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1

Dominion Articles / Re: Better than nothing?

« on: February 06, 2013, 03:41:00 pm »

I also don't understand what you are trying to say that sometimes it's good for the bad cards to come earlier.

I think he's saying it's better for the good cards to come earlier. Example:
If you have a Pearl Diver and Estate in hand and a [good card] on deck. Opponent plays Bureaucrat, putting Estate on top of the [good card]. Then you draw it with Pearl Diver and get the [good card] next turn. If you had not bought the Pearl Diver, then [good card] would be in this hand (drawn instead of Pearl Diver) and Estate in next, which is usually better.

If you want a strong example of a card that you really want to draw earlier, think of Hunting Party. Playing a Hunting party earlier rather than later greatly increases deck cycling and hence your chances of replaying those hunting parties.

2

Dominion General Discussion / Re: Watchtower+Trader

« on: February 05, 2013, 05:30:00 pm »

Impressive florrat!

Ok, between florrat's simulation and Drab and Kirian's analysis and the fact that I wasn't even the first one to come up with this opening, I do feel like

a) We should be able to conclude and write a cute little article.

b) That I shouldn't be the primary author. How do you guys want to organize it?


I guess before we get to b) we first need to compile all this nice data and compare the opening to both double silver and  joat/silver. I want the comparison to joat, because it is a very strong opening that achieves similar objectives: trashes estates, floods silvers and defends cursers. It therefore will be good on similar boards (presence of cursers, pro-silver boards, non-essential $5).

3

Dominion Articles / Re: Single tactician decks

« on: February 05, 2013, 02:21:09 pm »

KC and crossroads (which scales, I don't know why it isn't a full-blown thing here) don't really pull you to single tac over double tac. I think the biggest thing there is how reliant you are on treasure. But then there's also all of the points about just using it to get the double-large hands sometimes that's nice.

I would say that lots of these have similar themes - KC, TR, Tournament, baron - all these cards are looking to get particular cards paired together, which isn't really the same as scaling, but is another definite benefit of larger handsize. You could also mention goons and scaling T4B in that context, off the top of my head.

I think WWs post hits the nail on the head. Some of the other criticism is legitmate but sometimes peripheral. For general comments on tactician combos, read theory's article. It covers all the strategies that greatly benefit from tactician. What I'm trying to talk bout here is a bit more niche, and consists of decks that rely 100% on tactician and would rarely be playable otherwise. I mean, you can use any scalable card after building an engine to ramp up your payload, but tactician is unique at doing this much faster and despite the copper-flood. Tournament, baron and all those cards greatly benefit from tactician turns, but you will still play them on your non-tact turns. The same cannot be said for coppersmith, and to some degree for bank and HoP if you don't have an engine. If you have an engine, then the tact is playing a secondary role.

Goons definitely scales with number of goons, which I somehow completely missed. TfB is kinda the whole savager end-game story all over again: you grab a quick province/peddler and just cycle fast to end the game with a little lead. Or am I missing something beyond the fact that its easier to match the TfB with a high value card?

KC and Xroad help double tact just as much as single tact, if not more. I indeed mostly talk about treasure-based payloads and stress that, unless scheme is involved, they usually trail behind double tactician. With scheme it is board-dependent, but I can think of a few pretty solid (but not fast) double-tact boards that loose to tact-scheme-coppersmith/bank. More importantly my point is that even in absence of virtual coin you can set up this very stable tact/scheme decks if KC or Xroad is there to scale your turns appropriately. They aren't full-blown here because, as you stated, with virtual coin they actually tend to favor double tact over single tact.


As for Jomini's very accurate outpost/haven comment, I will add it as a very good other enabler for treasure-based tacts.


Would it put everybody's mind at ease if I rename the thread Treasure based Tactician engines? Or maybe Scaling Tactician decks, as opposed to Tactician combos and double tact? I mean, nothing prevents you from mixing these archetypes, but as WW pointed out, they present very distinct elements. The presence of virtual money as well as cards that combo with tactician without really needing it as the main engine kind of sidetracks the main point of my little post. I want to provide another strategy in your toolbox that behaves a bit differently from the others. Whether its better or not than the previous depends on the board. On some boards, the other tactician strategies might not be available or viable (lack of engine/trashing/virtual coin).

4

Dominion Articles / Re: Single tactician decks

« on: February 05, 2013, 10:26:43 am »

I would note that compatible +buy is sometimes critical for these kinds of decks. Simply double-provincing every other turn is not necessarily that great unless your deck is very quick to set up.

Agreed. The scheme-less version crucially requires +buy for multi-province turns (typically 3 with two banks). The scheme version sets up so quickly that +buy isn't necessary (or automatically included in the case of HoP). I will add it to the works with/conflicts section.

5

Dominion General Discussion / Re: Watchtower+Trader

« on: February 05, 2013, 10:19:47 am »

I somehow missed the trader on watchtower play. Probably didn't turn up in the couple of games I played. Good catch!

This definitely strengths my intuition that this is a strong opening in cursing games, and probably also very good in alternate green and boards with weak $5s. To make an article however we need the probabilities of all these events.

Any other ideas?

6

Dominion General Discussion / Watchtower+Trader

« on: February 05, 2013, 06:28:25 am »

I want to share an opening I once saw. I can't remember whom I copied it from, but it struck me as interesting at the time, although maybe for niche boards. After some practical experience, it's amazing against sea hag (and most other cursers), and pretty decent on silver-dominated boards (as opposed to engines or boards where hitting 5 is important). I do not know the probability of the following relevant events, and am too lazy to compute or simulate them out. Can anybody give me a hand?

1) Typical case: Watchtower misses Trader, hits $3 hand. Topdeck silver. Trader hits estate.

2) Good collision: Watchtower hits Trader together with estate. Topdeck two silvers. Most likely buy gold.

3) Bad collision: Watchtower hits Trader without estate. Cry. Trash watchtower with trader. Buy watchtower or silver depending on board.

4) Watchtower misses trader and does not hit $3, Trader hits estate.

5) Trader does not hit estate, Watchtower hits $3. Topdeck silver.

6) Trader does not hit estate and Watchtower does not hit $3. Cry.



1) + 5) are essentially equivalent to opening silver+Trader at the cost of getting hit by one bureaucrat. The defense provided by WT makes it totally worth it in cursing games.

2) is amazing, as it compares to having a double-silver opening that draws into a gold on first reschuffle. You get hit by a ghostship but trash an estate.

3) + 6) are pretty bad.

4) means replacing an estate by a watchtower, but getting hit by a ghostship (as both the trader and WT didn't do anything significant), which is pretty bad.

7

Dominion Articles / Re: Single tactician decks

« on: February 05, 2013, 06:16:44 am »

• Bridge, Highway and King's Court, which all scale quadratically in the number of copies you have of them in hand.

Nitpicking: While of course KC really profits from large handsizes, it does not scale quadratically.  The number of actions you can King's Court given n KC in hand is 2n-2.

Good point :P. I will correct that immediately.

8

Dominion Articles / Single tactician decks

« on: February 05, 2013, 05:57:21 am »

This post is intended as an extension to Theory's original tactician article on the blog.

Theory's article does an amazing job at explaining what tactician does and in describing in depth the mechanisms of double-tactician decks. I feel however that it is lacking when it comes to single-tactician decks. This is somewhat unfortunate, as I really meet a lot of players who cannot distinguish between good and bad single tactician boards. I believe this is because the article does not really address the question of full single tactician decks, rather than just cards that benefit from a single tact.

To explain what I mean, I'll introduce the notion of a scaling card. In its most strict definition, its not just a card that benefits from increased handsize, but actively creates payload in at least a linear fashion from hand size. Vault benefits greatly from the tactician hand-increase, but essentially does not increase the payload when compared to just playing out all the treasures you discard: there is a combo, but its of qualitative nature, not a scaling one. Baron matching an estate is an example of a quantitative benefit, but it does not truly scale with hand size and merely benefits from it. The cards that fit the most strict version of scaling are:

• Bank, which increases dollar output either linearly or quadratically, depending on how greedy and bank-heavy you go
• Coppersmith, which behaves in exactly the same manner
• HoP, which will hit 8 and snowball very quickly.
• Bridge, Highway and King's Court, which all scale in more than n when you have n copies of them in hand.

Crossroad deserves an honorable mention. It's drawing ability scales linearly in hand size, but that does not translate into scaling payload unless you have an effective way of gaining a lot of treasure or virtual coin. Hoard and Haggler fit the bill, amongst many other.

Why does this scaling matter? First and foremost, because the three first scaling cards are treasures and do not fit in the double tactician framework unless black market is in the kingdom. On a more down to earth note, you are skipping a whole turn to play your tactician in a single tactician deck. As theory points out, this means the tactician turn better pay off. Cards like Baron, forge or treasure map do greatly benefit from tactician, but they don't expect to only work through it. Think of it more as a preliminary phase to building your real deck. This is more obvious for forge, which really gets a huge boost from the first tactician, but then usually proceeds to make the tactician irrelevant by trashing your deck to the point where you can draw it every single turn anyway. In the case of treasure map, you will keep on playing tactician whenever your hand does not hit 8, but that is really secondary and you are essentially playing a BM variant. In particular, you don't stage with any form of consistency a multi-province turn. All the card matchers (Tournament, Explorer and Baron) again greatly benefit from a single tactician, but its usually a boostrapping mechanism to engineer a deck that mostly does not need tactician. Scaling cards are the only ones that truly form single tactician decks, rather than just some acceleration mechanism for some other deck.

What makes up a legitimate single tactician deck? How do you recognize one? What's a good metric to evaluate it by? Well, basically you have to compare it to double tact. Double tact usually makes a province a turn in steady state. Single tact decks need to make n provinces a turn every n turns to be competitive. This means that if you have a 15 card deck and one tact, you need to scale your tacticians so that they produce triple province turns. Unfortunately, the 'instability' of the deck makes it hard to reach the steady state, and you can often end up either with a lucky lead, or an unfortunate trail off despite your best intentions. This makes the matter a bit more complicated in practice as border conditions do matter. Steady state analysis is weakened a fair bit when you start buying a third of the green in one turn.

How do I build a single tactician deck? First, you need a scaling card. Second, you need to figure out how frequently you will have tactician turns. The aim is to scale your deck according to that frequency. It is therefore very important to get the appropriate number of scalers. This number depends on a few parameters. In the absence of scheme, you essentially have two possibilities: green early, or go for a mega-turn. If you green early, you are trying to grab an early lead in green using a few lucky turns and then hope to close down the game very quickly. Cards that can trash provinces into provinces (salvager being the top one) greatly boost this game plan. The other possibility is to build up to a one or two-turn super frenzy. This usually means a triple and a double province turn. In this case, you scale a lot more and green a little later.

Scheme? Yes scheme. Scheme changes everything. Scheme makes this deck much closer to double tactician than to super-turn decks. Scheme turns this from a good to an amazing deck, even with very little support. I am surprised at the number of games where people don't realize this and waste time thinning their deck towards double tact, when scheme+tact+scaler is just plain faster. When scheme is in the kingdom, you have one very simple objective: make two provinces every second turn. You can do that extremely efficiently: scheme+tact+scaler. In the case of coppersmith/bank, you usually attain that goal either by hitting that initial silver you bought to boostrap yourself to tactician, or by playing two scalers. The typical deck therefore looks around the lines scheme, silver, tact, 2 Coppersmith/bank, 7 coppers, green. In the case of HoP, you need to grab HoP right after your first tact and start gaining stuff. There is usually enough of an engine present to both grab enough diversity to hit 8 and keep drawing everything every second turn.

Finally, strong trashers (chapel, ambassador, remake, steward and forge) tend to favor double tact over single tact-scheme. Single-tact without scheme is usually weaker than a solid double tact deck regardless of the trashing but can be played when the other alternative is to play a non-tact strategy.

Works with

• Scalers
• Scheme!
• Cards that enhance your scaler (apothecary for Coppersmith/Bank, mint for HoP)

Conflicts with

• Double tact if no scheme
• Lack of +buy if no scheme/HoP
• Strong trashers (makes double tact and engines more valuable)
• Cursers

edit: random additional comments.

Haggler technically is also a card that scales with hand size. If you produce n dollars, it will grant you a card costing n-1. But because this card cannot be a green, it is not well-suited for single tact decks, and much better for double tact as it also provides virtual coin.

Alchemist can replace Tactician as the card that enables scalers. It doesn't set itself up nearly as fast (it takes time to grab the 5 alchemists necessary to start with a 10 card hand) but doesn't require you to skip a turn once it is set up.

9

Dominion Articles / Re: Combo: King's Court/Scheme

« on: February 04, 2013, 09:17:00 pm »

uhhh...I think Familiar is one of the weaker cursers. You cant get it nearly in time! And the Potion can be kind of annoying, too.

1) I already stated that, in the context of this combo, familiar is probably the weakest curser.

2) If you mean *in general*, I urge you to read this blog post: http://dominionstrategy.com/2011/11/14/the-five-best-potion-cards/


Here is going to be my question: are you going to go out of your way to buy a witch if you could buy an early gold, wharf or tactician: cards that help you hit 7 and help you match KC to scheme.

The case doesn't present itself for mountebank (which is virtual coin anyway) and to some degree with sea hag (because it attacks immediately, and is especially good with scheme). Familiar we've already ruled as as skippable, and ambassador cursing most likely isn't going to cut it either.

Again, cursers might help you by hindering your opponent's ability to reach the combo... but they don't actually matter as much once the combo is setup if your payload is virtual coin. Once you have your combo set up, would you rather be KC-ing a sea hag, or a woodcutter? One is strictly stronger than the other: at worst, a duchy compensates 3 curses.

Of course, the argument is moot if somebody starts his combo snowballing anyway, but that is exactly my point: focus on getting the combo. If cursers help you in racing to the combo, so be it. But once a virtual $ KC-scheme combo has been set up, cursing can still be useful but secondary to greening, which this deck does indefinitely with a decent source of virtual coin.

So yeah, when you rule out the in vacuum best cursing attack, I don't call it a no-brainer. There is clearly some more strategy involved. The combo is neat however, and the original statement perfectly holds when the payload of the deck are treasures.

10

Dominion Articles / Re: Opening develop/terminal 4$

« on: February 04, 2013, 08:46:39 pm »

Really interesting and I appreciate the analysis. Two points to note:

1. If you want to get to $5, it still seems better to go for silver/$4, which (as theory has previously pointed out) has something like an 80% chance to reach $5 on the first shuffle. Your analysis didn't include the chance of getting to $5 on T3/T4, but I would have assumed that silver/silver or equivalent would do better.

2. I don't agree that topdecking a $5 is equivalent to a 5/3 open, because if you topdeck on T4, your $5 will miss the next shuffle. I'd say that this is closer to the more conventional silver/silver open that buys a $5 on T3 or T4 than it is to a 5/3 open. On the other hand, if you topdeck on T3, then you get to play your power card twice, which indeed is amazing. But the chance of that happening must be like 15%, which should be weighed against the 10% chance that your develop eats a copper.

1. 30% chance of getting $5 through topdeck. 60% chance of hitting estate with develop. half of the times, the develop will be before the $4, half of the time, after. If its before, then you want to compute the probability that the remaining two estates hit the hand with the terminal (only case where you don't hit 5) = 60% . If it is after, you don't hit $5 if you draw your top decked silver with both remaining estates AND without the terminal 4 = 70%. Lastly, the probability that you hit $5 in the worst case scenario is 12%.

So that adds up yo 0.3 + 0.3*0.6+0.3*0.7+0.1*0.12 = 70%.

It's really as if you traded up 10% chance of hitting 5 (essentially the 'bad' scenario) for a 30% chance of hitting the 5$ on first shuffle.



2. True. But the fact that your 5$ card is combined with a 3$ one is particularly sweet, as it often guarantees you a particularly nice turn (if anything, a guaranteed second $5 card before second reschuffle, which you therefore have to compare to 15% of hitting 2 $5 cards of silver/silver).

This actually finished to convince me that you probably end up, in expectation, with roughly the same number of $5 cards then your opponent, even disregarding the advantage of playing $5 on the first reschuffle.

Indeed, you have a 30% chance of having collision, which really guarantees 2 $5 on most boards. Then a remaining 40% chance of hitting at least one. That means, on average, 1 $5 card. The standard opening has 1.06, which given my approximations, is probably equal.

11

Dominion Articles / Re: Opening develop/terminal 4$

« on: February 04, 2013, 06:06:04 pm »

dondon, I'm surprised you don't have more to say on this topic. I seem to remember you saying in no uncertain terms that the purpose of opening Develop/$4 was NOT to have them collide. I'm not claiming you're right or wrong, but as someone who holds a view diametrically opposed to the OP, you'd make an excellent devil's advocate for this article.

Well, I didn't understand the OP very clearly (but now I do), and my point was that your plan should not bank on a 30% chance of success if you're opening Develop. Or if it is, then you were really far up a creek without a paddle in the first place. Typically I do not open Develop to get a 5/3 topdecked during the first reshuffle; I get it to turn my Estates into something good, and then maybe later on I can use it to do other cool stuff.

Yeah, I see the type of board you are taking about. Engine decks with lots of 3/4 pieces (where 5 is not important). The fact that devel trashes and grabs a few engine pieces make it nice, especially if your other opener is not a terminal (caravan, fishing village...).

And this deck doesn't purely bank on the 30% probability event. Even in the 60% case, it doesn't really fall behind a standard opening. In some cases, it would actually still be ahead (stables board, igg board). In most cases, the two would be toe to toe in that 60% event. Of course, the 10% is horrible. Again, this is a lot like nomad camp openings, which I guess are better understood.

12

Dominion Articles / Re: Opening develop/terminal 4$

« on: February 04, 2013, 03:51:13 pm »

Well, the tempo lost is the result of not playing your $4 or the Silver (or other $3) you could have bought instead of that Develop. You're getting a $5 for your $4, but you're getting it a turn later.

Exactly. That develop and 4$ card still took up space in your first hand. So it's like you open 5/3(say, scheme+stables as you suggested), because you get to play both those cards on  your first reschuffle, but your *first* hand on that reschuffle will have been hit by a discard attack, as two of the cards did 'nothing'.


Think of it the following way:

1) you buy devel/militia, draw 3C, D, M on first reschuffle. Develop the militia and buy something for 3.
2) you open scheme/stables, draw 3C, Scheme, Stables on first reschuffle. Get hit by a ghostship and topdeck scheme and stables.

These two scenarios are essentially the same. It's therefore as if you opened 5/3, but got hit by a ghostship.

edit: My view is not diametrically opposed to dondon. I suggest this opening when 5/2 is a good opening. His arguments might hold on a different board (with lots of good 3s, for example and no good 5, in which case silver/terminal 4$ isn't that great either).

13

Dominion Articles / Re: Combo: King's Court/Scheme

« on: February 04, 2013, 10:41:15 am »

Kc-scheme-curser is *not* a no-brainer. Anything that produces virtual coin and buy will actually be -more- valuable than a curser. The power of this combo is that you can ignore most of your deck!

I recently won a game with KC, scheme, bridge and familiar (strongest curser in vacuum). The other player lost even though I ended up with all 10 curses, just because I could set up the combo two cycles faster. This might be a borderline case (familiar has the strongest tempo loss, and bridge is the best KC target) but I strongly suspect that you would much rather have at least one woodcutter than a witch as your KC-scheme target, all other things being equal. You probably want the curser anyway, but racing the combo should be the top priority, which usually means trying to not lose tempo.

Edit:  Let me try to be a bit more precise.

The combo is KC-scheme-action+payload. The payload can coincide with the action. If your payload is through virtual coins, the cursing becomes a lot less relevant, as you can essentially disregard the rest of your deck. If your payload are treasures, then cursing is very relevant. In the first scenario therefore, the curser may be skippable if it leads to too much tempo-loss. Or you might just want to curse people to slow down the combo, but the virtual-coin card is going to be a lot more important in the long run.

14

Dominion Articles / Opening develop/terminal 4$

« on: February 03, 2013, 05:00:40 pm »

Develop is #30 on the current ranking of 3$ cards that I find myself strangely attracted to these days. My win-rate is pretty average with it (1.18) but I still would like to share a little thought experiment that goes through my mind every time I spot develop in the kingdom.

The question asked is: what does it mean to open develop/terminal 4$ card?

Lets assume for now that the 4$ card is a terminal silver (e.g. militia, monument or navigator) to keep things simple. Then there are three essential scenarios:

1) The typical one: no terminal conflict and develop hits estate. Probability: 60%

2) Terminal conflict. Probability: 30%

3) Develop misses both the terminal and the estate. Probability: 10%


The crucial point to understand is that you need to compare develop to both the classical 3/4 and 2/5 openings, and keep track of how much cycling speed you've lost.


In scenario 1, you essentially replaced one of your starting estates with a develop, at the cost of one card cycling, which is like saying that you got hit by a bureaucrat. In a shortform notation I will quantify this as: 3/4 opening, -1E(estate), +1D(devel), -1C(cycling). This opening is therefore equivalent to opening 3/4 but replacing one of your initial estates by a devel and cycling one less card on the first reschuffle. Note that because you topdeck the gained silver, this is not at all equivalent to gaining it via, say, a jack of all trades or bureaucrat.

In scenario 2, I assume there is an interesting 5$ card that you are partly racing for with your opponent. You can find a list of 5$ cards that work particularly well below. The point is that you avoid the terminal conflict by developing your 4$ card even if you have an estate. The net effect is: 3/5, +1D, -2C. This is therefore equivalent to opening silver+devel/5$ on T2/3 (not a shabby opening) but giving a free ghost ship play to your opponent. I stress that because you topdeck the 5$ card, this must be compared to a 2/5 opening, not a 3/4 one. Therefore this scenario (and hence the devel/4 opening) typically shines on boards that favor 5/2 openings. In that sense, develop works a lot like nomad camp, which is the only other card that can allow you to gain a 5$ card on your first reschuffle from a 3/4 opening.

Finally, scenario 3 is very very bad. If you had bought a silver instead, this would have been a 6$ hand. instead you get another poor 3/4 dollar cycle for the very meager benefit of trashing one copper.


So, this is a gamble opening. The interesting scenario is terminal conflict, which happens roughly with probability 30%. How much this event is worth depends heavily on the 5$ card you are targeting, but also on how useful the develop will be later in the game. Don't forget, the develop will stay no matter what! The cards that therefore work best are either very strong 5$ cards that you want as early as possible (e.g. witch, mountebank, igg, vault on grand market board) or non-terminal hand increasers (e.g. laboratory, stables, tactician). The first one is because of the sheer impact of gaining one of those cards a shuffle earlier than your opponent, which will compensate any momentum loss from the free ghost ship you give them. Of all these cards, IGG shines the most, as it also provides an amazing develop target throughout the game. The second scenario is a little more subtle, but basically hinges on the fact that all these cards give you a very high chance of matching your develop with your three remaing estates, usually paving the way for a very strong engine or BM+non-terminal draw deck. This time, stables gets a mention as it takes care of the 'trash' that develop does not want to bother with (coppers), while helping develop those estates into silver. Tactician is also noteworthy, as a lot of tactician decks (tact-bank, double tact-black market...) are decided by who plays his tact first. Clearing the estates quickly is the cherry on top of the cake.

Lets turn our attention to scenario 1. It happens roughly with probability 60%, and is essentially equivalent to replacing one of your starting estates with a devel, at the cost of mild tempo loss. First, while that does not sound altogether positive, don't forget that at each cycle, you will still have a decent shot at the above gamble. The way I think of it therefore, the tradeoff is basically between giving your opponent a free bureucrat attack, and having a chance at a surprise 5$ card on the second reschuffle. Given that this opening does not hurt your odds of hitting 5$ on your first reschuffle, this can still lead to interesting play. However, barring a powerful 5$ card or an overall good develop board, this is still just 'equalizing' with the standard 3/4 opening.

Scenario 3, which has roughly a 10% chance of turning up, is extremely bad, esepcially given that you choose this opening to hit 5$.


So, in a nutshell, this opening is a gamble opening. It trades off a 30% chance of getting a lead for essentially a 10% of badly losing the game. In the remaining 60%, it behaves in a similar fashion to a standard opening, with some slight subtleties that make it better or worse depending on the specific kindom (basically how important the develop is for a possible engine). Whether this gamble is worth the risk is highly dependent on the 5$ cards available. Whether the board is develop-friendly does not really come into the equation directly, as the optimal strategy in most such boards is to first ramp up moneyness and then add the develop to create valuable 5=>6+4 or what not combos.


Works with

• Boards with significant 5/2 advantage
• Otherwise not played 4$ terminals (e.g. navigator, militia on some boards)
• IGG
• non-terminal +draw
• tact

 
conflicts with

• lack of the above (develop remains a weak card)
• strong cantrip 4$ (e.g. tournament, caravan)

15

Dominion Articles / Re: The Combo Deck

« on: January 22, 2013, 09:42:38 pm »

You quote me pretty much completely out of context.

Are you actually saying you would use the same metric to compare a TM deck and a BM deck mid game? Because that was what the quote was referring to.

When I play a BM deck, I might have a vague notion of when I'll reach 43 points (game winning state for BM), but first I keep track of my moneyness to decide what I buy.

In a TM deck, I quickly compute the probability of collision at next cycle to decide what I buy. And there is an easy formula that relates collision probability to average turns until collision.

Golden deck, average number of turns until I reach the golden deck stage.

NV/Apo, average number of turns until I get the golden apo deck.

KC/bridge: average number of turns until I buy everything. etc...

In an engine building phase, my first metric is usually: what percentage of my deck do I go through?

Somehow, I see the golden deck and TM as being closer related to each other than BM or engine. A combo is something that makes this 'average turn until state X' metric explode. Maybe the word 'winning' was poorly chosen, as you tend to win a few turns after a state X (and sometimes lose if the state X arrives too late: think late TM collision, or late bridge-combo). BM and engines just tend to behave linearly/quadratically, but don't make you reason as hard in terms of probability of events.

In a nutshell, combos need to go through a pretty specific game state before winning, and try to minimize their expected time to that event. Engines and BM don't have such dominating events before the game actually ends. Hence their primary metrics will differ.


Edit:

I guess another way to explain my vision of deck classification/metric is as follows. Answer the question: when do I green/make my points?

BM: if moneyness > threshold (simplified)
Engine: if I draw my deck with proba > x and have enough money
Combo: after event x happens.

And unlike BM and engine, that event is very specific and a one-time thing.

16

Dominion Articles / Re: The Combo Deck

« on: January 22, 2013, 08:58:49 pm »

Combo decks aren't always consistent. Some play off a low probability (per turn) of getting a huge payoff. And given enough turns, that low probability event will happen. Warehouse/TM is a weak version of such a combo. Tact/bank is another, unlike double-tact. Most HoP decks are actually not 'stable', and just keep building up while they wait for a good turn. Or at least, they shouldn't be stable in a mirror-match, because that makes you lose.

I mean, imagine you can build a completely stable tact/vault, or HoP-super turn deck in X turns. You can most likely build one slightly less stable one such that, in expectation, it wins in less turns. Hence the unstable version will win in a mirror match. How much stability you actually need is dependent on the matchup. Same often goes with golden decks: if an engine is present on the board, you can sometimes just do a not completely stable golden deck and squeeze out a little bit of extra win probability. Mind you, some combos are hard to tinker with (e.g. NV\apo).

I like theory's definition the most. Some combos are actually a lot more than 2 cards, but the crucial point is that some parts are irreplaceable (or very hard to replace). Also, the metric you use is very different from other decks.

Money-based strategies basically measure their 'value' in terms of moneyness per turn, that is, their average game state.

Engines in how consistently they go through their deck and reproduce a game state. (Hence why minion, HP and alchemist are usually engines)

Metrics for combo decks vary a bit more, but tend to be 'expected number of turns until winning state', whether that winning state is some completely stable golden deck type thing, or an actual insta win (or just connecting two TM in the case of weak combos).

17

Dominion General Discussion / Re: Talisman -- oh how little we meet

« on: November 04, 2012, 12:42:15 am »

Talisman bridge with cantrip 3$ and 5$ come to mind. Definitely fueled more than one bridge combo-deck with stuff like talismaned  apprentice/village or city/wishing well. They key is to get the cards in the right order (depending on how the cards fit, that means bridge or talisman first) and often get 2 talismans to threaten 3-piling or building up to a super-bridge turn. If the other player does not have sufficient +buy and cannot take advantage of the three-piling potential, this dual threat of just 3-piling *or* dragging on the game really makes this shine.

18

Game Reports / Re: Scout board

« on: October 22, 2012, 08:41:41 am »

Agreed. That's what you want to do in vacuum.

What prevents you though from playing smuggler to steal combo pieces in the process though? I mean, except maybe on the last 'mega' turn, smuggler serves the same purpose as Herbalist.

19

Game Reports / Scout board

« on: October 20, 2012, 09:58:46 am »

http://dominion.isotropic.org/gamelog/201210/20/game-20121020-065322-2207f529.html

Well, really, chapel/smuggler/HW lock followed by sneaky scout-deck building. My opponent followed suit: was that a mistake?

20

Dominion Articles / Re: Deck Archetypes

« on: October 03, 2012, 08:58:29 am »

Here is my proposed classification:

-mean-value decks
=> try to get the best average turn (big money, HT/duke, plain attack decks without engines).

-near-deterministic decks
=> try to end up with nearly exactly the same playmat every turn (golden deck, HP, scrying pool, double tact, masq-pin, torturer chain...).

-spike decks
=> try to take advantage of unlikely(for any given single turn) but extreme events (single tact+coppersmith/bank, mega turn...).

All three correspond to secondary objectives that players follow in order to win the game. These mostly coincide with the usual taxonomy, but differ in some important cases:

Chancellor/stash is a near-deterministic deck, hence not classified together with BM/envoy
Golden deck is also a near-deterministic deck.
A BM variant that plays non-terminals (markets, say) would be classified together with BM/envoy.
Megaturn decks and other 'unstable' decks would be separate from engines.

It might not be as easy to classify decks within those archetypes, because you have to sit back and think rather than just look at the deck list, but I think it corresponds more to a fundamental truth behind the mechanics of the game. The first objective in the game is to manage randomness. Once that is done, people green and attempt to win.  All three archetypes correspond to a way to manage the inherent randomness of the game. I wrote an article earlier in the year where these ideas were presented (bundled up with other random thoughts of mine).

21

Help! / Re: Merchant Ship BM vs. University/Market/MS

« on: June 23, 2012, 08:41:02 pm »

Why not open embargo/potion?

Embargoing gold should hurt BM a fair bit. The engine deck does need it's early buying power for the early turns, but not as much mid-game (when you want to maximize university/market cycling), so the opportunity cost of embargo vs silver is not that high. Oh, and no terminal collision.

22

Dominion Articles / Re: Merchant Ship

« on: June 14, 2012, 11:24:46 pm »

On the engine vs BM debate.

Another way of classifying strategies is by their objective in terms of turn-structure: what we generally consider an engine tries to replicate a nearly identical playmat every turn (usually obtained either by drawing through most of the deck via tact/smithy/village chain/scrying pool/menagerie/library/alchemist/HP...) while what usually drives BM is a high average hand output (hence all the talks of 'moneness' in BM). Under that classification system, an action heavy deck with no drawing capacity would be 'BM'-ish. You would reason mostly in average money output of your village/merchant ships rather than in terms of deck drawing reliability. Of course the line gets blurred when you draw say, a quarter of your deck.

It's not uncommon for your 5-card hand to be a quarter of your deck well into a big money game...

I don't know that I think the 'identical playmat' thing is a very good indication of things either - chancellor/stash isn't an engine, and there are quite a few engines that have great big mega-turns... only about half the time.
I think an engine is an engine if I am chewing through lots of cards in my deck on a fairly consistent basis, roughly.

Hm, somehow, in my mind, stash/chancellor *is* an 'engine', as every chancellor play leads to a perfectly predictable next turn. It's not a BM, because the average moneyness of the deck is low. Maybe I should rename those groups and just make it a separate classification to engine/BM. My point is, they provide a pretty good metric to compare or contrast strategies differently than just 'action heavy' or 'treasure heavy'. And big mega turn decks are a (third) group of their own.

Basically, the idea is to reason in terms of the probability distribution of the money output per turn. If you try to make it very consistent and near identical from turn to turn (probably a multiple of 8 ), it's an 'engine', if you try to get the highest mean it's a 'BM' and if it is just some very fat-tailed distribution (no money most of the time, lots of money in one turn) then it's a "mega turn" deck. Then there are messier things where the distribution is all over the place.

With this classification, people have a clear objective in mind: if they go for an 'engine', consistency is in order. If they go for 'BM', moneyness is the key metric. A 'mega turn' is defined by the average time it takes to close the game.

23

Dominion Articles / Re: Trader

« on: June 14, 2012, 08:51:19 pm »

No mention of watchtower+trader opening?

It's pretty fun and defends particularly well against cursers.

24

Dominion Articles / Re: Merchant Ship

« on: June 13, 2012, 10:26:22 pm »

On the engine vs BM debate.

Another way of classifying strategies is by their objective in terms of turn-structure: what we generally consider an engine tries to replicate a nearly identical playmat every turn (usually obtained either by drawing through most of the deck via tact/smithy/village chain/scrying pool/menagerie/library/alchemist/HP...) while what usually drives BM is a high average hand output (hence all the talks of 'moneness' in BM). Under that classification system, an action heavy deck with no drawing capacity would be 'BM'-ish. You would reason mostly in average money output of your village/merchant ships rather than in terms of deck drawing reliability. Of course the line gets blurred when you draw say, a quarter of your deck.

25

Dominion Articles / Re: Merchant Ship

« on: June 09, 2012, 09:07:19 pm »

1) It's *two* buys, which is a significant boost to any card
2)Large terminal draw is probably the cardtype given the largest boost by +buys.
Because +buy on large draw

Okay... how often are you using all 5+ buys that you get when you have a Wharf chain out? If you're looking to build an engine, you don't usually need more than 2-3 buys; if you're trying to green, you won't usually have enough money to buy more than 3 Victory cards at once.

Very often: bridge, highway, quarry, peddler, trader!, goons, watchtower!, 3piling on cheap piles (buy curse to finish game anyone?). Actually, if you don't *need* the extra buy from wharf, you are probably better off buying other cards (as in, not as many wharfs, but rather gold/plat/lab/rabble or simply green cards!) after you have reached your 3rd wharf.

I don't even see how you can get 5+ buys out (from wharf alone) unless you seriously outplayed your opponent (grab more than half the wharfs), or have been seriously outplayed (as in, one of the rare situations where wharf is sub-optimal). This means that the argument 'this card is good without the +buys because with you can get too many buys' self-negates because if it really were that good (which it often is), you will not get more than half the wharfs (leading to probably 3ish buys a turn). And you definitely need the 3 buys a turn in an engine.

Also, non-engine decks usually don't play a wharf every turn, but have a wharf out every turn: and 2 buys almost guaranteed per turn is big, even if you get the occasional overshoot 3 buys. Having to tweak out money to buy a market for +buy (and risk drawing it dead) is not cool.