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recfish

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A Different Way To Look at Dominion
« on: November 15, 2019, 11:10:05 pm »
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This is my first article so please give feedback!

Generally speaking, a large part of dominion is determining which available overarching strategy will be fastest to end the game. This is obviously not the whole story, as you need to end the game with more points than your opponent, as well, but speed is clearly a factor. If you build a massive engine, and pile out in a megaturn on turn 25, where smithy big money was available what was really the point? Of course, this assumes no attacks, or other interactive cards/events that may interfere with the simpler strategy are present on the board. Even within a given overarching strategy, there will be a question of when to make the transition from building to greening. If ending as early as possible is important, then it is important to get this right. IF.

The above reasoning leads to statements about average game length for strategies where piling out the provinces or colonies is the goal. While interesting, it means that in evaluating a strategy, you need to think its absolute speed, a tedious, painful and often impossible task for humans. Instead, let me present another way of looking at the game. with this method, the megaturn on turn 25 is not a bad thing, even when there was a way to end the game earlier, even far earlier than that.

In Dominion, you are competing with another player. You are NOT competing against yourself. If winning is your goal, then ending as early as possible in absolute terms, should NOT be important to you. You want to make sure that whenever the game happens to end, you have more points than your opponent. This statement may seem trivial, but it can greatly simplify your life. If you are building an engine, you will always be wondering when enough is enough. How many actions/drawers/payloads do you need before it is purely gratuitous. If the answer depends on your opponent's behavior, then you have a very easy heuristic to answer your question. While both of you are building up, ask yourself this question: who has the more powerful deck (where power is defined loosely by ability generate coin consistently)? If you believe it is you, then you should strongly consider making it even more powerful and not greening. Powerful decks are able to buy more things. You can buy more actions/drawers/payloads than he can on every turn. Ceteris paribus, this means that the balance of power between the two of you will continue to get more lopsided. There is no reason to convert your power to victory points until...

Your opponent starts greening. You can usually divide dominion into two segments - building and greening. Building is akin to raising an army; Greening akin to going to war. If you are the stronger power, it is very likely that you can allow your opponent a preemptive strike in the form of the first province (or the equivalent). Once he does this, he has declared war. the statement he is making (that you have forced him to make) is that he can defeat you in battle, even though both of you know that is is you with the stronger army.

Well, there are three questions/concerns that you may have at this point.

  • If your army is stronger why not make the first move?
  • What if his preemptive strike actually gives him the headstart he needs to win the war?
  • what if the game is getting close to ending via 3-pile (at this point the only metaphor I can think of for that is environmental disaster)?


I will answer in order. First the reason you want him drawing first blood is because in this way you know that he is no longer in the prep stage. If you make the first move, it is possible that you slipped up. Perhaps you should have waited to green so that your army doesn't lose its vitality while at war (i.e. it becomes difficult to green). If this is the case, then he has the opportunity to keep building his army. and perhaps he will choose the optimal time to strike, beating you in the long run. On the other hand if you allow him to make the first move, you are telling him "any day of the week, I'll meet you on the battlefield. You choose." When he strikes first, he is stating "I believe I can win this war. Let's go." But you both know this isn't true. Your army is superior. And you now have the added benefit of knowing that he is in battle mode. The concern that he will continue to build his army and strike and some more optimal time has dissipated.

For the other two questions the answer is really the same. The reason for this is that the questions are really the same. Gaining a huge headstart is really the same idea as reducing the length of the game. In the first case he is moving rapidly toward the goal. In the second case the goal is moving rapidly toward him. Both of these reduce the distance between your opponent and the goal.

The answer is: Be careful with this perspective. while both of you are in building phase, you need to ask yourself on every turn (well not every, but you know what I mean): How much damage can he do now, if he starts greening? Can he three pile? Fortunately, these are much easier questions to answer than "Is now the optimal time to start greening in order to minimize numTurns?" You see how many coins, gainers and buys he has on every turn. Just imagine that he greened during his past turn. How many point would he have received? add a little to that, as his deck is now slightly more powerful. You see how many cards are in each pile. Can he end the game in his next few turns and maintain a point lead?

Now the question is what you should do if you find yourself with the weaker army. Well, you need to hope he trips over one of the pitfalls listed above. If he greens first, that may give you the opportunity you need to achieve military superiority and start greening later, watching his army die in a frozen wasteland of 4 or 6 coin turns. If he is not careful, you can trigger a natural disaster and end the game before his army a chance to flex its muscle, or pre-empt his attack with a vicious air raid scoring several provinces in one turn, again rendering his powerful army futile.

I want to mention that there is an oversimplification being made here. I stated that once he has greened, you know he is in battle mode, and will not be improving his army further. This is not technically true (though it usually is, in practice). He can green once and then change his mind with little damage. however this is of no real concern to you. If he backs away from war, you can feel free to do the same, knowing that you likely came away the victor in your first skirmish, as you went in better prepared. You are both now back in building phase. both of your armies are slightly weaker, but yours is still the superior force. No harm done.

Finally, I want to mention a special type of pre-emptive strike. There are engines that take a while to get off the ground. If you look at power as a function of turn number, these engines take a while for the desired exponential growth to occur, and it is even possible to have negative power growth for several turns. ambassador, or chapel can lend themselves to these types of engines, for example (finally, I mentioned a dominion card). If you are aiming for an engine like this, know that you will be in a vulnerable state for some time. Your opponent might have the opportunity to attack you while your pants are down, so to speak. When deciding to build this kind of engine, you should ask yourself how long you think you will be vulnerable for. It may not be worth it. This is probably, the hardest evaluation you will have to make with this learning paradigm, but I find that in practice, it is usually not too hard to avoid the pitfalls of a long gestation period, to mix metaphors for a moment.

Ok, with all the flowery language above, there will be cases when you just don't see the sneak attack coming. For example, I did not know about Artisan/Scepter combo until it was used against me to end the game when I thought there was no earthly way to bring about this calamity. This is frustrating, but live and learn. Add these losses to your playbook. this perspective still succeeds in changing the learning paradigm from "minimize(numTurns) over every (strategy, implementation) pair available" to "find all sneak attack and rush strategies available." And that is a much more human question.



« Last Edit: November 15, 2019, 11:35:11 pm by recfish »
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markus

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Re: A Different Way To Look at Dominion
« Reply #1 on: November 16, 2019, 09:58:06 am »
+2

  • By not knowing when it is the optimal time for greening, but relying on your opponent to signal it, you're still giving up some of your win chances.
  • Greening first in the weaker position can make sense, if you rely on a bit of luck that you draw well in the next couple of turns.
  • A common situation is one where players build up to double-Province turns. In that case, being the first to green can give you quite an advantage: gaining 3 Provinces while your opponent only has 2 Provinces, puts them in a difficult situation on their next turn.
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recfish

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Re: A Different Way To Look at Dominion
« Reply #2 on: November 16, 2019, 03:51:10 pm »
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That is why you need to track what the player's sprint will look like. If it gets to a point where a sprint will give him too strong of an advantage (you notice him drawing 14 coin consistently, for example), that is when you need to green. You are still reliant on signalling from your opponent though, even if you decide to green first. Of course knowing the optimal time to green is great if you can do it, but many times this is simply a very difficult question to answer.
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apostolosoruler

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Re: A Different Way To Look at Dominion
« Reply #3 on: November 16, 2019, 06:17:10 pm »
+1

Some interesting ideas, analysis. Just a few points:
Greening (also based on point 3 of markus) has some distinct economy targets. So if you green and your econ is 10 or 11 you are at the 1prov per turn. Keep building when you are at 9-10 11-12 is a decision you often have to make go for double go for single+ ? is there a reason to go more than 8?
Another point is single gain-buy boards. In these boards p1 p2 matters when you start greening e.g. Masterpiece guildhall money board. Imagining a double masterpiece per player if p2 starts provincing first he wins. Cause he doesnt have to duchy dance and you cant follow as p1.
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Seprix

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Re: A Different Way To Look at Dominion
« Reply #4 on: November 18, 2019, 07:13:11 am »
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None of this is new strategically, and the idea sometimes falls apart when we start talking about really consistent money strategies, but overall the idea is there, and you'd expect some exceptions with a concept article.
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markusin

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Re: A Different Way To Look at Dominion
« Reply #5 on: November 18, 2019, 09:37:01 am »
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A nice article all around, reminding one of the things they should be considering when in the heat of Dominion war.


 If you are building an engine, you will always be wondering when enough is enough. How many actions/drawers/payloads do you need before it is purely gratuitous. If the answer depends on your opponent's behavior, then you have a very easy heuristic to answer your question.


Yes..."easy". Your article touches the surface on just how complex the interaction between you and your opponent can actually get. Understanding when to start greening, or if you should even bother to green before the last turn of the game that ends on a pileout, is among the toughest things in Dominion, and a thing that players screw up all the time.

I'll throw in some additional thoughts.

There are games where neither player ever has the "stronger army" by the time the start of their turn rolls around, because both players keep one-upping each other's deck with the cards they gain. The logical conclusion to this is that the game ends on 3 piles with one player winning by a single green card they gain on the last turn. It's quite possible to see who will be the chosen victor in this conflict, just like you can foresee the result of the "loves me - loves me not" game by counting the number of pedals on the flower ahead of time. If you are not favoured in this situation, then you can't let it play out to near its conclusion, and you must green so that the other player cannot both overtake your points and pileout. You have to consolidate between having a strong enough deck to green over a few turns, while not waiting until the point where your opponent has such a strong deck that they can green better than you while having little to no risk of dudding. If the shoe is on the other foot and you have better capability to reach your deck's full potential every turn and empty piles, just be sure you can afford multiple green cards too if your opponent can already do so.

Another thing is to take lessons from shoot'em ups, and make decisions not solely based on where they are, but where they are going to be. You want to understand what kind of deck your opponent is building before they succeed in building it. You want to know how much time it will take your opponent to, for example, start getting two provinces instead of one each turn. If your opponent is going to double their coin output in the near future, then maybe you want to green early and then looks for ways to end the game soon after, either with 3 piles or by draining the Province pile with stuff like Remodel Province to Province or Salt the Earth. If you can't foresee beating their future deck by maintaining your current pace, then you should probably build some more in the hopes of at least matching their output. If you can't do either, well then you messed up somewhere (e.g., "letting yourself" have bad luck  :P) and have to make the plays that give the highest chance of your opponent having a dud or making a wrong decision (I mean, maybe they haven't read articles like this one  ;) ).
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Titandrake

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Re: A Different Way To Look at Dominion
« Reply #6 on: November 18, 2019, 05:37:19 pm »
+2

I think this article is getting at the right idea, it's just using more words than necessary to explain it.

One criticism is that personally, I've found that worse players tend to green earlier than I do and better players green later than I do, so it's very easy for me to "wait for the first move" when it comes to greening: I win when worse players start greening before me and lose when I start greening before them. But the problem here is that it isn't really about when the greening happens. It's that better players build their decks faster and then put me in a position where I don't think I can catch up in time if I keep building - the mistakes happened well before any VP cards were bought. It may be a mistake to start greening first in the worse position, but often it's an induced mistake that's the least bad out of the many bad options.
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recfish

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Re: A Different Way To Look at Dominion
« Reply #7 on: November 18, 2019, 07:11:13 pm »
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thanks for all the feedback! I see the point Markus and several others are making - essentially "sometimes this doesn't work" in one form or another, which is definitely true. So perhaps a better way to sum up my wordy article would be "determining when to green should be a decision that can be made easier by looking at the position of your opponent" and, fair enough, that is not a novel concept, though I still like my framing :)
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segura

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Re: A Different Way To Look at Dominion
« Reply #8 on: November 19, 2019, 01:16:43 pm »
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It is a decent article but I dislike the focus on engines and building vs. greening.
We all like these games but there are also hybrids (neither money nor engines, e.g. a few Stables and some Silvers) or engines that are only able to buy one Provinces per turn, money decks and above all different sources of VPs.
Not trashing a starting Estate in Kingdoms without (easy) extra Buys or gainers, Landmarks, VP tokens etc. are all more tricky.

Timing and closely watching your opponents still matter but it is not as trivial as just timing the greening moment.
There are also sea-saws, volatile (e.g. when something like Festival is your only village, chances of missing your terminal draw is larger) decks which require you to oscilate between greening and further building. Not every engine glides into the overdraw realm before it goes into the greening territory.

I also think that you can exaggerate interactiveness. If you judge the Kingdoms correctly and see that the best way to play is aim for a 2 Provinces per turn engine, you should build until that very moment, i.e. relatively independently of what the opponent does. The notion that you should build up (although you reached the sweet spot) further because it is not a solo game is then highly dubious.
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Awaclus

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Re: A Different Way To Look at Dominion
« Reply #9 on: November 19, 2019, 03:04:15 pm »
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We all like these games but there are also hybrids

BM/engine hybrid is a meme strategy.
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Cave-o-sapien

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Re: A Different Way To Look at Dominion
« Reply #10 on: November 19, 2019, 06:01:22 pm »
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I also think that you can exaggerate interactiveness. If you judge the Kingdoms correctly and see that the best way to play is aim for a 2 Provinces per turn engine, you should build until that very moment, i.e. relatively independently of what the opponent does. The notion that you should build up (although you reached the sweet spot) further because it is not a solo game is then highly dubious.

I think the greater sin is people not paying enough attention to their opponent. Knowing what your opponent's deck can do in general, and in particular next turn (or next shuffle) seems absolutely key to me.

Why would this not matter? IMO this sort of tracking and assessment separates good players from great ones.
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Re: A Different Way To Look at Dominion
« Reply #11 on: November 20, 2019, 04:08:49 am »
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I also think that you can exaggerate interactiveness. If you judge the Kingdoms correctly and see that the best way to play is aim for a 2 Provinces per turn engine, you should build until that very moment, i.e. relatively independently of what the opponent does. The notion that you should build up (although you reached the sweet spot) further because it is not a solo game is then highly dubious.

I think the greater sin is people not paying enough attention to their opponent. Knowing what your opponent's deck can do in general, and in particular next turn (or next shuffle) seems absolutely key to me.

Why would this not matter? IMO this sort of tracking and assessment separates good players from great ones.
I used a particular example: evaluating a Kingdom ex ante correctly (obviously you can only guess that you did so in hindsight) with the result that an engine that gains 2 Provinces per turn is best. Now if the opponent starts to green before you do (to make the argument more forcefully, suppose he plays money), throwing your entire plan into the sink hole and not building up another turn until you have the greening power that you actually want could end up being contraproductive.

Of course you gotta watch the opponents but you also gotta trust your assessment.
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markusin

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Re: A Different Way To Look at Dominion
« Reply #12 on: November 20, 2019, 08:57:20 am »
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I also think that you can exaggerate interactiveness. If you judge the Kingdoms correctly and see that the best way to play is aim for a 2 Provinces per turn engine, you should build until that very moment, i.e. relatively independently of what the opponent does. The notion that you should build up (although you reached the sweet spot) further because it is not a solo game is then highly dubious.

I think the greater sin is people not paying enough attention to their opponent. Knowing what your opponent's deck can do in general, and in particular next turn (or next shuffle) seems absolutely key to me.

Why would this not matter? IMO this sort of tracking and assessment separates good players from great ones.
I used a particular example: evaluating a Kingdom ex ante correctly (obviously you can only guess that you did so in hindsight) with the result that an engine that gains 2 Provinces per turn is best. Now if the opponent starts to green before you do (to make the argument more forcefully, suppose he plays money), throwing your entire plan into the sink hole and not building up another turn until you have the greening power that you actually want could end up being contraproductive.

Of course you gotta watch the opponents but you also gotta trust your assessment.

Assessments are allowed to change though. You should always be reevaluating as much as your mental stamina will allow you. Say on your example, the opponent greens two turns before you can double Province, then the decision becomes trickier, as it can lead to a 4-4 Province split if you aim for double Province and come down to estates.
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segura

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Re: A Different Way To Look at Dominion
« Reply #13 on: November 20, 2019, 09:18:17 am »
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I also think that you can exaggerate interactiveness. If you judge the Kingdoms correctly and see that the best way to play is aim for a 2 Provinces per turn engine, you should build until that very moment, i.e. relatively independently of what the opponent does. The notion that you should build up (although you reached the sweet spot) further because it is not a solo game is then highly dubious.

I think the greater sin is people not paying enough attention to their opponent. Knowing what your opponent's deck can do in general, and in particular next turn (or next shuffle) seems absolutely key to me.

Why would this not matter? IMO this sort of tracking and assessment separates good players from great ones.
I used a particular example: evaluating a Kingdom ex ante correctly (obviously you can only guess that you did so in hindsight) with the result that an engine that gains 2 Provinces per turn is best. Now if the opponent starts to green before you do (to make the argument more forcefully, suppose he plays money), throwing your entire plan into the sink hole and not building up another turn until you have the greening power that you actually want could end up being contraproductive.

Of course you gotta watch the opponents but you also gotta trust your assessment.

Assessments are allowed to change though. You should always be reevaluating as much as your mental stamina will allow you. Say on your example, the opponent greens two turns before you can double Province, then the decision becomes trickier, as it can lead to a 4-4 Province split if you aim for double Province and come down to estates.
Sure and of course there are other sources of VPs. For example if somebody goes heavy on Chariot Races, greening earlier to increase the likelihood of his Chariot Races missing can be an option.
My only point was to follow a good plan as much as it is tactically feasible.

It's like in chess. Of course you have to react to what your opponent is doing but if you have no ideas of your own and no plan to follow through you are unlikely to play well.
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