Print

Please login or register.
1 Hour 1 Day 1 Week 1 Month Forever
Login with username, password and session length

[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?

[TheExpressicist]

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?

The basic premise is that, by the time you have 5 silvers in your deck, your money density will be around $1.5 per card. So any card that offers +1 card automatically offers +$1.5. (You already have a 45-50% chance of replacing the silver with that +1 card).

The second basic premise is that we're operating under the assumption that you haven't already maxed yourself out on terminal cards and can add another terminal.

The third basic premise is that there are most likely alternatives to any crappy card you mention. By the time you have 5 silvers in your deck, you only have a ~5% chance of drawing a hand with exactly 3 coins. And, there is only a ~5% chance that the kingdom has exactly one <=$3 card. So in 1 out of 400 hands, you'll be faced with a dilemma of "Silver vs. One Specific Crappy $3 Card".  The odds are even less for "Silver vs. One specific crappy $4 card".



Wishing Well: It's a cantrip, so $1.5+ Utility. If you haven't done any trashing, you have between a 30-40% chance of hitting Copper if you name it, which adds $.3 to $.4 to its value. So, overall, Wishing Well is worth on average $1.85 per play. So strictly speaking, it's slightly less valuable, $-wise, than silver. But it provides two key utilities: if you do hit Copper, you have filtered a copper out of your next hand which increases your next hand's value. And you have the ability to do the hail-mary Wish (if you have 5 coins and you need one province to win, WW will always be more useful than silver).  .

Embargo:  $2+, Utility, thus more valuable than silver. (As long as it doesn't collide).

Pearl Diver: Cantrip, so $1.5+ Utility. The utility is fairly marginal. You have a ~50% chance of hitting a >=$2 card on the bottom of your deck, thus increasing your next hand's value by ~$.7. So that's ~$.35 worth of utility making it worth ~$1.85. It's highly situational, but yes I would agree that in the 0.25% chance that this is the only <=$3 available, it would likely be preferable to buy silver.

Chancellor: $2 + Utility, thus more valuable than silver (as long as it doesn't collide).

Lookout: The filtering increases the value of your next hand by ~$1, and the trashing and increases the value of all future hands by ~$.20. So it pays for itself in 5 turns. Probably not better than silver, but board-dependent.

Caravan: Cantrip so +$1.5, provides another cantrip so another +$1.5, so $3 of total value.

Thief: Except in extremely specific situations, less useful than silver. But, that's counterbalanced by the fact that there's approximately a .01% (1 in 10000) that you will have exactly four coins, and that this will be the only <=$4 card available. 

Mine: Provides +$1 in value, plus trashing, (the result of which increases the average value of your future hands by $.25). So in four turns it pays for itself. Probably not better than silver.

To answer your question re: "What any action you could purchase?"
1. Any card that provides +$2 (Worth $2+ utility)
2. Any card that provides 2 or more cards, regardless of whether or not there's a discard involved.   (Worth $3+ on average)
3. Any card that provides $1 + 1 card. (Worth $2.5 + utility on average.)

Again, let's all take a step back and remember that this is for the average scenario. Edge cases need not apply. There are definitely individual cards that in almost all circumstances are worse than silver, but the odds of that one card being the only available option range from extremely low to astronomically low.

[TheExpressicist]

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?

I can't think of any non-edge case scenarios where you'd have that choice when it doesn't involve Ambassador.

I based #4 and #5 off the following thread: http://forum.dominionstrategy.com/index.php?topic=9828.msg323096#msg323096 , where the simulation data suggested "that returning 2 coppers over 1 estate is a bad idea." There was a lot of skepticism re: that, so I also looked at it from a statistical perspective. Statistically, removing 2 coppers from your money supply has more of a negative effect on your money density than removing 1 estate, until you have approximately $30 in total money in your deck.

That said, I'm not 100% sold on the order of those two just yet, so I could be convinced to swap them.

[Davio]

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?

Doctor if you happen to know that the next 3 cards are Estate, Copper, Copper?

[DG]

I still think you're completely wrong about the 5 silvers and the logic you are backing it up with shows flaws. Could you please drop the silver thing before you make me completely deconstruct it?

[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?

I can't think of any non-edge case scenarios where you'd have that choice when it doesn't involve Ambassador.

I based #4 and #5 off the following thread: http://forum.dominionstrategy.com/index.php?topic=9828.msg323096#msg323096 , where the simulation data suggested "that returning 2 coppers over 1 estate is a bad idea." There was a lot of skepticism re: that, so I also looked at it from a statistical perspective. Statistically, removing 2 coppers from your money supply has more of a negative effect on your money density than removing 1 estate, until you have approximately $30 in total money in your deck.

That said, I'm not 100% sold on the order of those two just yet, so I could be convinced to swap them.

Many decks would rather have card density than money density. Mostly this applies to action cards, but I'd also rather have a Silver and an Estate than two Copper, even though they have the same density.

The trade-off between two Copper and one Estate isn't money density--it's that you'll get to the Ambassador faster, and you're also more likely to hit it with two Estates. Particularly notable is the case where you return one Estate twice, vs. two Copper and then two Estates. In the second case, you've returned two extra cards over two turns, and your opponent just gets one Copper instead of one Estate.

[Mic Qsenoch]

Average money density is a crappy way of evaluating your deck, with rare exceptions.

[TheExpressicist]

Many decks would rather have card density than money density. Mostly this applies to action cards, but I'd also rather have a Silver and an Estate than two Copper, even though they have the same density.

Yeah, and these heuristics are definitely not for engine decks. And good points regarding the other aspects of Ambassador. Since those last two only apply to Ambassador anyway, I'm going to change them.

Average money density is a crappy way of evaluating your deck, with rare exceptions.

That's why there are few references to it in the "rules of thumb". It's too complicated of a concept for beginners, and by the time you're good enough to really understand it, it's not really all that applicable in its basic form.

[WanderingWinder]

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?

The basic premise is that, by the time you have 5 silvers in your deck, your money density will be around $1.5 per card. So any card that offers +1 card automatically offers +$1.5. (You already have a 45-50% chance of replacing the silver with that +1 card).

This is a terrible premise. I basically NEVER get money density that high (in a non-colony game, anyway) unless I'm awful AND playing against someone else who is also awful.

The second basic premise is that we're operating under the assumption that you haven't already maxed yourself out on terminal cards and can add another terminal.

This is another awful assumption. If I'm playing BM, why in the world would I not have bought more terminals by the time I am looking at silver #6? I mean, seriously, I have had many turns of being able to produce any amount of money for which I could have gotten the terminal - why am I waiting until now to do so?

The third basic premise is that there are most likely alternatives to any crappy card you mention. By the time you have 5 silvers in your deck, you only have a ~5% chance of drawing a hand with exactly 3 coins. And, there is only a ~5% chance that the kingdom has exactly one <=$3 card. So in 1 out of 400 hands, you'll be faced with a dilemma of "Silver vs. One Specific Crappy $3 Card".  The odds are even less for "Silver vs. One specific crappy $4 card".

These "odds" (which aren't actually odds) are entirely made up. Who knows what my deck consists of by the time I have five silvers?
Nevertheless, this point actually shows the utter uselessness of the rule. I mean, so it's a first of all bad rule of thumb, because in this situation, you really should be looking long and hard at that silver (and indeed, in BM and slogs, the only reason you don't want more silvers is because you'd rather have other things....). So if you ever need to resort to it, it's just bad advice. Fortunately, it comes up pretty rarely - though more often in some cases (masterpiece, slogs, feodum) - so it won't actually hurt you very much in reality.

Wishing Well: It's a cantrip, so $1.5+ Utility. If you haven't done any trashing, you have between a 30-40% chance of hitting Copper if you name it, which adds $.3 to $.4 to its value. So, overall, Wishing Well is worth on average $1.85 per play. So strictly speaking, it's slightly less valuable, $-wise, than silver. But it provides two key utilities: if you do hit Copper, you have filtered a copper out of your next hand which increases your next hand's value. And you have the ability to do the hail-mary Wish (if you have 5 coins and you need one province to win, WW will always be more useful than silver).  .

Embargo:  $2+, Utility, thus more valuable than silver. (As long as it doesn't collide).

Pearl Diver: Cantrip, so $1.5+ Utility. The utility is fairly marginal. You have a ~50% chance of hitting a >=$2 card on the bottom of your deck, thus increasing your next hand's value by ~$.7. So that's ~$.35 worth of utility making it worth ~$1.85. It's highly situational, but yes I would agree that in the 0.25% chance that this is the only <=$3 available, it would likely be preferable to buy silver.

Chancellor: $2 + Utility, thus more valuable than silver (as long as it doesn't collide).

Lookout: The filtering increases the value of your next hand by ~$1, and the trashing and increases the value of all future hands by ~$.20. So it pays for itself in 5 turns. Probably not better than silver, but board-dependent.

Caravan: Cantrip so +$1.5, provides another cantrip so another +$1.5, so $3 of total value.

Thief: Except in extremely specific situations, less useful than silver. But, that's counterbalanced by the fact that there's approximately a .01% (1 in 10000) that you will have exactly four coins, and that this will be the only <=$4 card available. 

Mine: Provides +$1 in value, plus trashing, (the result of which increases the average value of your future hands by $.25). So in four turns it pays for itself. Probably not better than silver.

To answer your question re: "What any action you could purchase?"
1. Any card that provides +$2 (Worth $2+ utility)
2. Any card that provides 2 or more cards, regardless of whether or not there's a discard involved.   (Worth $3+ on average)
3. Any card that provides $1 + 1 card. (Worth $2.5 + utility on average.)

Again, let's all take a step back and remember that this is for the average scenario. Edge cases need not apply. There are definitely individual cards that in almost all circumstances are worse than silver, but the odds of that one card being the only available option range from extremely low to astronomically low.

Again, you don't actually have $1.5/card. By the time you reach that, you've lost the game.
Your math continues to be really wacky. How do you come up with these numbers? Your chance of hitting the copper is based on how many cards in your deck? Your trashing added-value-to-the-deck-in-the-future is calculated how? How are you taking into account that besides right now, the game will go on for some time longer? How do you know how much longer?

Money density is somewhat reasonable to look at if you're playing a treasure-based deck. Unfortunately, it misses extra "utility", which is often pretty important, timing, which is always important, and most importantly, most treasure-based decks just aren't that good....


Your other rules of thumb are similarly bad (well, silver/silver does get you around a 90% chance of hitting 5, but this is covered (and more precisely)) elsewhere.

I love your enthusiasm, but in terms of strategic advice, this stuff just isn't good.

[dondon151]

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.

Even this rule of thumb has a lot of exceptions.

[Polk5440]

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.

Even this rule of thumb has a lot of exceptions.

I was under the impression that most of the big money + x optimized bots can get 4 provinces in 15 turns on average. Jack may be a couple turns faster. But that's the fastest, right? Is my knowledge of the sims not right?

Now, using the question to determine whether your province strategy is good enough or not, sure. That one question won't tell you whether you have a winning strategy (e.g. "I can't get to 4 Provinces in 15 turns, but there are attacks! The attacks will slow my opponent down, but not me! I'll go with that..."); however, I think it sums up what you need to know about the speed of big money + x when you are also going for a Province strategy, which is what I thought was the stated point of OP.

[TheExpressicist]

The basic premise is that, by the time you have 5 silvers in your deck, your money density will be around $1.5 per card. So any card that offers +1 card automatically offers +$1.5. (You already have a 45-50% chance of replacing the silver with that +1 card).

This is a terrible premise. I basically NEVER get money density that high (in a non-colony game, anyway) unless I'm awful AND playing against someone else who is also awful. [/quote]

"Money density" is a bit of a misnomer in this situation as I'm actually referring more specifically to "Value per Card". E.g. If you Wishing Well and then draw a Smithy. Your literal Money Density may be <$1.5 but the collective impact of the Smithies in your deck means that functionally speaking, every card you draw will, on average, result in $1.5ish.*

edit: The "value per card" is fairly self-evident; if your average value per card was less than 8/5, you would almost never have enough money to buy a Province. Also, this number is going to differ depending on how much gold/treasure/card draw/etc. you have. The actual number is a bit lower but 1.5 is a nice round number.

This is another awful assumption. If I'm playing BM, why in the world would I not have bought more terminals by the time I am looking at silver #6? I mean, seriously, I have had many turns of being able to produce any amount of money for which I could have gotten the terminal - why am I waiting until now to do so?

You should have at least 2-3 terminals by the time you're looking at silver #6. By turn 10 or so, you can afford to add a 3rd-4th terminal to your deck. If you're unlucky enough to be put into a situation where you already have 4 terminals, 5 silvers, and can't afford anything else, then yes, you should probably buy a silver. But the odds of that happening are fairly slim.

These "odds" (which aren't actually odds) are entirely made up. Who knows what my deck consists of by the time I have five silvers?

If you're playing BM you'll probably have 3 terminals and 5 silvers. There are plenty of situations where this isn't the case, but remember, this is not a guide for expert players to reevaluate how they play the game. They're simple rules for beginners to follow to raise the bar of their level of play.

Again, you don't actually have $1.5/card. By the time you reach that, you've lost the game.

See above re: "money density" vs. "value per card".

Your math continues to be really wacky. How do you come up with these numbers? Your chance of hitting the copper is based on how many cards in your deck? Your trashing added-value-to-the-deck-in-the-future is calculated how? How are you taking into account that besides right now, the game will go on for some time longer? How do you know how much longer?

The numbers are just statistical analysis using "average situations" as the assumptions. Chances of hitting copper are based on 7 copper in a deck consisting of between 18-23 cards.  The trashing added-value-to-the-deck-in-the-future is based on statistical simulation of a deck consisting of [X..Y..Z] and the same deck minus Y. As for the length of game, this is assuming that your "silver vs. action" dilemma happens sometime between turns 8 and 13. If it happens beyond that, then it probably doesn't matter at all what you purchase.

[dondon151]

I was under the impression that most of the big money + x optimized bots can get 4 provinces in 15 turns on average. Jack may be a couple turns faster. But that's the fastest, right? Is my knowledge of the sims not right?

I was going for more of the "you can lose 5/3 on Provinces but win 6/2 on Duchies" kind of implication there.

Yeah, you're right, attacks and alt VP confound that rule of thumb even more. Kingdoms containing those cards, in addition to the possibility of winning when down on Provinces, are common enough that at least in my opinion, there are more exceptions to this rule of thumb than there are instances proving it.

[flies]

Many decks would rather have card density than money density.

i always try to build decks with one card per card.  getting your card density higher than that is tricky, but i bet Stef can do it.

[TheExpressicist]

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.

Even this rule of thumb has a lot of exceptions.

I was under the impression that most of the big money + x optimized bots can get 4 provinces in 15 turns on average. Jack may be a couple turns faster. But that's the fastest, right? Is my knowledge of the sims not right?

Now, using the question to determine whether your province strategy is good enough or not, sure. That one question won't tell you whether you have a winning strategy (e.g. "I can't get to 4 Provinces in 15 turns, but there are attacks! The attacks will slow my opponent down, but not me! I'll go with that..."); however, I think it sums up what you need to know about the speed of big money + x when you are also going for a Province strategy, which is what I thought was the stated point of OP.

Yeah as far as I'm aware, 15 is the limit. That's where I got the 14 from; if you can consistently achieve your goal in 14 turns, you can consistently beat BM.
 
Also , after reading the input from everyone re: the un-aptly named "5 silver rule" I'm going to go ahead and recant. The circumstances where it is applicable are few and far between especially if you're following solid greening heuristics. Thus making it not a great "rule of thumb for average cases"

[shark_bait]

Average money density is a crappy way of evaluating your deck, with rare exceptions.

Gotta give my love to Masterpiece/BM.  Average money density works like a gem for this strategy as the vast majority of your hands are 5 card hands that play solely treasure. 

[shark_bait]

Many decks would rather have card density than money density.

i always try to build decks with one card per card.  getting your card density higher than that is tricky, but i bet Stef can do it.

Using Island returns cards to your deck at the end of the game implying that during the game they are not part of your deck.  But if you think of the ratio in terms of cards / cards in deck you in fact can get higher than 1 because you own the cards from Island but they are not in your deck!

[Kirian]

Many decks would rather have card density than money density.

i always try to build decks with one card per card.  getting your card density higher than that is tricky, but i bet Stef can do it.

Celestial Chameleon is able to increase his density to as high as one deck per card.

[silverspawn]

i like seeing posts being picked apart that aren't mine. it's so... peaceful.

[markusin]

i like seeing posts being picked apart that aren't mine. it's so... peaceful.

I'm beginning to suspect it's some sort of secret hazing ceremony.