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Topics - Empathy

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1
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.


2
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.

3
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)


4
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?

5
Game Reports / Two refreshing games
« on: May 14, 2012, 09:57:16 am »
One where I get trounced at the only BM strategy I enjoy: trader.  I thought it was the standard trader/gardens pool. Saw the scheme/peddler combo (had actually played it a couple of games before), but thought it would put you down too much in the trader/gardens race, failing to foresee Hampuse's brilliant trader on peddler play. I saw all the combo pieces separately, but Hampus saw the big picture.

Now the next game is less impressive, because my opponent just went for a boring alchemist loop, leaving me all the time in the world to do some non-sensical comboing via mint, HoP and KC. I do wonder, however, what the optimal tactics is if both players went for the 'complicated' strategy. Any thoughts?

6
Game Reports / Feast fun.
« on: May 12, 2012, 10:05:54 am »
Gaining feast on feast is fun.

I'm pretty sure I played very far from optimum in terms of tactics, but it was one of those unforgiving strategy games.

7
Game Reports / Unusual HP vs Crossroad/Vault opening
« on: May 07, 2012, 09:38:33 pm »
http://dominion.isotropic.org/gamelog/201205/07/game-20120507-081505-520e44c9.html

Crossroad/Vault as p1 was going to be hard to beat. Luckily, the board allowed for a nice quarry/horse trader interaction, although I pulled off the combo very late (T8), considering the presence of HP to accelerate the collision. Because of that, I was far too behind on the province race and had to look for alternative greening, leading to a weird HP deck that, despite 8 HPs, did not systematically draw itself every turn (but Crossroad helped). The transition from perfect (but vp-wise behind) HP engine to messy HP/XRoad/fairgrounds deck was fun to play, and I think, unexpected by my opponent.

8
Simulation / Challenge: asymmetric p1/p2 equilibrium
« on: May 05, 2012, 02:44:50 pm »
I want to ask you simulators out there if there are striking examples of simulation bots where the optimal strategy for p1 and p2 differ notably. My intuition tells me that p1 should opt for a low variance strategy, while p2 should aim for a high variance one, and that the game is probably very short.

So far, my first quick attempt is the following:

Set the first players to open with Governor/duchess and goes through the standard Governoring, finishing the game on average within 15 turns:
Code: [Select]
<player name="Governor 5/2"
 author="Empathy"
 description="A very strong p1 opening.">
 <type name="TwoPlayer"/>
 <type name="Bot"/>
 <type name="SingleCard"/>
 <type name="Province"/>
 <type name="BigMoney"/>
 <type name="UserCreated"/>
  <start_state>
    <hand contents="2 Copper, 3 Estate"/>
    <discard contents=""/>
    <drawdeck contents="5 Copper" shuffle="false"/>
  </start_state>
   <buy name="Province"/>
   <buy name="Duchy">
      <condition>
         <left type="countCardsInSupply" attribute="Province"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="4.0"/>
      </condition>
   </buy>
   <buy name="Estate">
      <condition>
         <left type="countCardsInSupply" attribute="Province"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="2.0"/>
      </condition>
   </buy>
   <buy name="Duchy">
      <condition>
         <left type="countCardsInSupply" attribute="Province"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="6.0"/>
      </condition>
   </buy>
   <buy name="Governor" strategy="GoldEarlyTrashMid"/>
   <buy name="Silver"/>
   <buy name="Duchess">
      <condition>
         <left type="countCardsInDeck" attribute="Duchess"/>
         <operator type="equalTo" />
         <right type="constant" attribute="0.0"/>
      </condition>
   </buy>
</player>

Now if p2 tries to catch up using his own governor deck,
Code: [Select]


<player name="Governor"
 author="Empathy"
 description="A strategy traying to catch up to an early governor opening.">
 <type name="TwoPlayer"/>
 <type name="Bot"/>
 <type name="SingleCard"/>
 <type name="Province"/>
 <type name="UserCreated"/>
 <type name="BigMoney"/>
 <type name="Generated"/>
   <buy name="Province">
      <condition>
         <left type="getTotalMoney"/>
         <operator type="greaterThan" />
         <right type="constant" attribute="18.0"/>
      </condition>
   </buy>
   <buy name="Duchy">
      <condition>
         <left type="countCardsInSupply" attribute="Province"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="4.0"/>
      </condition>
   </buy>
   <buy name="Estate">
      <condition>
         <left type="countCardsInSupply" attribute="Province"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="2.0"/>
      </condition>
   </buy>
   <buy name="Gold"/>
   <buy name="Duchy">
      <condition>
         <left type="countCardsInSupply" attribute="Province"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="6.0"/>
      </condition>
   </buy>
   <buy name="Governor" strategy="GoldEarlyTrashMid"/>
   <buy name="Silver"/>
</player>
He loses 58-37. Note that, in both cases, the optimal Governor policy is "GoldEarlyTrashMid". Also, buying governors over Gold is optimal for p1, but not p2 (which kinda makes sense). The average game takes 15 turns.

Now consider the following smuggler bot:
Code: [Select]
<player name="smugglers counter"
 author="Empathy"
 description="A smuggler-based counter to the strong p1 opening. Note that it plays the governors much more aggressively!">
 <type name="TwoPlayer"/>
 <type name="Bot"/>
 <type name="SingleCard"/>
 <type name="Province"/>
 <type name="BigMoney"/>
 <type name="UserCreated"/>
   <buy name="Province"/>
   <buy name="Duchy">
      <condition>
         <left type="countCardsInSupply" attribute="Province"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="4.0"/>
      </condition>
   </buy>
   <buy name="Estate">
      <condition>
         <left type="countCardsInSupply" attribute="Province"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="2.0"/>
      </condition>
   </buy>
   <buy name="Duchy">
      <condition>
         <left type="countCardsInSupply" attribute="Province"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="6.0"/>
      </condition>
   </buy>
   <buy name="Gold"/>
   <buy name="Governor"/>
   <buy name="Smugglers">
      <condition>
         <left type="countCardsInDeck" attribute="Smugglers"/>
         <operator type="smallerThan" />
         <right type="constant" attribute="1.0"/>
      </condition>
   </buy>
   <buy name="Silver"/>
</player>
It actually nearly ties with the insanely fast governor 5/2 opening: 49-45! Note that the optimal governing policy for this bot is "Standard", but the optimal policy for the first player is still "GoldEarlyTrashMid" (it actually loses otherwise). The average game lasts 14.5 turns

Did I make a blatant mistake in the p1 bot (a "garbage in, garbage out" type thing)? Can other such situations be simulated?


9
Dominion Articles / Thoughts on Strategy vs Tactics
« on: May 04, 2012, 10:11:42 pm »
[Thoughts on Strategy vs Tactics]

The aim of this article is to revive a distinction made by a top player a little while ago:
At its very core, I think Dominion only tests two skillsets; to identify the strongest strategy, and to execute that strategy optimally. Is there a difference between very strong players and exceptionally strong players in these areas, you think?

I'll reformulate the two skillsets with my own wording:

Strategy is defined as analyzing the board, and either consciously, or unconsciously, appreciate its richness. It involves planning out not just your opening, or your most likely deck construction path, but also means taking into account other outcomes than the 'typical' one (i.e. so called 'strategy switches').

Tactics is how you execute your plays, and focuses on the actual, every-turn decisions you make. It involves how you play, buy or trash cards and more importantly, in which order. It also crucially involves the greening stage, moneyness and engine-building decisions.

In more mathematical terms, Tactics solely relies on a probability framework, while Strategy includes a dose of uncertainty, due to the inherently complex nature of some boards.  The usual approach towards the study of Tactics, brilliantly illustrated by both the Geronimoo and Dominiate simulators, is to simplify the dominion board to the clash between two 1-3 card strategies. This makes the problem of finding the optimal execution policy actually tractable, greatly improving someone's understanding of how a particular strategy works, and how it interacts with a particular competing one. Now, technically, the simulator is also supposed to answer questions of strategic nature. And it does so quite well for certain strategies, but I would like to stress the limits of that approach. My aim is not to diminish the importance of simulation: it is probably one of the biggest achievement in our strategic thinking, having discovered simple and elegant strategies such as Double-jack and Fool's gold. But I do think it pre-conditions us to think of strategies that have a low level of tactics involved... though paradoxically, the people who then use these strategies by default end up with a very high level of tactics.


In order to illustrate my point, let me review what are considered the two most common families of strategies, and how they relate to Tactics and randomness. My claim is that both try to reduce randomness in order to make tactics-related decisions easier... and of course, improve your chances of winning:

I'll start with the more obvious link. Engine building is a difficult but rewarding subgame of Dominion. It often involves more cards than big money, but not necessarily more types of cards. Most of the engines can be summarized by two cards, with often a third card being splashed in practice: Torturer chains,, Hunting Party engines, King's Court/Scheme shenanigans, Scrying pool engines, Hamlet/Menagerie interaction or the brilliant Apothecary/Native village Combo of Mean Mr Mustard. What all of these engines have in common, is that they try to defeat randomness by building a deck that will behave nearly exactly in the same manner every single turn. This often involves either heavy trashing (let's not forget that chapel is still probably the best card in the game) or drawing your whole deck (e.g.: brilliant win by O.G.), but can also involve scheme or hunting party (or both). The point is, you want to be able to play exactly the same set of cards every turn. I cannot end this paragraph without quoting the impressive Marin and his amazing engines.

Big Money is the other grand line of strategy. It comes in various shapes and sizes, often as BM+card. The most elegant version of it is probably double-jack, which not only truly encompasses the core value of 'moneyness' of the archetype, but also single-handedly defends it against pesky attacks such as sea hag or witch. An extensive review of the paradigm behind big money, read WanderingWinder's two articles on the topic. The man is the master of the field, and one of the two most skillful players I have had to chance to play with. Now, after you read about money density, about the relationship between deck size, hand size, and the ratio of green to treasure, I hope you appreciate what truly lies behind the spirit of Big money: the law of large numbers! Indeed, whereas engines try to defeat minimize randomness by building towards a near-deterministic play-mat every turn, big money attempts to minimize randomness by placing itself in the most favorable 'average' scenario. By keeping the strategy nice and simple, it avoids non-linearities, letting its tempo, and the law of large numbers, simply slide itself to victory.

Now you see why these strategies lend themselves to somewhat easier decisions in terms of tactics: they involve a relatively limited amount of cards, and the aim is to reduce the number of encountered scenarios inside a same game. This allows for a more rigorous training in the exact set of tactical skills you need to perfectly execute the strategy: by playing a simple, 1-2 card strategy over and over again, you will learn in which order to buy the cards, when to green and how to best close the game. You can also have a hope of simulating the strategy with a decent bot, greatly bootstrapping your analysis. But this only works for simple strategies. With simple, I don't mean 'simplistic' but rather elegant. And even the simplest of strategies, BM+Envoy, includes a learning curve in terms of greening decisions.

I am going to propose a third group of strategies, one that is in my opinion somewhat under-evaluated. It might also often be confused, or maybe just mixed, with engine strategies. I will dub them messy strategies, in the sense that they often are played less tactically skillful than the previous two, maybe because they are undervalued, but mostly because they have an inherently higher learning curve. This is because they often involve either cards that are less powerful (and with which players have therefore less experience), or just a greater number of different cards (and the combination therefore appears less often, leading to less experience as well). The essence of these strategies is to embrace, rather than fight, randomness or uncertainty. They reward risk, although in a measured manner. Probably the most known example are treasure map based strategies. I in particular believe those strategies to be well adapted to a player who faces a severe bias against him, due to for example to First player bias. Here are two examples of such plays: One successful noble brigand gamble, and another not immediately successful treasuremap/black market gamble. Of course, the first game is biased by the sheer fact that I hit Wanderingwinder's silver, but regardless, it added a fair amount of variance to a game that would otherwise have been dominated by a BM-variant. The second game is really just me attempting two initial gambles (black market and treasure map), but transitioning to a menagerie engine powered by exactly that variance in card types (crossroads,treasure mapand black market all work well with menagerie). The opponent's strategy was a standard pirateship/crossroad engine that would have perfectly messed up a BM in position 2. Messy strategies often also rely on one particular 'non-linear' event to happen, which of course strongly increases their variance. This awesome play michaeljb needs him to buy exactly one province (but not more, lest I finish the pile!), a few tournaments (without overcomiting, as I will have more provinces) all this to get the one princess that will allow the mega-turn. Of course, it's embedded in a more standard wharf engine, but that is secondary. A card I really enjoy using for messy strategies is navigator. Now in that particular example, the non-linear event is tactician with several banks (with some wharf help). It's not really an engine, as I do not pull of the thing with anywhere near enough regularity. Nor is it big money, given how I do not rely on the law of large numbers. It truly means I set up one or two very big turns to swing the game in my favor, often forcing my opponent into plays he did not foresee having to do (like getting duchies early). Navigator helps a lot in this situation, because it allows you to virtually hit more hands, increasing your odds of getting that magical non-linear one. KC-Navigator in particular I would rank as a full combo, probably very typical of the messy strategy: first, similarly to warehouse a lonely navigator increases your odds of having a KC paired up with an important target (like another KC), but more importantly, KC on navigator nets you 6$, and often guarantees you that your next hand will have KC+target. Of course, sometimes the wanted non-linear event just happens too late (I still think it was the correct play on that board, at least as p2).

Messy strategies face a big hurdle, however. Because they often rely on a mix of variance, non-linear effects and more than 2-3 types of cards, they are very hard to re-encounter, simulate and evaluate. This makes it very hard to anakyze certain weird strategies (like this talisman=>feast=>city idea) and leads to discussions where it is unclear whether the elegant strategy is necessarily the best one (I much prefer the ironworks/smuggler opening, which also grabs a ton of silvers, but obviously does not have the spy effect. On the up side, it can grab islands as well as lucky golds and duchies. But while I prefer it (because more decisions are involved), I am not convinced it is the better move).

To summarize, I tried to reintroduce an old concept,  Strategy versus Tactics, illustrating it on the two dominant classes of strategies. Then I argue that a third class of strategies exists (and maybe more?), which is in a weird sense more tactics intensive (because it is intrinsically harder to be experienced in it) and paradoxically played by less tactically skilled players (because tactics-players tend to hone their strategies by repeating them). This presents an interesting conundrum to players that are willing to push their strategic thinking a bit further, at the expense of losing their tactical edge. I hope you enjoyed the read.


Edit: replaced "Skill" by "Tactics". Thanks for the feedback!

10
Game Reports / Embargo
« on: February 04, 2012, 01:10:01 pm »
http://councilroom.com/game?game_id=game-20120203-135714-3012606a.html

Embargo decisions were, in order: apo, apo, minion and city. Next one would have been gold.

While the game is frankly boring, I think it illustrates well embargo dynamics. I am very fond of those because I used to overrate embargo a lot, but now it has become one of the cards I am most comfortable with.

So here is some piece of advice, though feel free to criticize and comment.
  • Don't ignore it. Assess the board, then ignore if it is no threat.
  • Ignore it if ambassador, masquerade, JoaT or chapel are on the board. (http://councilroom.com/game?game_id=game-20120114-085710-15ddf643.html)
  • Never overextend into a strategy or engine. The typical examples are potion, minion but also plain BM if it conflicts with what there is else on the board.
  • Go heavy on the trashing and gaining effects. Don't hesitate to take otherwise not-so good trashers. Remodel shines in embargo games (embargo grand market, remodel into them anyone?). Remake is a beast. To be the only one allowed to get the embargoed card without a curse, or able to trash the curse, is extremely valuable.
  • Embargo cards you already have but your opponent doesn't. Mountebank is a great target, because of all the cursers, it is the one with most variance. (http://councilroom.com/game?game_id=game-20120111-065321-bdcf46ac.html)
  • The best embargo targets are: 5s (if there are only a few good ones, like in this game), gold, plat, sometimes silver (someone opening lookout might find themselves in a bind), embargo if you have an engine to protect. Embargoing  green can also be a neat trick, though that would warrant a discussion of its own.
  • Be flexible. Don't go BM envoy, because if he embargoes gold/silver, you will need actions, and envoy doesn't like those usually. But don't jump into an engine where one embargoed component could kill you. Your best bet is usually some highly hybrid, adaptive strategy. (http://councilroom.com/game?game_id=game-20120117-071346-33ebb2d9.html)

I'm sure most of those don't come as surprises.

11
Game Reports / Chancellor, Inn and Counting house
« on: January 06, 2012, 05:23:02 am »
Not as powerful as Chancellor, Inn and Conspirator (http://councilroom.com/game?game_id=game-20111214-150017-618245a6.html), but sweet nevertheless.

http://dominion.isotropic.org/gamelog/201201/06/game-20120106-021715-5877b4e9.html

Question: with +buy, should I grab a few extra coppers? If yes, how many (my gut feeling is 2)?

12
Game Reports / Farmland/Highway fun
« on: November 03, 2011, 10:58:34 am »
http://councilroom.com/game?game_id=game-20111030-115646-30834484.html

Highway-farmland makes for a very green deck that trashes coppers into provinces for 8point turns. 40 points by turn 15 sounded good.

The plan was then to switch into a bishop strategy once I saturated in farmlands (because bishop on farmland sounds sweeeet)

I trashed my bishop to get a province lead, hoping to simply farmland-remodel anything into a bishop again.

And this is where I failed, given that farmland is not like remodel. I basically fizzled for 2-3 turns, having no money in the deck and only being able to get stuff that costs 6 or more with the highway/farmland combo...

chwhite played a much more conservative and well played bishopping strategy which overtook me during the fizzling period, niftly finishing the game with one more point.


I'm sure I misplayed a fair bit, and the strategy could have been much faster, more impressive and so on in more able hands.

I still have the impression that highway always finds *some* combo on half the boards it's present on. You just have to look hard enough.

Farmland is really inflexible, however.
 

13
Dominion General Discussion / The advantage of going first
« on: September 16, 2011, 08:04:48 am »
I was wondering if anyone had ideas and thoughts about the natural bias the game has towards the first player. I'm pretty sure it's statistically verified, and it seems to be non negligable. Most players I know have a 0.1-0.2 point difference between their first player and second player game stats.

More importantly than evaluating the statistical advantage of the first player, I was wondering if it had any impact on strategies, in particular openings.

A basic heuristic seems to imply that yes. Assume the optimal strategy is some nearly deterministic chapel strategy that takes exactly 17 turns to grab more than half the points. Then, clearly, if both players play the optimal strategy, the first player will win with probability 1. Any sub-optimal strategy with higher variance is therefore preferable for the second player. Treasure mapping, even if it will on average only win on turn 20, might be preferable because it has a small chance of winning much earlier if lucky.

I think that could be a reasonable rule of thumb: as the first player, go for the best, safest strategy. As a second player, go for one that is just as good/slightly worse, but has higher variance to maximize probability of winning.

Any ideas on the matter? How important do you think it is to adapt your opening strategy to your table position?

14
Simulation / Another approach: metric on games
« on: September 13, 2011, 10:50:40 pm »
New to the forum, but I was wondering if anyone had explored the following possibility in addition to simulations.

We have huge amounts of played games on the council room server. I don't know the exact amount, but I would assume a few millions.

Now there are many many more combinations of kingdoms than that. That being said, many kingdoms look alike: say, you group together most of the villages into a class, or disregard weak cards in a pool where a stronger strategy clearly dominates.

So, if we could manage to group games together by how close they are, it would probably be possible to "simulate" the results of a game just by hashing average scores statistically from previous games that looked similar enough.

There are clearly two problems with this approach, however. First, the grouping method must be both convincing and lead to a sufficient amounts of games to allow for useful statistical evaluations.

One possibility is to just define a metric, a distance, between two games. Then, given a set of kingdom cards (possibly never played before), you could then search for the, say, 1000 closest games given that metric and use those for your statistics and sample games.

Now defining a metric between games seems a daunting task of its own, given that a lot of (somewhat arbitrary) factors could go into it. Fine-tuning the metric could take a fair bit of time, though a good human player should be able to spot if the results "make sense". Lastly, the ideal case would be to have an algorithm that could search for "the closest games" in real time.

I have a rather simplistic metric in mind that would fulfill some of those criteria, though I would first like to hear reactions and propositions before going into any more details.

The code I have is a very crude R script, but it runs nearly in real time for a small database of 100k games. The results are somewhat convincing but the metric clearly has to be tweaked.

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