hybrid and a cantrip Scavenger. Can you name any one, such that adding it to a non-engine 9-card kingdom turns it into a kingdom with an engine? Is there any one which turns a bad engine into a good engine? Are there any such pairs of cards?

My best bet is adding Sentry as the only trashing on the board. So, uh, base added a trasher that's decent but a bit slow and on the expensive side of trashers, and that's why [say it loud and say it proud] we all play engines now? Maybe Artisan for its gaining with an aftertaste of epsilon percent extra reliability [play Village, Village, Artisan-for-Smithy, Smithy]?

Intrigue gets Courtier, Diplomat, Lurker, Mill, Patrol, Replace, Secret Passage. Same test as before: which of these, when added to a kingdom, takes it from having no (or a bad) engine to having an (or a good) engine?

If Patrol is the only draw and everything else is there, sure. I can see how Secret Passage increases reliability, how Mill rewards overdraw, how 2xLurker is a gainer and how Replace can be a cursing attack if you twist your own arm. Diplomat and Courtier, eh? Not to poo-poo those cards, but on what boards do they make the difference between engine and no engine? And even the engine-friendly cards aside from Patrol... while nice, I don't think they move you from no engine to engine.

So, uh, the second editions add Sentry and Patrol and maybe Artisan as engine enablers? I'm thinking Adventures and Empires are much more responsible, then.

Also, if you watch some of the youtube'd games between Qvist and Adam Horton, you'll see plenty of engines in the pre-Adventures games (first 66 out of 73). Maybe it's not a perfectly random sample, but I think there were plenty of engines before Adventures.

[This is not "you're wrong (on the internet, of all places!)", this is "I half-agree and here's a footnote articulating and presenting arguments for the other half".]

317

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

« on: May 29, 2017, 10:04:07 pm »

LUNATIC MODE: 2-player game, your opponent tries to prevent your combo. (Your opponent won't play Lighthouse, reveal Moat.)

I have a 2-player solution that requires no cooperation from my opponent (revealing Moat and such), except for not playing treasures and not buying anything. It does not involve Possession.

It was my personal goal to find a solution that didn't involve using Mandarin/Crown. I succeeded in that as well. Apart from not scaling to more players, I think this works in expert mode.

SPOILER WARNING: IT BEGINS HERE

There's an elaborate setup.

Phase 1: use Cutpurse, Masquerade and Thief to delete your opponent's deck.

Play Cutpurse until they reveal a hand with no copper; then, for each estate in their hand, do the following:
  play Masquerade, pass Copper, receive Estate (no other choice), trash the Estate
  play Cutpurse to make them discard the copper (makes "no other choice" remain true)

Then play Pirate Ship to trash some of their coppers. Eventually they will have nothing left.

(For convenience, you can pass them your estates the first three times if you like.)

Phase 2:
  Repeatedly Ambassador them a Copper, then trash it with Pirate Ship. (This is to increase Pirate Ship's value.)
  When Pirate Ship is big enough, pass them your last Copper.

Phase 3:
  You're ready! In addition to the action cards in the main loop below, your deck should also contain 2xVilla and a Scrying Pool. There should also be something in the trash (below).

Main loop:
  Scrying Pool, drawing your deck (including a second Scrying Pool)
  King's Court on King's Court on 3xLurker
  King's Court on King's Court on 2xLurker and one payload action (the first time, the payload will be Pirate Ship)
  Cutpurse (they discard a Copper)
  Thief (you trash and gain their Copper)
  Ambassador on 2xVilla (one goes to the supply, the other to their hand)
  Masquerade, drawing a Copper, passing it and receiving a Villa.
Buy Phase:
  Buy Travelling Fair 9 times ($18)
  Buy Bonfire 8 times ($24), trash all the cards you played in this iteration.
  Buy Villa ($4), return to your action phase, do the main loop again.

The total cost of this is $46; to pay for this we have $2 from Cutpurse and $15 or more per Pirate Ship. IIRC there are 60 Coppers minus starting decks in the supply, so there's no risk of running out before Pirate Ship gets there.

Counting carefully, you play 15 action cards and play Lurker 15 times. Before the first iteration, the trash should contain a copy of each card you play in the first iteration, which you will regain with Lurker. On subsequent iterations, you will regain the cards you played in the previous iteration, except you may choose which payload card to regain if there are multiple payload cards in the trash.

Note that this requires 5 Lurkers to be in the trash and 5 in your deck, leaving none in the supply. In other words, there's very little room to add things to the infrastructure bit of the loop.

However, you can repeat the loop with Pirate Ship as the payload any number of times to rack up any amount of money. Using Travelling Fair, you can empty all the piles.

You can also save up $46 to afford an iteration with a different payload card. If you omit the payload card (King's Court says you *may* play an action card thrice), you use 14 action cards to generate 15 Lurker plays, effectively making the last Lurker play your payload. (Instead of omitting a card to KC, you can also Throne Room a King's Court on 2xLurker if you like).

Kingdom, by cost:
2: Lurker
2p: Scrying Pool
3: Ambassador, Masquerade
4: Cutpurse, Thief, Pirate Ship, Villa
7: King's Court
Events/Landmarks: Bonfire, Travelling Fair

Note that this is a 9-card kingdom. You can either add a convenience card or an alternative payload. I like Scheme and Monument here.

So, that was feasibility. Future work is playtesting against Masquerade/BM to see how strong this is

(I guess that with Scheme, setting up the pin is enough to basically guarantee a win: simply trash your opponent's deck and all the Coppers, and they'll be helpless. Scheme'ing 2xKC+3xPool should make your deck remain reliable with up to 8 Provinces in it. So I don't think going infinite is strategically relevant on this board. But it's possible.)

I hope you enjoyed

318

Dominion Articles / Re: Money density math: Gold/2xSilver/Cache, Silver/Peddlers, trashing estates

« on: May 26, 2017, 12:23:52 pm »

In the thread on simulating two-card combos, there was some discussion about Bonfire/Jack vs. Counterfeit/Jack, with simulator results reported.

Let's do some math: Bonfire, m1=-2,c1=-2 vs. Counterfeit, m2=-1,c2=-1, dc = (-1)-(-2) = 1

Code: [Select]

    (m+m1)*dc > (c+c1)(m2-m1)
<=> (m-2) > (c-1)((-1)-(-2))
<=> m - 2 > c - 1
<=> m > c + 1
So each purchase of Bonfire does more for you deck than each play of Counterfeit, when they both trash Copper, so long as your (current or target) money density is greater than 1.

Note that purchasing Bonfire costs $3 whereas playing Counterfeit gives you $2 (above the $1 you would've gotten from playing the trashed copper normally); Bonfire is available on every turn whereas Counterfeit is only available on some of your turns; and Counterfeit can sometimes be used on Silver and Gold with benefit.

So, the math alone agrees with the simulator results, the paragraph of commentary suggests that the math isn't the whole story, and the simulator results suggest that the costs and non-copper-trashing effects don't alter the conclusion produced by the math. That is, the money density model produced the right answer even though it left some potentially important aspects of the game un-modeled.

319

Dominion Articles / Re: Money density math: Gold/2xSilver/Cache, Silver/Peddlers, trashing estates

« on: May 26, 2017, 09:23:20 am »

"you can overcome Minion attacks if you have four silvers per initial junk card"

Minion gives a 4 card random hand.

You are correct. I edited my post to say Urchin instead of Minion. It was late when I wrote that post, I first put in Urchin, then updated to Minion to refer to an earlier set (likely known by a larger fraction of players), and then forgot to cross-check against assumptions elsewhere in the text. I kno how teh card work, I swears!

[Against Minion the first chunk of math holds: there you want a money density of 2, and no amount of silvers can get you there; at most you can get arbitrarily close, pretending the silver supply is infinite. But due to not only drawing average hands, of course sometimes you will still hit Province in a Minion-attacked silver flood. This does not imply that Silver counters Minion ]

320

Dominion General Discussion / Re: Playing Vassal

« on: May 25, 2017, 09:17:23 pm »

hunting grounds-BM is barely any better than BMU according to simulator data.  not the best example =P

That just makes my edge case even edgier

321

Dominion Articles / Re: Money density math: Gold/2xSilver/Cache, Silver/Peddlers, trashing estates

« on: May 25, 2017, 09:00:56 pm »

Specific money densities for <treasure>-flood, now with terminal draw

Just for fun, let's do some more money density calculations on particular decks. This time, Smithy/silverflood. You're playing 7-card hands and want to hit $8 with a deck of estate, copper and silver. In fact, let's do it generically first; you want a money density of t:

Code: [Select]

    (c + 2s)/(c+e+s) >= t
<=> c + 2s >= t(c + e + s)
<=> (2-t)s >= (t-1)c + t*e
<=> s >= c*(t-1)/(2-t) + e*t/(2-t)  [assuming 2-t > 0, or equivalently t < 2]

For t=1.6, I have already calculated this; for t = 8/7 ~= 1.14, we get

Code: [Select]

<=> s >= c*(1/7)/(6/7) + e*(8/7)/(6/7) = (1/6)c + (8/6)e = (1/6)c + (4/3)e
So you need to add ~5.16 silvers before Smithy hands can hit Province. And indeed, SCCCCCC and SSSSEEE are Province hands.

With a gold flood, we get

Code: [Select]

    (c+3g)/(c+e+g) >= t
<=> (3-t)g >= (t-1)c + t*e
<=> g >= c*(t-1)/(3-t) + e*t/(3-t) = c*(1/7)*(13/7) + e*(8/7)/(13/7) = c*1/13 + e*8/13 [assuming t < 3]
Yay for coprime numbers; 3*8/13 = 24/13 ~= 26/13 = 2, so add two+ golds per three blanks and ~half a gold to cover for the coppers, when you're playing 7-card hands. (Let's round up and say three golds compensates for the initial deck.)

Province hand sanity check: with 7 Copper and 4 blanks we need 7/13 + 32/13 = 39/13 = 3 Golds to meet our targets; and we can partition such a deck into GGCCEEE and GCCCCCE which are two province hands.

For six-card hands (Masquerade, Moat, etc.), the target is 8/6=4/3 ~= 1.33 and the silver and gold flood coefficients are:

Code: [Select]

s >= c*(t-1)/(2-t) + e*t/(2-t) = c*(1/3)/(2/3) + e*(4/3)/(2/3) =   c*1/2 + e*2   (= 3.5 + 6 = 9.5)
g >= c*(t-1)/(3-t) + e*t/(3-t) = c*(1/3)/(5/3) + e*(4/3)/(5/3) =   c*1/5 + e*4/5   (= 7/5 + 12/5 = 19/5 ~= 4)

For eight-card hands (Council Room, Hunting Grounds), the target is 1 and you need one silver or half a gold per estate, and nothing for the coppers.

Corollary: for five card hands, greening with a single Hoard in play moves you away from your target (towards exactly $1.5 is away from "at least $1.6"), but for any larger hand size, i.e. any kind of terminal draw BM, Hoard-ing moves you towards your target money density. Said another way: buying a Duchy with a Hoard in play is not greening-with-slower-degradation, it's building! (Caveat: you don't have you Smithy in every starting hand, of course...)

Let's also do the math for hand size attacks; for 4-card hands, t=2

Code: [Select]

s >= c*(t-1)/(2-t) + e*t/(2-t) = c/0 + e*2/0 = :( [we violated the assumption that t < 2]
g >= c*(t-1)/(3-t) + e*t/(3-t) = c*1/1 + e*2/1 = 7+3*2 = 13
So for Urchin, no amount of silver can bring you to your target money density, even though SSSS is a Province hand; I guess this highlights what average means and doesn't mean. A very large amount of Gold can bring your money density to 2.

For 3-card hands (Militia), t=8/3 ~= 2.33

Code: [Select]

g >= c*(5/3)/(1/3) + e*(8/3)/(1/3) = c*5 + e*8 (= 35+24 = 59)
So if you add 59 Golds (there aren't that many) to your initial deck, it has a money density (average treasure value) sufficient to buy you a Province after getting Militia'ed. I recommend against using this strategy ;-)

Unlike all other money density math I've done, for reduced hand sizes there's no way of dividing your deck into n-card Province hands, even though the deck has the right proportions of high-valued treasures to coppers and blanks. But the reduced hand-size math is misleading: you don't discard two random or average cards, you discard your two worst cards. Which means that a high-variance deck does better than a low-variance deck, and averages alone are much more insufficient than usual.

But, a simple analysis maybe points somewhere in the right direction: you can overcome Urchin attacks if you have four silvers per initial junk card (or 40 silvers in total), and you can overcome Militia if you have three golds per two initial junk cards, or 15 golds in total. [This assuming really good shuffle luck.] If you're never hitting $12 and 2 buys, that's at least 15 turns worth of building before you can start greening.

So, the lesson: don't play Big Money with small hands.

322

Dominion Articles / Re: Money density math: Gold/2xSilver/Cache, Silver/Peddlers, trashing estates

« on: May 25, 2017, 08:28:43 pm »

Cool formula.  In situations where it's valuable to assess money density, target money density (i.e. what money density you expect to have while greening) can be a more important metric than current money density.  Let's see what the results are for some common situations with Delve, Trade, and Bonfire. [...]

Thanks, I'm glad you like it, and your applications are cool. And I agree: m and c can refer to the money density of any deck, either the one you have now or the one you're intending to build or... anything else, although those two seem the most relevant.

[Early Bonfire: h]ere's a situation where using only the target money density will get you to make some bad plays.

Yup, similar to my example with trashing a Copper vs. gaining a Silver: the move only takes you towards your desired money density when you're already sufficiently close. I think experience and understanding will be better than math at telling you when to Bonfire (etc.) a little early, when it's too early, when it's too late to matter, etc.

[Trade on Estate/Copper: a]nother blowout - this time a little surprising (to me).

Cool. It sounds like the math had an impact, which I consider to be successful math :-)

Let's extract another general rule: when total money is the same but on fewer cards, money density is higher. In math, assume m1=m2 and c1 < c2 (implying dc > 0); then

Code: [Select]

    (m+m1)*dc > (c+c1)(m2-m1)
<=> (m+m1)*dc > (c+c1)*0
<=> (m+m1)*dc > 0
<=> (m+m1) > 0
So when your total amount of (additional) money is positive, you want it on as few cards as possible. By that logic, Silver+Silver > Estate+Copper+Gold.

Even more generally, assume m1 >= m2 and c1 <= c2, implying dc >= 0; then

Code: [Select]

    (m+m1)*dc >= (c+c1)(m2-m1)
<=> (m+m1)*dc + (c+c1)(m1-m2) >= 0
which is true if (m+m1) >= 0 and (c+c1) >= 0, which they always are.
That is, if you have more money (or the same amount) in fewer cards (or the same amount), you're better off.

(Until you start greening, that is: then you want a big deck for reasons already explored. But for each incremental change the above logic is probably strategically valid most of the time.)

323

Dominion General Discussion / Re: Playing Vassal

« on: May 24, 2017, 09:26:17 am »

I more or less concur with everything said so far. You only really want it in very action-dense engines, which requires good trashing, which means you should get a trasher early. Opening Vassal seems a little odd.

In those engines, it adds "+$2" to the next card on your deck (assuming it's an action). It has very nice synergy with deck inspection, but building a Sentry/Vassal/maybe-also-Harbinger engine sounds a bit slow and very wonky. In a more vanilla Village/Smithy engine it probably has a place; it's nice but not super-OMG-awesome. It's a payload silver that most often will (effectively) give back the card and action you spent to play it; sort of like Conspirator. If the engine draws deck, you'll want Vassal early in your turn (so you're not playing the top of an empty deck) where you normally want Silver late (because you want Village/Smithy early so you can continue drawing cards). Although: if you have 5 Vassals in hand and 4 cards left in your deck, discard 4 vassals to Cellar, then play Vassal to make a big Vassal chain, woop! ;-)

1. If there are not other terminal actions that you plan to buy early on, then might as well take Vassal over Silver

Edge case: you want to play Hunting Grounds/BM, or BM with some other expensive terminal draw: you probably won't buy it until late in the opening or in the early mid-game (which for some value of ... is not "early on"), but once you do you definitely want to have silver over vassal. More clearly stated: whether you want Vassal early depends in part on which terminals you want late(r).

Opening Vassal doesn't seems appropriate when there's an engine but no trashing, because then you don't want Vassal at all. It also doesn't seem good in expensive terminal draw/BM, where you want a Silver. It doesn't go into a Workshop/Gardens rush; so it only really seems good in something that smells a lot like BMU. And in that case, you don't probably want Vassal at all, definitely at most one, because the risk of collision vastly outstrips the chance of having one vassal in hand plus one on top of your deck, and the infrequent upside seems like it shouldn't outweigh the frequent upside; just buy silver and gold, man. (Okay, maybe the increased cycling of a single Vassal helps enough in the beginning to outweigh the badness of cycling late, while greening, but that margin is probably very slim; it's probably positive, because you cycle a larger fraction of your deck early, maybe?)

The strongest case for opening Vassal is probably the wonky Sentry/Vassal/cantrip-heavy engine thing; open Silver/Vassal, then get two or maybe even three Sentries ASAP to get thin; the +$2 helps you get to $5 and you also want it later on; also, you won't ever draw the one Vassal dead when all other actions are cantrips. Once you get thin, add more Vassals. Until then, add other cantrips, e.g. some of Harbinger, Merchant, Poacher, Market. Maybe. I think it has to be a weird board for that kind of strategy to be dominant, but hey, weird board sometimes come up, especially in base set only. I remember a game where I played a Sentry/Market/Merchant deck and it worked decently; one or two Vassals probably would've been a fine addition to that deck.

324

Dominion Articles / Re: Money density math: Gold/2xSilver/Cache, Silver/Peddlers, trashing estates

« on: May 24, 2017, 08:14:30 am »

Since you are comparing two situations where you believe the density difference to be narrow, the difference in spiking $8 hands may be more important.

(Emphasis added.) The general rule I'm trying to extract from between the lines seems like it should have an implication roughly like this: if treasure-bundle A lets you hit $8 two turns out of every three, that's better than treasure-bundle B that lets you hit $7 consistently, even if the money density with bundle B is higher. Is that roughly what you were getting at? (I agree with the assessment, FWIW.)

In any simple situation where it is bad to add a copper to a deck, adding one gold on its own to a deck is better than adding a copper and a gold, which is better than adding two silvers.

Let's math it! I already covered Gold vs. 2xSilver, which hinges on money density being above or below one, so the math already agrees with that part of your statement. Let's do Gold (m1=3,c1=1) vs. Gold+Copper (m2=4,c2=2 and dc=2-1=1):

Code: [Select]

    (m+m1)*dc > (c+c1)(m2-m1)
<=> (m+3)*1 > (c+1)(4-3)
<=> m + 3 > c + 1
<=> m > c - 2

So Gold+Copper is only good when money density is less than 1-(2/c) (~= 1). Obviously Gold+Copper impacts money density the same as 2xSilver; the difference is in the variance. What makes Gold+Copper better than 2xSilver? FWIW, I interpret Limetime as being in agreement:

Hitting certain price points is best done by high value treasure.

The first and obvious counterclaim is that the infinite silver deck hits province every turn, whereas the half-gold/half-copper deck sometimes doesn't hit province. In defense of Gold+Copper, it sometimes hits Province even after a Militia, where infinite silver doesn't; more variance makes selection/sifting better and selective card-loss less bad. So, uhm, I'm not sure that there's a clear-cut unequivocal truth here?

Future work: do combinatoric math or numerical simulations to assess the provincing rate of (GSSCE)xN vs. (SSSSE)xN and the like.

I conjecture that to reach a price point of x at least once out of k hands, if x is higher than your money density you want more variance and if x is less than your money density you want less variance. [Extreme case is no variance, in which case my conjecture is obviously true; and *mumble-mumble* by induction *hand-waving* it WLOG *appeal to authority* also applies in the general case.]

I was just saying that money density is definitely not the best metric to gauge your deck's performance.

Agree.

Resiliency is best done by having a million treasures.

Let's do more math. The change in money density when adding dm money and dc cards:

Code: [Select]

   (m+dm)/(c+dc) - m/c
= c(m+dm)/c(c+dc) - m(c+dc)/c(c+dc)
= (c*m + c*dm - c*m - m*dc)/c(c+dc)
= (c*dm - m*dc)/c(c+dc)
= dm/(c+dc) - m*dc/(c^2+c*dc)
= dm/(c+dc) - m/(c + c^2/dc)

When adding a green card, dm=0 and dc=1, so we get

Code: [Select]

= 0/(c+1) - m/(c+c^2/1)
= -m/c(c+1)

The c and c^2 terms in the denominators above suggest that the more cards you already have, the smaller the impact of adding more cards (duh). This suggests, at least at first blush, that resilience comes from a big deck, no matter its composition. A big, good deck becomes almost-as-good when greening, a small good deck deteriorates quickly, and a big bad deck only gets as much worse as an equally big good deck. (Once again, in terms of money density. The discreteness of strategically important price thresholds are not considered here.)

Which means that what I said ("resilience correlates with money density") is misleading; it's probably true in practice, since both money density and total number of cards go up over time (and in tandem), but it's the card part that's the stabilizing factor. As to what you said, a million anything, not just treasures, will make a deck very stable to greening, but of course a million bad cards will make your deck stably bad ;-)

Also, the math backs up the commonly held view that thinning, as distinct from un-junking, is not important in Big Money. BM prefers 20xSilver and 3xCurse+2xEstate to 4xSilver and 1xCurse (where an engine has the opposite preference), because the bigger deck suffers less while greening.

Your point about trashing estates is on point because every estate slows down growth (that estate will hurt you every single time you draw it) and is bad at making sufficient treasures collide to hit certain price points.
You can throw out everything I just said when you are playing an engine.

Cool.

325

Dominion Articles / Re: Money density math: Gold/2xSilver/Cache, Silver/Peddlers, trashing estates

« on: May 23, 2017, 11:09:58 am »

It is less about money density and more about being able to spike certain price points. Also resiliency when greening is important.

Is that an argument against any specific point, against all my points or against the use of money density in general? I'll happily concede that money density is at best a low-resolution pointer in maybe somewhere not far away from the right direction, rather than a tool you can use to 100% determine both your strategy and tactics. Is there any of my money density calculations you think lead more away from the right answer than towards it?

Of course, hitting $8 is more than ~14.3% better than hitting $7, that I agree with. However, getting to $8 correlates with increasing your money density, so I think the concept is not completely useless. Complication: given that you'll have treasures of varying money amounts in BM, selection is also useful (such as from Embassy); that is, on top of just the average you also have to consider the variance.

I think resilience while greening means sustaining your ability to green, which again correlates with having a high money density (and keeping it high, e.g. such as with Hoard).

Agree/disagree?