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[TheExpressicist]

Simple Version

Buy Priority AKA Your "shopping list"[/u]
Are there Junk attacks? If so, buy 2.
Are there cards that give +3 or more cards? If so, buy 2 and stop here.
Are there discard attacks? If so, buy 1. 
Are there cards that give +2 or more cards? If so, buy 2 and stop here.
Are there cantrip trashers? If so, buy 2.

Heuristics/Buy Priority:
1. Buy the first two items off of your shopping list as soon as possible.
2. Can you afford a Province? If so, buy it. 
3. Are there 5 or less Provinces? If so, do you have more non-Province VP cards than your opponent? If not, buy a Duchy.
4. Are there 3 or less Provinces? If so, do you have more non-Province VP cards than your opponent? If not, buy an Estate.
5. Can you afford a gold? If so, buy it. 
6. Is it after turn 5? Buy a third action.
7. If it after turn 10? Buy a fourth action.
8. Buy silver.
9. Buy nothing.


Complicated Version

Economy
Silver: Very rarely do you need more than 5 silver in your deck.
Terminal Actions: Buy no more than 3 in the first 10 turns.
Early Terminal Collision: If you draw a terminal, there is a ~40% chance of it will collide with another terminal.
Buying at least one 5 coin card by turn 5: Silver/Silver*= >99% chance. Silver/x = 70% chance.
Buying multiple 5 coin card by turn 5: Silver/Silver= 55%. Silver/x = 10% chance.
Buying 5-coin cards by turn 4**: Silver/Silver= 90% (15% of being able to buy 2).  Silver/x = 50%.  x/x = 5%
Provinces: Don't buy Province #1 until you have 2 "functional gold".***

Actions
+Cards: +1 card = +1 coin or +1.25 or +1.5 coins (early, mid and late game, respectively)
Trashing Rules****: If you have a trasher in hand, here are your priorities: 1:Trashing two+ Estates, 2: Trashing three+ copper, 3: Buying an extremely important card (Witch, Mountebank, etc.),  4:Trashing 1 Estate,  5:Trashing 2 Copper.
Curse/Junk: 1 junk card = opponent wins 1 turn slower

I'll explain the statistics behind these in a bit. I've got a few more for evaluating engines.

[edits]
*- This is specifically referring to opening Silver/X or Silver/Silver
**- Updated to include Turn 4 probabilities.
***- The "advanced" version states, don't buy a Province in slog/BM if it will drop your money density below $6/5c. An example of a "Functional Gold" includes cards like Smithy (eg. if your money density is $1.25/c, a Smithy on average is worth $3.75)
****- Updated the "trashing" section to further clarify.  The reason trashing 3 coppers is > than "buying extremely important card" is that, if the card is so crucial to grab that it's worth holding on to 3 copper, then it would be smarter for you to just open silver/silver, and pick up your trasher on turn 3/4.

[SCSN]

"You must take your opponent into a deep dark forest where 2+2=5, and the path leading out is only wide enough for one." - Mikhail Tal

I'll see you there

[TheExpressicist]

I'll start with explaining the silver. The first assumption is that most terminal actions are going to have an approximate value of at least 2 coins (whether that value comes directly from +coins, indirectly via +cards/trashing, etc.). The second assumption is that, the maximum density of terminal actions you want in your deck is 20% (Thus assuring an average of <1 terminal action per turn). 

The third assumption is based on the premise that, once your money density reaches 6 coins/5 cards, the % chance of you drawing a hand with exactly 3 coins is ~5%. The assumption is that, if you have 4 or 5 coins (and your money density is 6$/5c) it's going to almost always be better for your deck to buy an action than a silver.

To reach the 6$/5c number, you need a total of ~7 functional silvers in your deck.  If you purchase 5 silver, and 3 terminal actions, you stay below the "maximum terminal" threshold, and accounting for terminal collision, you end up with 7 functional silver and thus a money density of 6$/5c. You don't want to exceed the terminal threshold, so buying 4 terminals + 4 silver is a bad idea. And buying 6 silver, 2 terminals, although safer because it would decrease the likelihood of a terminal collision, lessens the utility of your deck. There are certain circumstances where you'd only want 2 copies of a specific terminal. For example, with BM-Wharf, the +cards from Wharf will already push your money density past $6/5c by the time you buy two Wharfs.

Long story short- there are very few "standard" circumstances that would call for buying more than 5 silver.

[TheExpressicist]

The next 3 economy-based ones are simple statistics that were verified via simulation.

The Province one is based on the notion that, if you somehow manage to get a $8 hand and don't have more than 2 gold, buying a dead VP card will push your hand below the $6/5c threshold, significantly decreasing your ability to buy additional gold.

[jonts26]

I think you should edit the $5 card gain to be by turn 4 instead of turn 5, since turn 5 is after the next reshuffle and represents a huge tempo change from getting it on turn 3/4. If I remember right opening silver/silver gives a 91.8% chance of a $5 on turn 3/4.

[DG]

Ooh I think you're on dangerous ground with some those rules of thumb. I wouldn't try to mend them even.

Silver can be a very tricky card, more tricky than gold or copper. The isotropic 'win rate without' for silver was staggeringly high suggesting that if silver isn't a good card for your deck then you should really work without it as much as you can. On the other hand I would say that when silver is good for your deck you can use it in very large quantities, and that was true even before masterpiece and foedum were released. Anyway I don't see where the rule of 5 comes from or what decision you are going to make instead of buying a sixth silver. I have my own rule of thumb for buying estates that I'm not sharing .

I would say that for a basic big money deck the rule of thumb would be one gold (or one platinum) before going green but it is only one of several indicators you can use. You can use the total coin in your deck if you can be bothered to count it. You can use shuffles as a guide as well. Assuming you've got at least one kingdom card in the deck then that will change the outlook too.

[jsh357]

(I swear I'm not trying to discourage you here)

I strongly disagree with the rule of buying 2 Gold before Province.  It may be 'true' for Big Money games, but Gold is a card you often should avoid buying unless there is no better choice in engines.  Of course, you didn't clarify what kind of boards you are examining, so that could have been what you meant. 

The rules about winning x turns faster are only 'true' if the other player is mirroring you or at least very close.  In fact, in general I think it's only useful to try and apply statistics to early game scenarios (Like, before the second reshuffle) since there is not much that can change the outcome of those.  Some decks want to keep starting Estates even.  If you rely entirely on statistic like these, a good player will crush you with strong tactics or even mind games.

[markusin]

Interesting that you say to get 2 Gold before the first Province. I assume this applies to Big-Money, but even then you usually have a good enough BM enabler that I'd expect 1 Gold before the first Province to be enough. Like, do you still want 2 Gold if you're using Jack of All Trades or Hoard or Haggler or Embassy?

[TheExpressicist]

I think you should edit the $5 card gain to be by turn 4 instead of turn 5, since turn 5 is after the next reshuffle and represents a huge tempo change from getting it on turn 3/4. If I remember right opening silver/silver gives a 91.8% chance of a $5 on turn 3/4.

I updated it to include both.  The reason I initially went for 5 turns rather than 4 is because you're still partially working with your "original" open on turn 5.

Silver can be a very tricky card, more tricky than gold or copper. The isotropic 'win rate without' for silver was staggeringly high suggesting that if silver isn't a good card for your deck then you should really work without it as much as you can.

Agreed. The "5 silver rule" is a maximum, not a suggested amount. Many $3 and $4 actions (both terminal and non-terminal) serve as "functional silvers". Militia is an obvious example, but trashers and filterers apply as well. In general, you want a total of 8 "functional silvers" in your deck to reach $6/5c. If you can replace a true silver with a "functional silver", all the better. This is heavily board-dependent. As you can see from the stats, the odds of being able to buy a $5 card without purchasing a "functional silver" of some kind are very low. That said, the $5 cards may be very weak on your board.

I strongly disagree with the rule of buying 2 Gold before Province.  It may be 'true' for Big Money games, but Gold is a card you often should avoid buying unless there is no better choice in engines.

Agreed. I need to clarify that it applies to Slog and Big Money, not Engines, Combos, or Rushes.

The "x turns faster" is a function of how typically, cursing someone lowers their money density by enough to statistically, they will most likely have at least 1 turn where they draw less money than what they need to advance their deck. Or, they can waste a buy on another treasure. Either way, they've wasted an early buy/turn.

In general, the idea is not that these are rigid rules that have to be followed in every scenario. Rather, it's a general guideline for the basic decisions.

[Awaclus]

Gold is a card you often should avoid buying unless there is no better choice

Isn't that always true for all cards?

[Mr Anderson]

No, Scout is a card you always should avoid buying even if there is no better choice.

[jsh357]

Gold is a card you often should avoid buying unless there is no better choice

Isn't that always true for all cards?

Yes, but I think it's particularly true for Gold since it's always competing with $5 Kingdom cards and Duchy.

[timchen]

The 5 silver rule is not that useful even if it is statistically correct, as the reasoning behind it relies on the other $3$4/$5 terminals, which is what you should be counting. It's not like, okay, I have 5 silvers so I have to stop getting silvers.

[TheExpressicist]

The 5 silver rule is not that useful even if it is statistically correct, as the reasoning behind it relies on the other $3$4/$5 terminals, which is what you should be counting. It's not like, okay, I have 5 silvers so I have to stop getting silvers.

The idea behind the rule is that by the time you reach 5 silvers, you most likely will be at a point where almost any action you could purchase would be a smarter purchase than silver.

[loppo]

i like theese rule of thumbs. They are basically a Dominion 101. So i will use them for new players to give them basic guidelines to weigh difeerent options Action/money/VP-cards against each other.

Of course they are not the be-all-end-all guidelines for the hardcore players out there. And they don't even want to be that. They help to play a sound BM game, without getting distracted with buying too many actions, even more so in 3+ player games.

Engine building comes later. At this point you can throw theese rules out of the window. You don't need them any longer then. Until then those rules will help you along.

[serakfalcon]

Provinces: Don't buy Province #1 until you have 2 "functional gold".***

It really, really depends on the board. If there are no extra buys I would buy a province as soon as I can consistently hit 8, 1 gold or not. And there's always the megaturn engines.

[SCSN]

i like theese rule of thumbs. They are basically a Dominion 101. So i will use them for new players to give them basic guidelines to weigh difeerent options Action/money/VP-cards against each other.

Of course they are not the be-all-end-all guidelines for the hardcore players out there. And they don't even want to be that. They help to play a sound BM game, without getting distracted with buying too many actions, even more so in 3+ player games.

Engine building comes later. At this point you can throw theese rules out of the window. You don't need them any longer then. Until then those rules will help you along.

I strongly disagree with the idea that new players should first learn to play "a sound BM game". It will do them more harm than good by establishing rigid ways of thinking and bad habits that are hard to get rid of.

New players should just buy lots of cards and goof around until they've developed a basic feel for what each card does, then try out all sorts of ways to combine them into interesting stuff and gradually learn from there how to build a consistent deck.

While playing BM would certainly get them the best results for their current skill level, it's like instead of learning chess you memorize some gambits that will give you quick success in Blitz games against oblivious opponents, but that won't provide you any understanding. Similarly, by focusing on BM you're not actually learning anything about Dominion.

[TheExpressicist]

i like theese rule of thumbs. They are basically a Dominion 101. So i will use them for new players to give them basic guidelines to weigh difeerent options Action/money/VP-cards against each other.

Of course they are not the be-all-end-all guidelines for the hardcore players out there. And they don't even want to be that. They help to play a sound BM game, without getting distracted with buying too many actions, even more so in 3+ player games.

Engine building comes later. At this point you can throw theese rules out of the window. You don't need them any longer then. Until then those rules will help you along.

This, this, this.   

The best way to learn more advanced deck-building is to observe better players. But if you're a new player who gets beaten, you don't have any real way of knowing if you got beat by a legitimately good strategy, versus a bad strategy that just happens to be good enough to beat you. I've seen many new players stall in their development by mimicking the latter type of strategy.

Following these basic rules of thumb holds your opponents to a higher standard. It ensures that if your opponent beats you consistently with a strategy, it's a good strategy. As opposed to trying to build your own sub-par engines which will likely get beaten by all kinds of slightly less-sub-par engines. It makes the learning process infinitely easier.
 

[TheExpressicist]

I strongly disagree with the idea that new players should first learn to play "a sound BM game". It will do them more harm than good by establishing rigid ways of thinking and bad habits that are hard to get rid of.

Everyone learns differently, but as I mentioned in my previous post, I would argue that the best way to learn is by observing good players playing good strategies. To further your chess analogy, goofing around and buying all types of cards is the equivalent of just moving pieces around pell-mell until you get an idea for what works and what doesn't.

When you're new at chess, you don't have the skills or context to evaluate the effectiveness of strategies beyond simply "Did it beat me or didn't it?" But, if you play garbage chess, almost every strategy will beat you. Including very mediocre (even awful) strategies, e.g. Scholar's Mate. It's a middling tactic that can only beat the most unprepared opponents, much like a lot of Dominion strategies. But it will still pass the only real heuristic criteria you have available.

The difference with Dominion is, BM is the "baseline" by which all other decks have to evaluate themselves by. When you're new, you still only have that "Did it beat me or didn't it?" criteria. But, a strategy that can consistently beat BM is considered a viable, effective strategy. So that heuristic becomes extremely useful. If you strictly play Big Money according to these rules, and pay attention to every game you play, you will quickly learn A.) Which strategies beat BM and why, and B.) Which strategies don't beat BM and why.

[LastFootnote]

Everyone learns differently, but as I mentioned in my previous post, I would argue that the best way to learn is by observing good players playing good strategies. To further your chess analogy, goofing around and buying all types of cards is the equivalent of just moving pieces around pell-mell until you get an idea for what works and what doesn't.

…And what's wrong with that? Is that inherently bad in some way?

When you're new at chess, you don't have the skills or context to evaluate the effectiveness of strategies beyond simply "Did it beat me or didn't it?" But, if you play garbage chess, almost every strategy will beat you. Including very mediocre (even awful) strategies, e.g. Scholar's Mate. It's a middling tactic that can only beat the most unprepared opponents, much like a lot of Dominion strategies. But it will still pass the only real heuristic criteria you have available.

The difference with Dominion is, BM is the "baseline" by which all other decks have to evaluate themselves by. When you're new, you still only have that "Did it beat me or didn't it?" criteria. But, a strategy that can consistently beat BM is considered a viable, effective strategy. So that heuristic becomes extremely useful. If you strictly play Big Money according to these rules, and pay attention to every game you play, you will quickly learn A.) Which strategies beat BM and why, and B.) Which strategies don't beat BM and why.

I'm trying to come up with a situation in which this is good advice and I think I've got one. Let's say someone came up to you and said, "Play 50 games of Dominion. If you win at least 10, I'll give you a million dollars." And you didn't know how to play Dominion. I guess in a situation like that, where all you care about is winning as often as possible while improving as quickly as possible, your logic makes sense.

Here in the real world, most players play Dominion because they enjoy coming up with their own strategies on the fly and seeing how they fare. If you play by this algorithm:

Check to see if one or more strategies you've learned are available. If so, pick the best one and play it. If not, play a boring BM game. Then if you lose, incorporate your opponent's strategy into your repertoire.

What's the point of that? I guess if you just like winning for the sake of winning regardless of what game you're playing and you don't mind playing boring strategies repeatedly, then go for it. Seems to me there have to be better games to scratch that itch, though.

[TheExpressicist]

Everyone learns differently, but as I mentioned in my previous post, I would argue that the best way to learn is by observing good players playing good strategies. To further your chess analogy, goofing around and buying all types of cards is the equivalent of just moving pieces around pell-mell until you get an idea for what works and what doesn't.

…And what's wrong with that? Is that inherently bad in some way

Nothing's wrong with it whatsoever. It's just a question of what you enjoy about playing Dominion. You really hit the nail on the head here: "n a situation like that, where all you care about is winning as often as possible while improving as quickly as possible, your logic makes sense."

Personally, I enjoy the process of quickly evaluating a system and developing optimal strategies for managing that system. And I also find it just as fun to watch someone else implement a creative strategy as I do to implement it myself (probably because I'm not that creative). If that's not your thing though, you'd probably find my "meta-algorithm" for approaching Dominion terribly boring.

[Polk5440]

i like theese rule of thumbs. They are basically a Dominion 101. So i will use them for new players to give them basic guidelines to weigh difeerent options Action/money/VP-cards against each other.

Of course they are not the be-all-end-all guidelines for the hardcore players out there. And they don't even want to be that. They help to play a sound BM game, without getting distracted with buying too many actions, even more so in 3+ player games.

Engine building comes later. At this point you can throw theese rules out of the window. You don't need them any longer then. Until then those rules will help you along.

This, this, this.   

The best way to learn more advanced deck-building is to observe better players. But if you're a new player who gets beaten, you don't have any real way of knowing if you got beat by a legitimately good strategy, versus a bad strategy that just happens to be good enough to beat you. I've seen many new players stall in their development by mimicking the latter type of strategy.

Following these basic rules of thumb holds your opponents to a higher standard. It ensures that if your opponent beats you consistently with a strategy, it's a good strategy. As opposed to trying to build your own sub-par engines which will likely get beaten by all kinds of slightly less-sub-par engines. It makes the learning process infinitely easier.

While I agree with this idea, I simply prefer the articles on the blog and the optimized BM simulators for a particular card to the rules of thumb laid out in the OP. In particular, see the Big Money article (http://dominionstrategy.com/big-money/), building the first game engine (http://dominionstrategy.com/2012/07/30/building-the-first-game-engine/) and the five fundamental deck types (http://dominionstrategy.com/2013/01/21/the-five-fundamental-deck-types-introduction/). Those old blog posts are real gems.

As for rules of thumb, having actual speed benchmarks in mind might better. For example,

Can I comfortably get 4 Provinces in less than 15 turns?

That about sums up what you need to know about benchmarking your Province strategy against a big money + X strategy.

And it gets you thinking about what your deck is going to be and how many turns it will take to get there. For example, say you are evaluating Village-Smithy: So I will want 2 Golds, a Silver, 5 Smithies, and 5 Villages (at least), then I can get those Provinces! Wait... that's at least 13 turns to get parts, then 4 turns to buy Provinces.... That's 17 turns. Too slow! Can I speed it up? Oh, look! There's Workshop... etc.

[TheExpressicist]

Polk5440 - that's actually very very similar to the wording I have been drafting re: evaluating engines.  In fact, the opening was:

You want to ask yourself: can you build an engine in X turns (including treasure and VP)

Start by scanning the board to figure out how many turns you have:
The baseline for X is 14.
Curse Attacks: Each curse and junk card you give your opponent buys you an extra turn overall and thus adds 1 to X.
Discard Attacks: Each purchased discard attack buys you an extra turn overall and thus adds 1 to X.
Trashers: Each 3+ card trasher you purchase typically uses up 3 of your turns to trash. Each 1-2 card trasher typically gobbles up 1 of your turns. So subtract from X accordingly

[DG]

The idea behind the rule is that by the time you reach 5 silvers, you most likely will be at a point where almost any action you could purchase would be a smarter purchase than silver.

I still completely disagree with that. Once you have 5 silvers in your deck you do not suddenly start buying wishing wells, lookouts, embargoes, pearl divers, chancellors, thieves, caravans, mines or in fact any alternative card at all. If you want something else than silver then you should generally get it very early before the silver fills the deck. If you are using a lot of silver then keep buying silver. Just what 'any action you could purchase' are you talking about?

[Stealth Tomato]

Trashing Rules****: If you have a trasher in hand, here are your priorities: 1:Trashing two+ Estates, 2: Trashing three+ copper, 3: Buying an extremely important card (Witch, Mountebank, etc.),  4:Trashing 1 Estate,  5:Trashing 2 Copper.

Ambassador suggests the last two should be reversed. Is there any non-Ambassador situation where you have a choice between trashing 1 Estate and 2 Copper?