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Titandrake

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Castles
« on: March 28, 2018, 02:40:07 am »
+10




Despite having lots of different effects, Castles aren't that complicated. Just think of them as having a 2nd pile of Provinces in the game. If it's the kind of game where that's appealing to you, then imagine when you'd start greening in a game with 2 Provinces, and start buying Castles about 1 shuffle or 1-3 turns before that.

If you do the math, buying 8 Castles gives you 45 VP, plus whatever VP you gained from buying Grand Castle. 8 Provinces gives 48 VP. In principle, this shows that buying only Castles in competitive with buying only Provinces. In practice, no one will ever let you buy all the Castles uncontested. At minimum, expect competition on the $8+ Castles. Sprawling and Grand are almost always worth more VP than a Province, and players will buy King just to deny VP from the player who has more Castles.

Having more VP in the kingdom leads to all the follow-on effects you'd expect. More VP makes the game go longer, and longer games favors building your deck more. Many of the Castles help with this - all the Castles between $4 and $7 give you more than just VP. The two Action castles, Small Castle and Opulent Castle, are particularly important. Small Castle can quickly upgrade itself into a better Castle, whereas Opulent is important because it can produce a lot of money when players start greening. This makes buying either Crumbling Castle or Haunted Castle a bit of a risk, because it gives your opponent the first chance at buying Small Castle and Opulent Castle respectively. Of course, how big a risk this depends on how long you think the game is going to go. The sooner the game end, the less the Action castles matter. Buying Haunted Castle also makes it less likely your opponent hits $7. I often find that the risk of revealing Opulent Castle is worth the 2 VP + Gold + topdeck attack that Haunted Castle gives.

As for Humble Castle, it's a little weird. It gives VP for every Castle, and there's only 1 Humble Castle, which can make it look like it's worth fighting over. However, it's still a genuinely bad card to buy. At the end of the game, Humble Castle is usually worth 3 VP to 5 VP, and although that's above-average rate for $3, buying it early on is a huge opportunity cost. There are two cases where it's worth buying Humble Castle early. One is Shelters games, to turn your starting Hovel into a Copper. The other is Keep. In a Keep game, Humble Castle is always worth at least 6 VP. Even in this scenario, I don't like opening Humble Castle. 6 VP for $3 is very cheap, but opening buys are very, very important. On most boards I'd gladly give my opponent 6 VP if they were forced to open Copper.

Besides these considerations, Castles are mostly a tactical decision, not a strategical one. They aren't like Gardens, or Duke, or Fairgrounds, where you have to plan a bit to get VP out of them. Castles are just there, and whether the VP is worth it or not depends on where you think your deck and the game are at.
« Last Edit: March 30, 2018, 04:14:33 am by Titandrake »
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faust

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Re: Castles
« Reply #1 on: March 28, 2018, 05:57:46 am »
+1

I feel like most of this article is wrong. Castles are absolutely a strategical decision, especially Opulent Castle. Castles in general are better in engines than in BM, a point that is missing entirely.

Considering tht the article claims Castles are mainly tactical, it provides suprisingly little infomation on the tactics of playing Castles. When is it worth it to go for e.g. Haunted Castle just for the attack and the Gold?
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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.

aku_chi

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Re: Castles
« Reply #2 on: March 28, 2018, 09:07:51 am »
+3

Great article, Titandrake!  The most important takeaway is to treat Castles as another pile of Provinces, except you should pick them up slightly before you would pick up Provinces (when compared with a kingdom with an extra pile of Provinces) - because the early Castles don't hurt your deck as much as completely dead green cards.  My biggest disagreement is: Haunted Castle is often the strongest Castle, so don't worry about revealing Opulent Castle (which is strong on a smaller subset of boards).

As for the strategic decision for when to pursue Castles, my current heuristic is: Castles are good in games where you would (otherwise) buy Provinces before the last turn of the game.

So, Castles are not good in games that are going to explosively end on piles.  Castles are not good in the face of a full Province megaturn.  Castles are not going to be good if Alt VP completely outstrips Provinces (e.g. Goons).  If the best payload involves remodeling into Provinces, Castles might not be competitive.  In most other situations, a greening strategy that involves Castles will be superior to a greening strategy that does not.
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faust

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Re: Castles
« Reply #3 on: March 28, 2018, 11:05:04 am »
+3

Some more detailed criticism.

Despite having lots of different effects, Castles aren't that complicated. Just think of them as another pile of Provinces, where you should start buying them about 1 shuffle or 1-3 turns before you'd normally buy Provinces.
This is good as an opening - so stylistically - in that it already states your main thesis. I don't think it is correct as there are plenty of boards where Provinces are good and Castles are not, most notably any BM game.

If you do the math, buying 8 Castles gives you 45 VP, plus whatever VP you gained from buying Grand Castle. 8 Provinces gives 48 VP. This comparison actually doesn't matter
This is just odd. If you make a statement and then say it doesn't matter, then the statement shouldn't be in the article to begin with.

Having more VP in the kingdom leads to all the follow-on effects you'd expect - games tend to go longer because people have a source of VP besides just Provinces, which encourages building your deck more. Many of the Castles help with this - all the Castles between $4 and $7 give you more than just VP.
So this is an important point since it implies that Castles are good for engines, as engines generally profit from more building time. But this should also be spelled out and not be hidden away like this; it's the most important insight into Castles.

Small Castle is important because the player can use it to quickly snipe the King's Castle.
I used to think that, but nowadays I feels like it mostly doesn't matter much. Having a Small Castle in hand just in time for sniping King's isn't all that likely, and until then your opponent has to keep a dead card around (assuming they're not going for Castles).

Opulent is important because it can produce a lot of money when players start greening.
A bit of an understatement, but true. I mean when you get Opulent Castle, there is a good chance you already started greening. Getting that Castle allows you to cut down on your other economy in order to keep a stable deck for longer. Certain decks you don't need to build up too much at all, just make sure you can hit $7 and then gun for Opulent, and use green cards for ecomony for the rest of the game.

This makes buying either Crumbling Castle or Haunted Castle a bit of a risk
While true, it should be mentioned that Haunted also makes it significantly less likely that your opponent will hit $7 on their next turn.

As for Humble Castle - I don't have the greatest feel for when to buy it, but I don't think it's worth going out of your way to do so. It's worth anywhere from 3 VP to 5 VP, and although that's above-average rate for $3, buying it early on is a huge opportunity cost. Special mention should be paid to Humble Castle and Keep. If both are on the board, Humble Castle is worth at least 6 VP. Even in this scenario, I think you're better off not opening Humble Castle. Opening buys are very, very important, and on most boards I'd gladly give my opponent 6 VP if they were forced to open Copper.
Humble Castle is a tricky one. I think if you mention Keep, you absolutely should mention Hovel, as trashing Hovel for Humble Castle is a decent move in the opening. It seems strange that you give a definite time in the start for when to buy Castles and then say you don't have a good feel for when to get Humble. Clearly the answer should be 1 shuffle before you would buy Provinces?
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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.

weesh

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Re: Castles
« Reply #4 on: March 28, 2018, 11:30:31 am »
+1

If a kingdom consisted only of silver/gold/estate/dutchy/province/castles...I would buy castles.
And if a kingdom had cards that liking having victory cards in your deck, I'd be...intrigued.

But when castles randomly show up, they just don't get purchased among my friends.
What I'd like to see in an article is an explanation of what you look for in a kingdom that makes buying the castles a good idea, and at what phase to start buying them in the game.

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Chappy7

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Re: Castles
« Reply #5 on: March 28, 2018, 11:35:11 am »
+1

Castles may not be crazy strong, but I think they are one of the most fun (and certainly one of the most unique) kingdom piles.  I'd love to see more piles like this in the future. 

I'm glad to see an article about them. 
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DG

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Re: Castles
« Reply #6 on: March 28, 2018, 11:49:19 am »
+2

To expand the discussion :-
- If you are the sole player buying castles, how you you build your deck differently compared to a province buying deck (more income, less income? less terminals? different trashing?)
- If you are playing against a player also buying castles, are there any castles you shouldn't buy as it reveals a key one for your opponent?
- If you are playing a mixed castle and province strategy, when should you switch between castle buying and normal deck building?

People always ask about multiplayer to be included in articles so ... there are a lot more castle points in multiplayer and it is a harder pile to ignore. The two humble castles become important when one player has both. The game is likely to be messy as you have multiple opponents messing up whatever plan you have for the unique castle cards.
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trivialknot

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Re: Castles
« Reply #7 on: March 28, 2018, 12:09:25 pm »
+1

I like and mostly agree with this article.

I agree that Castles should be treated as another pile of provinces, and the most important implication is that you need to build more.  When there are 16 Victory cards to distribute before the end of the game (even if some of them have utility), you want a deck that can handle lots of green.  This can be true even when you don't buy a single Castle, because if your strategy is too short-sighted, your opponent can always extend the game by choosing to ignore Provinces and go for Castles.  There are some exceptions, like when it's easy to drain Provinces, or when the game ends on piles.

In 2P, there's a rough rule of thumb for the VP value of each castle: 4.5, 3.5, 3.5, 3.5, 4.5, 8.5, 6.5+x, 7.5

The way you calculate the value of a Castle in 2P is by looking at the size of the VP swing.  For example, the Haunted Castle is a 4 VP swing by itself, plus an additional 3 VP if players have Humble and King's (regardless of which player actually has them).  That's a 7 VP swing, so it's a bit like Haunted Castle is worth 3.5 VP.  Generally two of the castles get trashed (Crumbling and Small), which means that Humble is a 9 VP swing and King's is a 15 VP swing, which is why I place their values at 4.5 and 7.5.  Obviously the rule of thumb ignores a bunch of wrinkles, like if a different number of castles get trashed, or if King's Castle doesn't get bought.  And the player with no castles would rather end the game than get King's castle, etc. etc.
« Last Edit: March 28, 2018, 12:10:40 pm by trivialknot »
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timchen

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Re: Castles
« Reply #8 on: March 29, 2018, 02:49:16 pm »
+1

Fundamentally there is a contradiction in the article: if the biggest effect is like another province pile, how can that be you should start buying them 1-3 turns earlier than you normally would with provinces? Should you not build for longer?

Now that I think about this a little bit... the effect of humble and king's is actually linear so that the split of the castles do not affect their value, at least if they are not left in the supply. So maybe the correct answer would be that normally one should not think about buying them earlier and it is a cognition bias somehow that accumulating those castles early on can get you more points later?
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Titandrake

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Re: Castles
« Reply #9 on: March 30, 2018, 04:21:31 am »
0

I made some edits.

Re the 1-3 turns thing: after thinking about it I agree that you usually start greening a bit later just because there's more VP, so I made that clearer in the heuristic.

Re Small Castle: I also find that I usually don't keep my Small Castle all the way to King, but I do find it useful to trash it in quickly to gain one of the more expensive Castles. In more engine-like games I've also found that having Small Castle in your deck helps exert a lot of pressure over the Castle pile.

I'm pretty sure in a BM game, mostly-Castles-and-some-Provinces beats Provinces-first-and-Castle-sniping-late. This should be reasonably simulatable because it's Big Money, I'd be curious to see the numbers.

Re Humble Castle: I mostly find the card very confusing, because the card text suggests that you want to pick it up early, but the payoff is so small that it's rarely worth buying early. I wasn't sure how to explain that, so I wrote something completely different instead. Changing it to say what I wanted to say.

Agreed that Haunted Castle is a pretty good VP card, added a note for this.
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faust

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Re: Castles
« Reply #10 on: March 30, 2018, 05:48:52 am »
+2

I'm pretty sure in a BM game, mostly-Castles-and-some-Provinces beats Provinces-first-and-Castle-sniping-late. This should be reasonably simulatable because it's Big Money, I'd be curious to see the numbers.
Well I have done some simulation, though it's not optimized.

The Castle-countering strategy was fairly simple. It would always compete for Grand and King's Castle, and competes for Opulent, Haunted and Small Castle if it cannot afford a Province.

For the Castles-centric strategy, I have tried to implement a strategy that goes for Castles earlier than Provinces (BMU goes for Provinces with $19+ in deck). I fiddled around with the number of $ needed to start buying Castles, but I got the best results leaving it at $19+ as well, and then it still loses to Castle-sniping 33-64.

Another way to do Castles is to dive straight in. Surpringly, a strategy that always prefers Castles over Silver (i.e. that would open Small/Crumbling on 3/4) performs better! But it still loses to the Castle Sniper 41-56.

Feel free to come up with better bots!
« Last Edit: March 30, 2018, 05:55:34 am by faust »
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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.

faust

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Re: Castles
« Reply #11 on: March 30, 2018, 05:58:35 am »
0

Full buy rules for my Castle Sniper bot. Feel free to try and beat it:

Code: [Select]
Buy Castles if cards in smallest supply pile < 3
Buy Province if total $ in deck > 18
Buy Castles if cards in smallest supply pile < 7 and > 3
Buy Castles if count in supply (Provinces) < 5
Buy Duchy if count in supply (Provinces) < 5
Buy Estate if count in suppy (Provinces) < 3
Buy Gold
Buy Duchy if count in supply (Provinces) < 7
Buy Silver
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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.

Screwyioux

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Re: Castles
« Reply #12 on: March 30, 2018, 01:30:45 pm »
0

This is a solid writeup, well done.

I agree with pretty much everything you said (especially the last sentence), there are just a couple of things I would add/ be curious to hear your analysis on.

One is Small Castle. You address it, but I'd like to hear some analysis on when it's a strong play to play it as soon as possible, when you hold out to trash Crumbling Castle with it, how long you want to hang onto it with hopes of a free Sprawling or King, etc (probably one of the weaker parts of my castles game).

There's also one other differentiating factor between Castles and a second Province pile. A province is worth 6 points no matter who buys it or when, whereas the castles hold asymmetric value to players based on who bought what and when. You kind of get at that by stressing that Castles are a tactic, not a strategy, but I think it's also worth mentioning that determining the importance/effectiveness of that tactic early on is more important to castles than it would be for Fairgrounds, Duke, etc.


Again though, good job, I quite like this article.

Short, to-the-point, narrow and specific scope using particular examples to convey a general idea. I'd like to see more writing like this out there.
« Last Edit: March 30, 2018, 01:51:02 pm by Screwyioux »
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JW

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Re: Castles
« Reply #13 on: March 30, 2018, 01:55:04 pm »
+1

This article only discusses the Castle pile as if 8 cards are it in. While itís fine to write an article only discussing Castles in the context of two player games, you should be more explicit about this in the introduction. I couldnít even tell you which Castles there are two copies of in 3 plus player games!
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Mic Qsenoch

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Re: Castles
« Reply #14 on: March 30, 2018, 02:24:56 pm »
+4

I couldnít even tell you which Castles there are two copies of in 3 plus player games!
The mnemonic is Castle counters and Actions.
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pacovf

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Re: Castles
« Reply #15 on: March 30, 2018, 02:49:10 pm »
0

This article only discusses the Castle pile as if 8 cards are it in. While itís fine to write an article only discussing Castles in the context of two player games, you should be more explicit about this in the introduction. I couldnít even tell you which Castles there are two copies of in 3 plus player games!

Thereís also up to 53 extra points in the Castle pile in 3-4 player games, while only 24 extra points in the province pile. I doubt you will be able to piledrive Castles in those games, but still.
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theorel

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Re: Castles
« Reply #16 on: April 06, 2018, 03:10:37 pm »
+2

I'm pretty sure in a BM game, mostly-Castles-and-some-Provinces beats Provinces-first-and-Castle-sniping-late. This should be reasonably simulatable because it's Big Money, I'd be curious to see the numbers.
Well I have done some simulation, though it's not optimized.

The Castle-countering strategy was fairly simple. It would always compete for Grand and King's Castle, and competes for Opulent, Haunted and Small Castle if it cannot afford a Province.

For the Castles-centric strategy, I have tried to implement a strategy that goes for Castles earlier than Provinces (BMU goes for Provinces with $19+ in deck). I fiddled around with the number of $ needed to start buying Castles, but I got the best results leaving it at $19+ as well, and then it still loses to Castle-sniping 33-64.

Another way to do Castles is to dive straight in. Surpringly, a strategy that always prefers Castles over Silver (i.e. that would open Small/Crumbling on 3/4) performs better! But it still loses to the Castle Sniper 41-56.

Feel free to come up with better bots!
I'm not sure what you did for the Castles-centric strategy...when I tried it, I got castles winning over the sniper you posted 57-40.  (I just added a Castle buy-rule above Provinces with the same $19+ requirement).

I wondered from discussion in this thead, if waiting longer would be better.  Increasing the wait time for provinces/castles beyond $19 improves things a bit, but hurts the mirror match.

So if we take the buy rules to be:
Castles if total money in deck > $X
Provinces if total money in deck >$18 and >$X
Duchies if Provinces < 5
Estate if Provinces < 3
Gold
Duchy if Province < 7
Silver

Increasing just the province start-money has minimal impact as far as I can tell.  I haven't played much with decreasing it below castles.

then for X=$18 I get: 57-40 over sniper (70-27 over BMU)
for X=$20 I get: 59-38, so it does just a bit better.  (but loses 48-50 vs X=$18)
for X=$22 I get: 61-36 vs sniper, but loses 47-50 vs X=$18.
Dropping X below 18 doesn't improve things much though, unless you drop it to 0, but even then it's barely squeaking out against X=$18 at 50-47.  And loses to the Castle Sniping (as noted by faust, 41-56).
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faust

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Re: Castles
« Reply #17 on: April 07, 2018, 12:40:00 pm »
0

I feel like this might be due to a certain lack of precision in the Castle Sniper... I could not implement something that checks the number of Castles left in supply, so I did "lowest supply pile". But in a game where the opponent hardly ever buys Castles (and your "Castle" strategies may easily lead to games where they never buy Castles), the lowest supply pile will be Province or Duchy, leading to suboptimal decision making.
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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.

theorel

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Re: Castles
« Reply #18 on: April 09, 2018, 09:59:54 am »
0

I feel like this might be due to a certain lack of precision in the Castle Sniper... I could not implement something that checks the number of Castles left in supply, so I did "lowest supply pile". But in a game where the opponent hardly ever buys Castles (and your "Castle" strategies may easily lead to games where they never buy Castles), the lowest supply pile will be Province or Duchy, leading to suboptimal decision making.
Either you misread my strategy or I misunderstood how the simulator works.  I put Castles above Provinces in the buy rules, and always gave them the same money cut-off (except when I gave a smaller one for castles).  My understanding is that it should always buy castles first, then provinces if it can't afford a castle (or the castles are out).
Geronimoo's simulator can check castles left in supply...so I went ahead and implemented that version...so the updated rules for the sniper are:

Castles if count in supply Castles < 3
Provinces if total $ in deck > $18
Castles if count in supply Castles < 7 and > 3
Duchy if count in supply Provinces < 5
Estate if count in supply Provinces < 3
Gold
Duchy if count in supply Province < 7
Silver
This does about the same (57-40 vs buying castles-then provinces at $19+).
In a sample game, the Castles strategy picked up, 2 Estates, 3 Duchies, 4 Provinces, and 5 of the Castles, while the Sniper got 2 Estates, 2 Duchies, 4 Provinces, and 2 of the Castles (Grand and King's...he bought Small as well, but trashed it for King's).  So I'm pretty sure these buy rules are accurate.  The Sniper in the sample only got 1 province before the castles strategy started in on them, but he got both the really big Castles.
« Last Edit: April 09, 2018, 10:01:13 am by theorel »
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faust

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Re: Castles
« Reply #19 on: April 09, 2018, 10:12:02 am »
0

Hm, for some reason I thought that that check would only look for cards named "Castles" in the supply... I have to check if I have the most current version of the simulator and then run some more tests.
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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.

Aleimon Thimble

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Re: Castles
« Reply #20 on: April 13, 2018, 09:46:25 am »
0

I added the article to the Wiki, since Castles did not have a strategy section yet. If you object to this, let me know.

http://wiki.dominionstrategy.com/index.php/Castle#Strategy
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