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Author Topic: Core Concepts of Dominion Endgames  (Read 1026 times)

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Titandrake

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Core Concepts of Dominion Endgames
« on: August 27, 2019, 03:31:39 am »
+7

(I found this draft in my old files. It's probably over a year old. I don't think I'll have time to polish it for a while, so I'll share it in its unfinished state.)

In my opinion, the most important thing you can do to level up your gameplay is improve your endgame. Dominion endgames are very difficult to play perfectly, but they give concrete edges, because tight endgame play lets you absorb bad luck and misplays without losing.


What is the Endgame?
--------------------------------------------

This is a deceptively tricky question to answer. I define it like this: the endgame starts when players start worrying about how much VP they have or can achieve. I don't define it by when players starting buying Victory cards, because plenty of endgames revolve around the threat of buying VP cards, rather than actually buying them.

Another way to put it is that the endgame is the point where players are thinking about win conditions. Is the board going to 3-pile soon? Am I positioned well? Do I have a lead of VP that I can hold until the end of the game, or can I catch-up to a VP deficit in time?


Level 0: Can I Win This Turn?
---------------------------------------------


On every turn, you should be considering whether you can win this turn. If you have a guaranteed win and you don't go for it, you're leaving free wins on the table.

Of course, this is all very obvious, but I've seen countless players miss clear wins, particularly 3-piles. It's easy to tell when you can empty the Provinces, but 3-piles can be more complex.

Roughly, in the endgame, each player has a certain amount of potential. When ending the game, you are usually bottlenecked by these constraints.

  • The money you can produce
  • The number of gains and buys you have, and what kind they are (Workshop gains are only up to $4 costs, for example).
  • How many points you need to end with a lead.

Your potential is defined along these 3 axes: money, gains, and VP. Different 3-pile endings hit these constraints in different way. For example. with $24 and 3 buys, I can buy 3 Provinces for 18 VP. If I have $16, I can't buy 3 Provinces, but if I have 8 buys/gains and two piles are empty, I can empty Estates for 8 VP. If, somehow, 2 piles are empty, I have $0, I have 10 buys, and have a VP lead of 11 points, then I could even buy 10 Curses to get the 3-pile ending.

The most complicated 3-piles involve overdraw, trash-for-benefit, cards that gain cards to the top of your deck, and so on. Many 3-piles are not this complicated. I generally follow this flowchart:

"Can I gain enough cards this turn to potentially trigger a 3-pile?"
"If I can, do I have enough money and the right types of gains to do so?"
"If I do so, how much do I have left-over to pick up VP, and is that enough?"

If the answer to all these questions is yes, then you have a 3-pile. Otherwise, you don't, which takes you to the next part.


Level 1,2,3,4,...: How Do I Make Sure my Opponent's Can't Win?
-------------------------------------------------------


Now we're getting to the fun stuff. If the most important part of Dominion is ending the game on a win when you can, then the 2nd most important part is making sure your opponent can't do this.

This is much harder because it requires tracking what your opponent's deck can do. Luckily, your opponent does you the favor of playing their turn right before yours. It's usually good enough to get a feel for how strong your opponent's deck is based on what it's previously done, and you can leave the card counting for high-stakes scenarios.

Like every other game, if you can't end the game, you want to make moves that make sure your opponent can't end the game. This is Level 1 - planning 1 turn ahead. Ask the same 3 questions, as if you were your opponent, and see what board states give them the guaranteed win. Then, figure out if that limits anything about what cards are safe to buy this turn.

More subtly, if your opponent is good (and you should always assume your opponent is good), then they're trying to do the same thing as you. So at the same time, you'd like to make moves that give you more endgame potential. The more pileout power your deck has, the more limited your opponent's moves become, since when they do their Level 1 planning, they'll have fewer safe buys because you win in more board states. This is Level 2 - planning 2 turns ahead by making a play that makes it harder for your opponent to play 1 turn ahead.

The levels keep going up from there, but it generally turns into intuition / "game sense" when you try going much further up the hierarchy. Dominion's a game of chance and it's just too hard to reason about the odds several turns in advance.

Once you know what parameters you can play with (what cards are and aren't safe buys), you have a few options.
  • Pick up a bunch of VP this turn. This protects you from losing because it forces your opponent to dedicate more resources to picking up points, which can give protection against pileouts. It can stop you from winning because your deck will generally become less consistent.
  • Pick up a cards that increase what your deck can do. This makes life harder for your opponent, because it opens up more potential pileouts, but it doesn't give you any points and it generally brings the game closer to an end.
  • Do a bit of both: buy some Actions and Treasures and then pick up some VP as well.

In correct play, you want to be spending all your gains on Actions, then flip a switch and spend all your gains on VP until the end of the game. Because of this, the 3rd choice of "do a bit of both" is something you want to do at most once, if you're on a in-between turn between deck improvement and cashing in your deck for points. If you end up doing this multiple times, you're probably playing loose, or the game's just weird.

When unsure whether you should build or buy points, building is usually better because it keeps your deck more consistent. If possible, you really want to keep your deck consistent in the endgame, because the endgame is about threatening what your deck can do. If your deck isn't consistent, then your opponent can respect your pileouts less, and that frees up their options.
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JW

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Re: Core Concepts of Dominion Endgames
« Reply #1 on: August 27, 2019, 02:22:12 pm »
+1

In correct play, you want to be spending all your gains on Actions, then flip a switch and spend all your gains on VP until the end of the game. Because of this, the 3rd choice of "do a bit of both" is something you want to do at most once, if you're on a in-between turn between deck improvement and cashing in your deck for points. If you end up doing this multiple times, you're probably playing loose, or the game's just weird.

One common situation when it's correct to keep picking up Actions while also buying cards that give VP has nothing to do with endgame conditions but just the lumpiness of $ that your deck generates.  If your deck generates $12 and 3 buys, there's a period of time (when the game isn't about to end) when you're going to pick up Province and another action (Smithy, Village, etc.), rather than Province and 2 Estates.  Of course, another element of building your deck is planning how much $ you build your deck to generate so that you can do the right amount of buying VP at the right time. In this example, building to $16 so that you can double-Province may be well worth it.
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Titandrake

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Re: Core Concepts of Dominion Endgames
« Reply #2 on: August 28, 2019, 01:43:21 am »
0

In correct play, you want to be spending all your gains on Actions, then flip a switch and spend all your gains on VP until the end of the game. Because of this, the 3rd choice of "do a bit of both" is something you want to do at most once, if you're on a in-between turn between deck improvement and cashing in your deck for points. If you end up doing this multiple times, you're probably playing loose, or the game's just weird.

One common situation when it's correct to keep picking up Actions while also buying cards that give VP has nothing to do with endgame conditions but just the lumpiness of $ that your deck generates.  If your deck generates $12 and 3 buys, there's a period of time (when the game isn't about to end) when you're going to pick up Province and another action (Smithy, Village, etc.), rather than Province and 2 Estates.  Of course, another element of building your deck is planning how much $ you build your deck to generate so that you can do the right amount of buying VP at the right time. In this example, building to $16 so that you can double-Province may be well worth it.

$12 and 3 buys is a bad example because I think I'd buy 3 actions in that situation, especially if I can expect to see 3 buys every turn.

I see the lumpiness point, but to me, if you're thinking of buying Province + Smithy, you're already in the endgame, you just haven't crossed the threshold of wanting to buy Duchies yet.
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faust

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Re: Core Concepts of Dominion Endgames
« Reply #3 on: August 28, 2019, 03:16:14 am »
+2

In correct play, you want to be spending all your gains on Actions, then flip a switch and spend all your gains on VP until the end of the game. Because of this, the 3rd choice of "do a bit of both" is something you want to do at most once, if you're on a in-between turn between deck improvement and cashing in your deck for points. If you end up doing this multiple times, you're probably playing loose, or the game's just weird.

One common situation when it's correct to keep picking up Actions while also buying cards that give VP has nothing to do with endgame conditions but just the lumpiness of $ that your deck generates.  If your deck generates $12 and 3 buys, there's a period of time (when the game isn't about to end) when you're going to pick up Province and another action (Smithy, Village, etc.), rather than Province and 2 Estates.  Of course, another element of building your deck is planning how much $ you build your deck to generate so that you can do the right amount of buying VP at the right time. In this example, building to $16 so that you can double-Province may be well worth it.

$12 and 3 buys is a bad example because I think I'd buy 3 actions in that situation, especially if I can expect to see 3 buys every turn.

I see the lumpiness point, but to me, if you're thinking of buying Province + Smithy, you're already in the endgame, you just haven't crossed the threshold of wanting to buy Duchies yet.
But the section quoted from the article implies that you'll start wanting to buy Duchies at the same time you want to get Provinces. That's not true as you yourself just stated, so it should probably be reworked.
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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: Core Concepts of Dominion Endgames
« Reply #4 on: August 28, 2019, 03:20:59 am »
0

Maybe there could also be a section on when to break this way of playing and just hope that your opponent duds out for a turn.
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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.

crj

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Re: Core Concepts of Dominion Endgames
« Reply #5 on: August 29, 2019, 05:56:14 pm »
0

I like this article; it says in plain language things that are obvious with hindsight, maybe even already known intuitively, and gives them greater clarity.

There are a couple of extra things I'd be interested to read your thoughts on:
  • Alt-VP (Gardens v. Provinces endgames, or whatever)
  • VP that don't clog your deck (Island, VP tokens, etc.)
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