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nasmith99

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Maximum possible scores
« on: January 12, 2019, 02:52:40 pm »
+1

Define the maximum possible score of a given kingdom to be the highest score it is possible to obtain on that kingdom in a single player game. Some kingdoms don't have a highest such number, and nothing exotic has to happen for this to be the case (the inclusion of monument will do, for instance.)

Among kingdoms with a finite maximum possible score, what is the highest maximum possible score? As an easier challenge, what is the lowest maximum possible score? (Note there is no restriction on the number of turns required to obtain the maximum possible, or on shuffle luck. All that is required is that the score is possible.)

My progress:

Highest:
The best I've done so far is 6940.

The kingdom is as follows: Goons, Groundskeeper, Scrying Pool, Gardens, Feodum, Silk Road, Fairgrounds, Cultist (any looter will do), Rats, Young Witch, Tunnel as the bane.

Exploration, Travelling Fair, Triumph, and Tower.

Colony/Plat yes, shelters no.

The outline of what I'm doing here:

Exploration gives you unlimited coins and actions, Tfair gives you unlimited buys. Scrying pool gives you draw and puts potion in the kingdom. Goons, groundskeeper, and triumph are your main sources of points. Here's the play-by-play:

-Buy exploration and pass on as many turns as needed to have enough villagers and coffers to do all the future steps.
-Buy 5 goons one by one, only buying the next once you draw all the goons you've already bought.
-Buy potion with 5 goons in hand.
-Buy Scrying Pool with 4 goons in hand.
-Buy the remaining 5 goons one by one, only buying when you draw all the previous goons. (Scrying pool makes it possible to draw all of them.)
-Buy 8 more Scrying Pools one by one, only buying with all 10 goons in play.
-Buy 10 Groundkeepers with all 10 Goons in play.
-Once you have a turn where you draw all the goons, all the groundskeepers, and your potion, buy the entire supply minus the estates. Then buy 8 Triumphs.

By my calculations, this gives 6940 points, though it is possible I made an arithmetic mistake somewhere. The amount of points possible on this board is in fact bounded since each individual point source can only give a bounded number of points (e.x. each triumph can't give you more points than there are cards in the supply, and you can only buy 8 of them).


Lowest:
I'm reasonably confident the answer is 43.

The only card-shaped objects that can force you to lose points are wolf den, wall, and bandit fort. On a board will all three of these and shelters, you can score 43 points by buying 3 silvers, then buying all the provinces and duchies. You score 72 from the victory cards, lose 29-15=14 from wall, lose 9 from wolf den, and lose 6 from bandit fort, putting you at 43 VP. It's not difficult to make a board with a bunch of useless kingdom cards that can't improve this strategy. While they could make you lose more points to wolf den, none of the heirlooms appear to make this situation worse since they all offer an improvement allowing you to score more than 43 points.
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faust

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Re: Maximum possible scores
« Reply #1 on: January 12, 2019, 05:46:25 pm »
+1

Lowest:
I'm reasonably confident the answer is 43.

The only card-shaped objects that can force you to lose points are wolf den, wall, and bandit fort. On a board will all three of these and shelters, you can score 43 points by buying 3 silvers, then buying all the provinces and duchies. You score 72 from the victory cards, lose 29-15=14 from wall, lose 9 from wolf den, and lose 6 from bandit fort, putting you at 43 VP. It's not difficult to make a board with a bunch of useless kingdom cards that can't improve this strategy. While they could make you lose more points to wolf den, none of the heirlooms appear to make this situation worse since they all offer an improvement allowing you to score more than 43 points.

You can trash Hovel here, so the score should be 3 higher.
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Since the number of points is within a constant factor of the number of city quarters, in the long run we can get (4 - ε) ↑↑ n points in n turns for any ε > 0.

nasmith99

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Re: Maximum possible scores
« Reply #2 on: January 12, 2019, 10:03:27 pm »
+1

Lowest:
I'm reasonably confident the answer is 43.

The only card-shaped objects that can force you to lose points are wolf den, wall, and bandit fort. On a board will all three of these and shelters, you can score 43 points by buying 3 silvers, then buying all the provinces and duchies. You score 72 from the victory cards, lose 29-15=14 from wall, lose 9 from wolf den, and lose 6 from bandit fort, putting you at 43 VP. It's not difficult to make a board with a bunch of useless kingdom cards that can't improve this strategy. While they could make you lose more points to wolf den, none of the heirlooms appear to make this situation worse since they all offer an improvement allowing you to score more than 43 points.

You can trash Hovel here, so the score should be 3 higher.
Good catch. 4 higher in fact, because of wall.
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sudgy

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Re: Maximum possible scores
« Reply #3 on: January 13, 2019, 01:26:03 am »
+1

I posted a thread with this same question years ago.  You might be able to find some ideas there, if you can find it.
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   Quote from: sudgy on June 31, 2011, 11:47:46 pm

Holger

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Re: Maximum possible scores
« Reply #4 on: January 13, 2019, 05:46:44 am »
0

Lowest:
I'm reasonably confident the answer is 43.

The only card-shaped objects that can force you to lose points are wolf den, wall, and bandit fort. On a board will all three of these and shelters, you can score 43 points by buying 3 silvers, then buying all the provinces and duchies. You score 72 from the victory cards, lose 29-15=14 from wall, lose 9 from wolf den, and lose 6 from bandit fort, putting you at 43 VP. It's not difficult to make a board with a bunch of useless kingdom cards that can't improve this strategy. While they could make you lose more points to wolf den, none of the heirlooms appear to make this situation worse since they all offer an improvement allowing you to score more than 43 points.

You can trash Hovel here, so the score should be 3 higher.
Good catch. 4 higher in fact, because of wall.
Pooka/Cursed Gold decreases your maximum score by 1 VP:
Cursed Gold reduces your score by another 3VP even if you never play it. You can buy Pooka to mitigate this, but AFAICS the best you can do is get 2 Pookas and 2 Gold instead of 2 Silvers and trash four of the six coppers in the end (so you can buy the last Province with GGCC). Then you end up with 7 non-VP cards on your deck instead of nine (2S, 7 C), saving you 2 VP from Wall, for a total of -1VP.
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Holger

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Re: Maximum possible scores
« Reply #5 on: January 13, 2019, 06:02:15 am »
0

Lowest:
I'm reasonably confident the answer is 43.

The only card-shaped objects that can force you to lose points are wolf den, wall, and bandit fort. On a board will all three of these and shelters, you can score 43 points by buying 3 silvers, then buying all the provinces and duchies. You score 72 from the victory cards, lose 29-15=14 from wall, lose 9 from wolf den, and lose 6 from bandit fort, putting you at 43 VP. It's not difficult to make a board with a bunch of useless kingdom cards that can't improve this strategy. While they could make you lose more points to wolf den, none of the heirlooms appear to make this situation worse since they all offer an improvement allowing you to score more than 43 points.

You can trash Hovel here, so the score should be 3 higher.
Good catch. 4 higher in fact, because of wall.
Pooka/Cursed Gold decreases your maximum score by 1 VP:
Cursed Gold reduces your score by another 3VP even if you never play it. You can buy Pooka to mitigate this, but AFAICS the best you can do is get 2 Pookas and 2 Gold instead of 2 Silvers and trash four of the six coppers in the end (so you can buy the last Province with GGCC). Then you end up with 7 non-VP cards on your deck instead of nine (2S, 7 C), saving you 2 VP from Wall, for a total of -1VP.
Damn, I forgot Necropolis. You can replace the 2 Gold by 6 Coppers (buying an extra Copper to have eight, plus the Pooka fodder - funny that there is a Wall board where you want to have extra Coppers  :P). Then you can buy the last Province with Necropolis and 2 Pookas, which draw you 8 Coppers (in addition to the two you just trashed).
So Pooka/CG is +1 VP instead of -1VP, i.e. it doesn't help to lower the score.
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Holger

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Re: Maximum possible scores
« Reply #6 on: January 13, 2019, 09:41:02 am »
0

I posted a thread with this same question years ago.  You might be able to find some ideas there, if you can find it.

Here it is:
I don't know why I like thinking up of next-to-impossible puzzles, but this one seems fairly interesting.  Without Monument, Fortress, Trader, Rogue, or Graverobber (so you can't get infinite points), what is the maximum amount of points you can get in a solitaire game?

Alright, easier definition (suggested by SirPeebles): Among kingdoms with an upper bound on available VP, what is the highest attainable score?

Faust got up to 8355 points pre-Adventures, with more than half coming from Goons. Just adding the ~100 new cards to the Black Market gives you >1000 extra points, without caring what the cards do. Museum adds another >600 VP, so we can easily get above 10,000 VP. With all the extra VPs from the other Empires cards and Landmarks, it can potentially get much higher still...
« Last Edit: January 13, 2019, 09:55:47 am by Holger »
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nasmith99

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Re: Maximum possible scores
« Reply #7 on: January 13, 2019, 06:21:03 pm »
+2

This isn't optimized yet, but I figured out a way to blow my previous attempt for the max score out of the water.

The basic idea is to play Priest as many times as possible (on Fortress), then use Watchtower and Travelling Fair to buy and trash everything left in the supply, generating oodles of coin with Priest, then converting the coins into points with Conquest.

I think the maximum number of times you can play Priest in a turn is 60 (possible with King's Court, Royal Carriage, Scepter, and Counterfeit). (Edit: more than 60 is possible, see the below posts) Once you do this with Watchtower in hand, you're pretty much off to the races. Apprentice is also a convenient source of draw to line everything up.

With much patience, I actually executed this (Game ID: 22362091). (Or rather, I executed everything except buying the 4022 Conquests at the end). The point total I obtained was 163,899. This could certainly be improved with perfect shuffle luck (i.e. drawing Priests early so you can play them before the Apprentices), but I think the most important thing is getting all 60 Priest plays, which I did. In retrospect, Goons wasn't really doing much here, since the points it gives you are dwarfed by all the points you're getting from Conquest. If I was going to do it over again, I would probably substitute Forge for Goons, and then buy 9 Fortresses instead of just 1. 

Edit: I switched out Goons for Forge and Delve for Sewers (Sewers is huge, basically doubling your payload). Here's (Game ID: 22365938) the more optimized build, scoring 418960 VP. Adding Bonfire instead of Triumph would push the total even higher.

« Last Edit: January 14, 2019, 08:09:54 pm by nasmith99 »
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faust

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Re: Maximum possible scores
« Reply #8 on: January 14, 2019, 02:51:31 am »
+1

I think the maximum number of times you can play Priest in a turn is 60 (possible with King's Court, Royal Carriage, Scepter, and Counterfeit).
I think you're forgetting Inheritance.
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Since the number of points is within a constant factor of the number of city quarters, in the long run we can get (4 - ε) ↑↑ n points in n turns for any ε > 0.

nasmith99

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Re: Maximum possible scores
« Reply #9 on: January 14, 2019, 08:09:14 pm »
0

I think the maximum number of times you can play Priest in a turn is 60 (possible with King's Court, Royal Carriage, Scepter, and Counterfeit).
I think you're forgetting Inheritance.
Yeah, plus you can also do stuff like Capitalism+Mandarin+Rogue. I'll edit to fix that.
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Holger

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Re: Maximum possible scores
« Reply #10 on: January 15, 2019, 05:34:26 pm »
0

I think the maximum number of times you can play Priest in a turn is 60 (possible with King's Court, Royal Carriage, Scepter, and Counterfeit).
I think you're forgetting Inheritance.
Yeah, plus you can also do stuff like Capitalism+Mandarin+Rogue. I'll edit to fix that.

Rogue leads to unlimited VP's as your can trash and gain Silvers back an unlimited number of times. Anything returning cards from play is potentially  dangerous too...
It seems your basic idea doesn't allow infinite VPs however, which surprises me. Great find!
 
I was about to post about my own improvement of the old ideas here to get about 12,500 points using just two "non-cards" (Triumph and TF) as recommended in the rules. But it seems pointless now. :-[
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