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mDuo13

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Theoretical Maximum Points in Deck
« on: May 16, 2012, 08:36:20 pm »
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querty31 challenged players, "What's the theoretical maximum number of points in your final deck, if you buy ALL the cards in the supply?" Obviously, the answer is "infinite" since you can use Monument or Bishop to gain VP chips forever.

But let us consider a different question: what's the theoretical maximum number of points in your final deck, discounting VP chips, and which Kingdom cards make this score possible?

EDIT: Ah, there were other topics. I should've known. Well, whatever, let's update the solution with Hinterlands cards. I'm sure at least a certain one will make a difference. Also, let's get more specific with the setup rules. For convenience, we'll base it on Isotropic's setup:

  • Solo game. (8x each for Victory cards)
  • Colonies included. (Bonus points for figuring out the Province equivalent to this puzzle, though.)
  • Black Market is allowed, but fixed to 25 cards (like in Isotropic). Your choice which ones.
  • Potions will be included if any of your Kingdom/BM cards has a Potion cost.
  • 53x Copper in supply (In addition to the 7x in your starting deck.)
  • 40x Silver, 16x Potion, 30x Gold, 12x Platinum, 10x Curse
  • If your deck includes Young Witch, you can decide what the Bane is.
  • You are not required to buy all the Curses. You can choose to buy some if you want, though.
  • Optionally, take into account how many cards it's legally possible to end the game with in your deck. You can't three-pile out early, so you'll probably need a source of +buy and either cost reduction or card draw in order to buy the last 1 of almost-everything; or you can see how high you can get without any +buy or other gaining.

Full disclosure: I'm not actually sure what the answer is. There are 11 kingdom victory cards, most of which would play well with each other except Vineyard -- which would only get points for your Great Halls, Nobles, and Islands. Each of the (8x) Vineyards is worth an additional ~3.3 points for each Action card in the Kingdom, which suggests that Harem is probably not a key card in the ideal Kingdom. Meanwhile, to optimize Fairgrounds, you need Black Market (and to a much lesser extent, Tournament) available. But on the other hand, Silk Road is worth an additional 2 points for each Victory card in the Kingdom, so it doesn't want you to waste Kingdom spaces on non-Green cards...
« Last Edit: May 17, 2012, 05:27:13 pm by mDuo13 »
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eHalcyon

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Grujah

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Re: Theoretical Maximum Points in Deck
« Reply #2 on: May 17, 2012, 03:35:04 am »
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Well, the Black Market rules state to agree on number of cards in it, so you could just put a copy of overy other action. That would make huge bonus for Fairgrounds and Vineyard (and Gardens, actually).
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mDuo13

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Re: Theoretical Maximum Points in Deck
« Reply #3 on: May 17, 2012, 08:33:35 pm »
+3

Did some calculations here. I think it's a complete solution now.

(Too big to spoiler, be warned)













Base VP cards = 8+24+48+80 = 160 points

There are 11 Kingdom victory cards to consider: Duke, Fairgrounds, Farmland, Gardens, Great Hall, Harem, Island, Nobles, Silk Road, Tunnel, and Vineyard. The fixed-value cards are easy to calculate:

Great Hall = 8*1 = 8 points total.
Harem/Nobles/Tunnel/Island/Farmland = 8*2 = 16 points total.

We should keep in mind for later that Farmland forces us to remodel a card if we buy it normally. Luckily, we can also probably arrange to gain it another way, depending on what Actions are available.

Duke is also easy: 8 Duchies means 8 points per Duke, for a pile worth 64 points total.

Vineyard is worth nothing with just the base cards, but it has the highest potential, with up to 344 points total. [25-action black market deck, a 10-action YW bane pile, 4 action-Prizes from Tournament, plus 9*10 actions in the supply (Vineyard takes a Kingdom space itself), for a max of 129 total actions, or 43 points per Vineyard, *8 Vineyards = 344 VP.] However, each normal kingdom Action card is worth (10/3 = 3.33 VP) per Vineyard, or 26.67 points overall. Each Victory-Action card is worth (8/3 = 2.67 VP) per vineyard, or 21.33 points overall. Young Witch is basically a free Action (26.67 points) in the supply as long as the bane is something we would've included anyway. Each Action card in the Black Market is worth 1/3 of a point per Vineyard, or 2.67 points overall, which makes Black Market worth up to (35 / 3 = 11.67 VP) per Vineyard, or 93.33 in total.

We can therefore conclude that no non-action Kingdom pile worth less than 26.67 points overall is worth including in the Kingdom, and no non-Action card worth less than 2.67 points is worth including in the Black Market deck, except where Vineyard's rounding means that we won't go below the threshold by including said card.

Gardens provides less challenge to the kingdom constraints. The 183 base cards (excluding Curses), and minimum of 8*10 kingdom cards (an all-green kingdom) still totals 263 cards, which we can supplement with 7 curses for a minimum of 216 Gardens points minus 7 Curse points for 209. By the way, buying Curses is good for Gardens if you can buy less than 8 to set it over a new threshold, and bad otherwise. Each non-Victory action card (including the bane) adds another (2/10 = 0.2 VP) to each Gardens or 1.6 points overall. Black Market adds another (25 / 10 = 2.5 VP) per Gardens, 20 points overall. Tournament adds another (5 / 10 = 0.5 VP) each, for 4 points overall. Again, Young Witch is basically a free bonus if you would use the bane. In grand total, Gardens' maximum value is 256 points [183 non-Curse base cards, 9*10 non-Victory Kingdom cards, 8 Gardens themselves, 25-card Black Market deck, 10 extra bane cards, and 5 Tournament prizes bring it to a grand total of 321 cards in deck, or 32 points per Gardens].

Silk Road is the real conflict with Vineyards. It wants an "all-green" Kingdom, where it's worth a maximum of 224 points total [(10 piles * 8 victory cards), plus the 32 base victory cards, equalling (112 / 4 = 28) points per Silk Road]. With just itself and the base Victory cards, a full stack of Silk Roads is worth (56 / 4 = 112) points. Each kingdom Victory card you add increases each Silk Road's value by (8/4 = 2) points, or 16 points total. Meanwhile, each Victory card in the Black Market is worth (1/4 VP per Silk Road) or 2 VP total. Given that this is lower than the value of having Action cards there for Vineyards, we probably won't do it except to round out some thresholds.

Finally we have Fairgrounds. With an ordinary set, the full stack is worth just 63 after accounting for Curse damage [10 Base Cards and 10 Kingdom cards means ((20/5)*2 = 8 VP) each or 64 total, minus 1 from having a Curse]. Adding Young Witch lets us buy the bane instead of a Curse, netting just 1 point. But then there's Black Market. 25 unique Black Market Cards means a net of ((25/5)*2 = 10 VP) each, or 80 total. Tournament's 5 Prizes also contribute 1 point per Fairgrounds for a total of 16 on the pile. In grand total, that means Fairgrounds is worth up to 160 points in the ideal situation: [9 non-Curse base cards, 10 kingdom cards, 1 bane, 25 Black Market cards, and 5 Tournament prizes = 2*(50 cards/5) = 20 points each].

Now we can start to draw conclusions. Including Gardens in our Kingdom is a no-brainer: it's worth a ton of points regardless of what else we include. It also seems hard to beat Vineyards' 26.67 points-per-pile base, so we'll throw that in. Now that we have at least 48 victory cards in the supply, Silk Road will be worth a minimum of 96 points as a pile, making it also a must-have.

We can evaluate how much we gain by including various different cards in our deck: a normal Treasure adds 8 points (Gardens only), an Action adds 29.33 points (Gardens + Vineyard), and a Victory card adds its own value plus 18.4 points (Gardens + Silk Road). Given this, it's safe to include both Duke and Fairgrounds, whose values are already much higher than these generics. That brings us to 5 cards in the Kingdom.

Next, let's consider hybrid cards Nobles, Island, and Great Hall: because [compared to, say, a Kingdom Treasure card] each pile makes Vineyards worth overall 21.33 points more and makes Silk Roads worth overall 16 points more, while being worth 8-16 VP on their own, and subtracting a mere 1.6 Gardens points each -- an overall increase of about 43-51 points each. The synergy with Vineyards makes even Great Hall worth more than Harem, Farmland, and Tunnel. Got to include them.

So we're up to 8 Kingdom cards, and we haven't even considered Young Witch, Black Market, or Tournament. Black Market is the easiest sell (hurr hurr) because it gives Gardens 20 points and, depending on how we stack it, up to 66.67 points for Vineyard. Tournament is worth (Gardens 4 + Fairgrounds 16 + Vineyard 31.67 = 51.67 points), while Young Witch with a random Bane is worth (Gardens 8 + Fairgrounds 1 + 26.67 Vineyard = 35.67 points). All three of these are above the 29.33-point baseline for a generic Action card (Tournament just barely). We can fit all three if we make Black Market or Great Hall the Bane.

Alright, we've included or ruled out all our candidates for the main kingdom except for Farmland, Tunnel, and Harem. Let's double-check those against the cards in our Kingdom. All three piles are worth 16 intrinsically, plus 18.4 points by powering up Gardens and Silk Road, for 34.4 points apiece. In other words, Tournament just barely edges out all of them, because it contributes better to Fairgrounds, Vineyard, and Gardens, despite not helping Silk Road.

So there's our final Kingdom:
Nobles, Fairgrounds, Duke, Gardens, Silk Road, Island, Tournament, Young Witch, Great Hall, Black Market (Bane), Vineyard.
"But wait!" you say, "How are you going to gain so many cards on the last turn?" That's what the Black Market is for. Let's load it up with good actions. Not only do they power up Vineyards, they'll enable the game-ending mega-turn. There are 21 piles, but we're not emptying Curses and we'll have already emptied two piles, bought out the Black Market, and won all the Prizes. That means we need to gain 18 cards, including the last Colony and Province. There are a lot of ways it could work out, but here's one:

Start with Throne Room, King's Court, and City in hand (all bought from the Black Market). TR->KC, using the first KC on City, and the second on Grand Market, which will draw a total of 9 cards while increasing our available actions to 8 and our buys to 7 total. Let's use Trusty Steed to gain the last Silver(s) and put the deck into the discard, then Counting House to get almost 60 Coppers to our hand. Followers gains us the last Estate, and then we play Princess to drop the cost of everything by $2 and get another +buy. We've got 8 buys now; that's enough to Haggle our way to emptying 16 piles, and we have plenty of cash and actions to do it. (Remember, we emptied 2 piles before this turn and used Followers and Trusty Steed to empty 2 more already.) There are a lot of other cards (Inn, Cellar, Crossroads) that would make this mega-turn way easier to pull off, but they're not strictly necessary.

Alright, now that we've gotten that out of the way, let's figure out what's in the Black Market. My solution to buying everything required Throne Room, King's Court, City, Grand Market, and Counting House to be in the Black Market, plus prizes that we would have already anyway. This means we have up to 20 cards in the Black Market to arrange as we like. We have a total of 96 victory cards in deck (8*4 basic + 8*8 kingdom), so even adding one copy each of the remaining 3 Victory cards to the Black Market won't help our Silk Roads at all. But on the other hand, if we make 23 of our Black Market cards actions, then we have 81 actions total, powering up our Vineyards to 27 points each. That means we still have 2 spots leftover in the Black Market which we can't use to power up Vineyards or Silk Road, so we may as well put Harem and Tunnel for 2VP each. We have 307 cards in the deck now, not having bought any Curses, so we may as well buy 3 of those to bring our Gardens to the next level and gain a net of +5 VP (-3 from Curses, +1 to each of 8 Gardens).

So our final deck has VP in the following amounts
Estates: 8x1 = 8
Duchies: 8x3 = 24
Provinces: 8x6 = 48
Colonies: 8x10 = 80
Curses: 3x-1 = -3
Great Halls: 8x1 = 8
Nobles: 8x2 = 16
Islands: 8x2 = 16
Gardens = 8x31 = 248
Vineyards = 8x27 = 216
Silk Roads = 8x24 = 192
Fairgrounds = 8x20 = 160
Dukes = 8x8 = 64
Tunnel = 1x2 = 2
Harem = 1x2 = 2

Grand total: 1081 points.

EDIT: fixed a couple typos as mentioned by the comments below
« Last Edit: December 12, 2012, 05:20:19 pm by mDuo13 »
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qmech

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Re: Theoretical Maximum Points in Deck
« Reply #4 on: May 18, 2012, 03:57:02 am »
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That's an impressive analysis.  Have you considered that Young Witch in the Black Market will still get you the Bane pile?
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Grujah

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Re: Theoretical Maximum Points in Deck
« Reply #5 on: May 18, 2012, 07:35:35 am »
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Curses: 8x-1 = -3

You probably mean 3x-1.
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Deadlock39

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Re: Theoretical Maximum Points in Deck
« Reply #6 on: May 18, 2012, 10:09:39 am »
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I believe the previous analysis was done before Hinterlands (and some of it before Cornucopia), but it had higher point totals than mDuo13's count because we did not work off of the Isotropic Black Market "House Rule" that includes 25 cards.

Black Market says:
"Before the game, make a Black Market deck out of one copy of each Kingdom card not in the supply."

Donald X. (and I think the not-easy-to-find FAQ for Black Market) says to pick the BM deck in whatever way is agreed upon by the players.

Using a complete Black Market will yield much higher point totals for Vineyards, Gardens, and Fairgrounds. 

Young Nick

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Re: Theoretical Maximum Points in Deck
« Reply #7 on: May 18, 2012, 11:08:18 am »
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One small qualm with mDuo13's analysis. When doing the SR math, he says that there are 80 + 48 = 112 Victory cards. Clearly, what was intended was that there are 32 base Victory Cards so 80 + 32 = 112. Great analysis, aside from that one typo.
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