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« on: April 03, 2019, 05:46:23 am »
I worked on quite a few, but often get results that don't fit into the suggested solutions. Now I wonder, if I didn't find the best solution
Cards costing >= 6 vp ~ 9^T
buy King's Court, Grand Market, and Goons
use a small number of banks to get enough coins
limiting factor is the number of buys, 3 cards (KC, GM, G) yield 6 buys so I triple the number of cards every turn
victory points grow quadratic in the number of cards
Cards with potion in cost vp ~ T^2 / 12
alternate between buying Golem and Vineyard
use Golem to discard deck, so that a single potion is sufficient
T/2 Vineyard, T/2 Golem => T^2/12 points
Cards and events with debt in cost vp ~ T^2 / 27
loop over the following three turns
1) buy Engineer
2) buy City Quarter
3) play all City Quarters, Engineers, gaining Estate, buy Triumph
sum(2x/3, x=1..T/3)/3 ~ T^2/27
Reserve cards vp ~ 11.16 T
loop over the following
37x play Wine Merchant, 4 Gold, buy 2 Provinces
4x call 1 Coin of the Realm, play 3 Wine Merchant, 2 CotR, buy Province, 2 Guide
8x call 2 Coin of the Realm, play 5 Wine Merchant, buy Province, 4 Guide
use Guide to cycle through the deck. Occasionally keep 2$ to recover all the Wine Merchant.
vp/turn = (37*12 + 12*6)/43
Treasures vp ~ a^T
General idea: Use idols to gain will-o-wisp, which allows to draw a large hand, get points from castles that are a fraction of the will-o-wisp.
We use crown on the odd idols and the will-o-wisp to improve the speed.
If I calculated correctly, you can gain 0.24 will-o-wisp per Crown + 2 Idol and draw 4/3 cards per Crown/will-o-wisp.
I currently don't know exactly how large of a fraction of the cards should be which, but you will grow exponentially.
Hamlet, Watchtower vp ~ 144/13 T
The limit is that I can have only 6 Gold in play.
Hence, loop over buying 2 Provinces and 1 Hamlet (12x), and 6 Watchtowers (1x)
vp/turn = 12 * 12 / 13
Events vp ~ between 1.06^T and 1.13^T
Fundamentally, this builds on the fact that Travelling Fair + Expedition costs less than the two Gold you can draw with it. Then you can dedicate a fraction of your gains to triumph to score points. I calculated that the optimal fraction is about 3.2%. Your victory points grow with the square of that because you gain points for every card gained. Then you may achieve up to another square by using mission, so you are somewhere between 1.032^2 to 1.032^4.
Travellers vp ~ 2^T
+card on peasant
a small fraction of soldiers for $
This allows you to one more peasant for every peasant in play. So my number of peasants grows like 2^T. Then I dedicate a tiny fraction of my gains to Provinces so that they grow at the same speed and use Fugitive to cycle over them.
Durations vp ~ 3.06^T
The number of cards and coins is irrelevant here, because of Wharf and Bridge Troll. The limiting factor is the number of buys I can get. For every 3 buys, I need to play 1 Fishing Village, so I can grow the number of buys like 1.75^T. Because of Outpost, the actual growth per turn is the square of this number.
Reactions vp ~ 9 T
I can grow my number of Market Squares and Caravan Guards exponentially (1.25^T), but unfortunately there is no way to convert that into exponential gains of points, because I cannot cycle past the provinces. With any of the +2 card reactions, I can cycle past 6 Provinces a turn. Hence, if the number of Provinces grows per shuffle like P(S), I need P(S) / 6 turns to cycle till the next shuffle. For exponential growth per shuffle P(S) = x^S the number of points per turn is 6 (x^(S+1) - x^S) / (x^S / 6) = 36 (x - 1) = 9
