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Author Topic: Are many kingdom sets essentially "solvable"?  (Read 4081 times)

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Jive Junkie

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Are many kingdom sets essentially "solvable"?
« on: August 28, 2012, 09:25:54 pm »
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I was browsing some older posts earlier, and one of the top-level players here (I forget which) was mentioning that when he saw a kingdom where Big Money + Envoy was the winning strategy, he would die a little inside (or something to that effect).

That got me thinking: Are there many kingdom sets that are essentially solvable, with such a dominant strategy that even if your opponent knew exactly what you were going to do, it would still make sense to follow suit?

I definitely do think that some kingdom sets are highly variable and depend very much on what other players are doing - a lot of the official sets seem to have been designed with this trait in mind.

But how often, when looking at a kingdom set, do you think to yourself: OK, I have to do strategy X no matter what. As a side question, how often do you think you are correct when you do so?
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ftl

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Re: Are many kingdom sets essentially "solvable"?
« Reply #1 on: August 28, 2012, 09:54:40 pm »
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Pretty often, I think. I think that in a large fraction of kingdoms, there's a roughly dominant strategy, and if one person does it and the other does not, that'll decide the game right there. However, most such matches aren't boring - even if both players have the same general idea, the devil is in the details. Sometimes it's worth it to grab slightly too many of a card to deny some to your opponent, sometimes you need to decide when to green based on what your opponent is doing, you can pick up engine components in a better order than your opponent, and so forth. There's a lot of things that add up to 'playing better' even if you've already decided on an overall strategy.

If you mean that you're going to buy the exact same things all game regardless of what your opponent is doing, probably never. At the very least, considerations like PPR will come up in every close game, even BM+Envoy.

...I guess it depends in the end on how narrowly you define "strategy X". Like, in a lot of games with, say, Goons, the optimal strategy is "an engine with Goons", but there's a lot of variation in how you can put together that engine, and with goons engines you basically always have to respond to your opponent based on how low piles are.
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Karrow

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Re: Are many kingdom sets essentially "solvable"?
« Reply #2 on: August 28, 2012, 10:14:59 pm »
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Open 5/2, see a Witch or Mountebank.  Boring, I don't even feel good after winning.
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Markov Chain

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Re: Are many kingdom sets essentially "solvable"?
« Reply #3 on: August 28, 2012, 10:26:31 pm »
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A four-player game with Pirate Ship.  Sometimes, there are counters (Secret Chamber, Lighthouse) or alternative strategies, but most games just depend on getting your Pirate Ship hits because they will be the only source of money, and they are determined by who gets to 4 first.
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popsofctown

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Re: Are many kingdom sets essentially "solvable"?
« Reply #4 on: August 28, 2012, 11:34:13 pm »
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"The devil is in the details" in cases where the best strategy isn't totally obvious, but players choose to mirror anyway.  So I think boards without divergent strategies are strictly bad. 

Solvable is pretty subjective.  I don't know what the percentage X is.  I played 4 games of Dominion on paper tonight, though, and one of the four kingdoms was solvable (Spice Merchant/Fool's Gold)
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Re: Are many kingdom sets essentially "solvable"?
« Reply #5 on: August 29, 2012, 01:06:23 am »
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A four-player game with Pirate Ship.  Sometimes, there are counters (Secret Chamber, Lighthouse) or alternative strategies, but most games just depend on getting your Pirate Ship hits because they will be the only source of money, and they are determined by who gets to 4 first.
Doubtful and honestly if you find PS that OP in 4player games why not buy it in 1st turn? :S
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Davio

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Re: Are many kingdom sets essentially "solvable"?
« Reply #6 on: August 29, 2012, 04:24:43 am »
+1

Often there will be a dominant strategy, but just as often you end up with turns where it isn't clear what you should buy even with that strategy. Should I get a 4th Silver with my $3, a Fortune Teller, an Oracle, or nothing? Should I just get the Gold with $6 or a $5 that I really want, like Jester?

These marginal decisions can be pretty decisive. That and shuffle luck of course.
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yudantaiteki

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Re: Are many kingdom sets essentially "solvable"?
« Reply #7 on: August 29, 2012, 05:03:19 am »
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A four-player game with Pirate Ship.  Sometimes, there are counters (Secret Chamber, Lighthouse) or alternative strategies, but most games just depend on getting your Pirate Ship hits because they will be the only source of money, and they are determined by who gets to 4 first.

Yeah, this is a big one -- the group I play weekly with (usually 4-5 players) has banned pirate ship because of this problem.  We've found that on many boards with Pirate Ship, the game comes down to largely luck on who can grab enough ships quickly and get them to $4 or $5 before everyone else.

Quote
Doubtful and honestly if you find PS that OP in 4player games why not buy it in 1st turn? :S

That's the point; you have to buy it first (or second) turn because if you fall behind in the PS race you're done unless the game has Moat, Lighthouse, *maybe* Secret Chamber, or a non-treasure source of money that can beat the pirate ships (Minion, for instance).  But in the latter case you can still be in trouble if you can't get enough of the cards before all your coppers are stolen.
« Last Edit: August 29, 2012, 05:08:53 am by yudantaiteki »
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HiveMindEmulator

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Re: Are many kingdom sets essentially "solvable"?
« Reply #8 on: August 29, 2012, 07:20:59 am »
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A good strategy should not rely on your opponent not knowing what your plan is. It should, however, be adaptable containing different branches depending on draws or what your opponent does. You want to have a strategy from the start. What you don't want to do is just start buying cards and hope a "strategy" materializes after a few turns.
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aaron0013

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Re: Are many kingdom sets essentially "solvable"?
« Reply #9 on: August 29, 2012, 08:30:48 am »
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There is a good percentage of the time when Fishing Village is on the board that you will buy it.  If a good drawer like Torturer or Margrave is on the board, it's a done deal. There are also many times when cursers will show a dominant strategy that must be played.
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methods of rationality

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Re: Are many kingdom sets essentially "solvable"?
« Reply #10 on: August 29, 2012, 01:05:46 pm »
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also, just because there is a dominant strategy, doesn't mean there is only 1 dominant way to play that strategy

(in terms of what you buy when, ...)
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eHalcyon

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Re: Are many kingdom sets essentially "solvable"?
« Reply #11 on: August 29, 2012, 01:47:14 pm »
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Sometimes it is better to go for the non-dominant strategy, e.g. as player 2 when player 1 has a huge advantage with the dominant strategy.  In this case, your only chance may be to play the risky strategy that has the best (if unlikely) returns.
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DG

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Re: Are many kingdom sets essentially "solvable"?
« Reply #12 on: August 29, 2012, 02:13:14 pm »
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There's some difference here between 2 player and 3/4 player. In a 2 player game you can plan some responses to your opponent's potential play and perhaps keep some options open. In a 3 or 4 player game you need to react quickly to the direction that your opponents are taking the game. On the other hand in a 2 player game you can try to control the endgame and have a very reactive vp strategy. In a 3 or 4 player game you lose that control and generally have to take your scoring opportunities whenever you can.
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Jive Junkie

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Re: Are many kingdom sets essentially "solvable"?
« Reply #13 on: August 30, 2012, 02:59:35 am »
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Often there will be a dominant strategy, but just as often you end up with turns where it isn't clear what you should buy even with that strategy. Should I get a 4th Silver with my $3, a Fortune Teller, an Oracle, or nothing? Should I just get the Gold with $6 or a $5 that I really want, like Jester?

These marginal decisions can be pretty decisive. That and shuffle luck of course.

This is a really good point, and one that I didn't specify in the OP.

What I was going for is more along the lines of the 'broad strokes' strategy of a board. For example:

-I'm gonna go for 2 Witches and then an Upgrade engine into Gold, and start buying Provinces when available.
-I'm gonna go straight Big Money + Courtyard x2.
-I'm gonna try to thin my deck with Steward, generate some card draw with Caravan, then go for a King's Court / Bridge megaturn.

I realize that the details of how to go about pursuing your strategy (how many Silver to buy, what distribution of actions/treasure, when to start greening, what 1x support cards are needed, etc.) are always in flux, depending on opponent and game state. That's what makes the game fun even in mirror matches.

But how often do you find that the broad strategy is clearly and decisively one-sided, such that pursuing anything else would be a lower percentage play?
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NoMoreFun

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Re: Are many kingdom sets essentially "solvable"?
« Reply #14 on: August 30, 2012, 01:10:09 pm »
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The kingdom in this topic:
http://forum.dominionstrategy.com/index.php?topic=4193.0

Where big money is the optimal strategy, with the exception of buying Border Village for Duchy when you have 6 or 7 and you'd buy a duchy anyway.
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NoMoreFun

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Re: Are many kingdom sets essentially "solvable"?
« Reply #15 on: August 30, 2012, 01:16:54 pm »
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Also in sets with all terminals, or where the only non terminals are inconsequential $2 cantrips like Vagrant or Pearl Diver, you need not look past simulation data to find the best strategy. There's still the issue of counters though - player 1 would need to pick the most optimal choice in light of what player 2 would be able to counter, so there's still a little bit of variety.
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Davio

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Re: Are many kingdom sets essentially "solvable"?
« Reply #16 on: August 30, 2012, 01:29:58 pm »
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It might be solvable, but you have to account for the fact that you don't have perfect information, so it all boils down to probabilities.

Say you're face with a PPR scenario and know 100% that you'll have $8 the next hand. Your opponent is in front and you're X% sure that he'll have $8. You need to calculate X to make a decision whether to take the PPR.

But wait, even if you know X you need to factor in the long term percentage. Say that X is very high, like 90%, it may still be correct to take the PPR if your long term win percentage is lower than 10%.

And the more you look ahead, the higher the uncertainty, thus the less meaningful the percentages.

Dominion for me is a game about reacting to what the current situation is. With tho identical setups I can be going for Duchies with 6 Provinces remaining in one and with just 3 remaining in another.
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FishingVillage

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Re: Are many kingdom sets essentially "solvable"?
« Reply #17 on: August 31, 2012, 06:31:52 pm »
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The only "strategy" that feels like a requirement is getting/playing cursers as often as possible in a kingdom with no trashing for curses. Personally I'd find such a game more appalling than Envoy/BM, at least for the latter I might be able to deny my opponent of a Gold or something every so often.
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