Thursday, 28 May 2015

Theory: Pace-Setting vs Chasing

The primary natural tension in Dominion is that you need victory cards to win, but those cards actively hurt your deck's ability to function. I believe that this is at the core of the greatness of the game, and a big part of what sets it apart from most other deck-builders. In terms of gameplay, what often happens is that the game is led to a position wherein one player - I will call her the "Pace-Setter" - takes a points lead, hoping to ride that to the end of the game, and the other player - I will call her the "Chaser" - delays greening for some time, hoping to ride their superior deck quality to overtake the Pace-Setter before the game ends.

Play as the Chaser
The most important thing here is that you need to have a good understanding of how much time you have. This means that you need to have a very good understanding of what your opponent's deck is capable of. You have a big question of when to green, and as with most tricky decisions, there are pressures coming from both sides. On the one hand, you want to move to greening sooner, because if you wait too long, then your opponent will simply lock you out by getting too many points for you to overcome. On the other hand, if you green too soon, you risk not having enough fuel to finish your comeback, sputtering out, and losing.

In practice, the latter is a much bigger problem than the former, at least for most players I've seen. The number one biggest problem I see for people in this role is that they panic, green too soon, and can't finish the job. I think this is a fairly natural reaction, as you see that you're behind on points, which makes you feel like you need to do something, and furthermore, it's easy to see what the Pace-Setter's deck is capable of right now and extrapolate that forward, not taking into account that this will deteriorate as they green.

In general (and there are lots of further factors that lead to exceptions to this rule), you should continue to build your deck until the point where if you wait any longer, your opponent will likely be able to lock you out. The bigger your lead (in terms of game positioning, not points), the more you want to protect against them having fortunate draws by turning for green slightly earlier yourself (this can in some cases also protect against you having bad draws yourself, though this is situational, as sometimes you're better off buying more components that give consistency). The more you are behind (again, this is in a game position scenario, not a point count), the more you need to play for the opponent to have deterioration, even if that's unlikely. Nothing is worse than turning for green when you yourself have insufficient deck quality to ever get through everything.

You always need to have a plan to actually win - just closing the gap somewhat is meaningless, as margin of victory (or loss) doesn't actually count for anything.

Play as the Pace-Setter
When you dive in and take a points lead, your goal needs to be focused on ending the game. It's not about scoring the most points as fast as possible, it's about having a lead when the game is over. This means you want your deck to be sufficiently built-up that you won't stall out completely before you can put the game away. At the same time, you need to make sure that you aren't going so slowly that your opponent can just turn to green and take the lead while still having the better deck.

You are generally trying to do one of two things in order to end the game: empty the Provinces (or Colonies), or take an insurmountable lead. The classic example of an insurmountable lead is having half of the VP in the supply, such that even getting every single point remaining, your opponent will still be behind; however, in practice, you usually don't need to go quite that far, as getting all the Estates together with other, expensive things, will usually prove to be prohibitive for a Chaser.

Which of these you go for depends a LOT on the particular circumstances of the board and game. However, the big question often comes down to what other kind of points are available; if there are only the standard ones, you usually go for Insurmountable Lead. Generally, this is only going to change if there is some reservoir of points which it's much easier for them to tap into than you, but it will change in those cases. The important factor, though, is that you keep building your economy with whatever particular goal in mind - you need to be able to power through to the end without sputtering out - but not so much that you lose your speed edge.

One last thing I want to mention is that, while you generally want to pick some method of closing out the game and focus that down, if you can afford to have flexibility, that's a definite positive. For instance, your opponent is likely to be building for quite a while, and if you can pick up some components which are necessary for them and only marginally worse than the alternative for you, it can sometimes be worth it - especially if this can also threaten pile endings. This won't come up terribly often, but it's the kind of thing to be on the lookout for.

Sunday, 24 May 2015

Engine Theory: Consistency and What You Need

Following on from these two posts, let's continue our look at engines. We know what the payoff is, and we know the difficulties of getting them set up reliably. So when do you go for them? Well, as with most questions about Dominion, this is going to vary a good bit based on what's available. You always have to ask yourself, for any strategy, "what's the alternative?". Nevertheless, there are some things we can cover in general, and as long as we know there are going to be exceptions, and remember that context is king, we can learn some things.

Ok, so the biggest problem we were left facing at the end of the reliability article is that it's difficult to get to the point where we're consistently drawing our deck. We have basically four main ways of dealing with this.
  1. Buy lots and lots of components for redundancy
    This one is tempting, because it's going to be possible every single time you have a draw engine that's at all possible, and getting stuff is what you want to do anyway. Unfortunately, if you check the math on things, it basically just doesn't work - to even get 3/4 reliable, you basically have to empty two stacks, and that's with pretty small payload. For sure this strategy is something you want to look to in order to complement the others, but in terms of getting it to work just on its own, you need to be gaining something like 3 components per turn every turn somehow, all while not emptying too many piles - and even then, it isn't great.
  2. Don't Care About Consistency
    This isn't really something you can do terribly often - you are just eschewing the big benefit of engine economies exploding in on themselves like breeder reactors. Nevertheless, it can really be a viable thing on some boards. Much as I think people tend to overestimate their chances of drawing their deck every turn when it's 75-90% (i.e. you SHOULD dud out every 4-10 turns on average), I think people feel cheated when the other person 'gets lucky' and strings things together. Well, if they're 25% to do so on any given turn and they have 5 shots... they're going to get there over 3/4 of the time. In order for this to be at all viable, of course, you need some REALLY powerful payload. Traditional Megaturns are the order of the day here - 7 Bridges or Horns of Plenty, and it won't really matter that you won't get them together again. And this can lean your engine a bit more towards a 'combo' feel.
  3. Thinning, as my friend Adam Horton would tell you, whinning. =D Seriously, though, the consistency numbers get a LOT better when you have fewer dead cards to draw. Good thinning also speeds you up quite a bit, because it's just a lot faster to get rid of cards from your deck than to add cards to be able to draw it, considering that whilst adding cards, you have to draw all of those, too! Now, it might surprise a lot of you that I'm listing this here, and not last, because you would think this is the biggest solution to the consistency problem. But while it does give you a very good amount of speed, and it helps the consistency some, it doesn't really solve the problem. You're still going to want payload at some point, and it's almost always going to be more than the 5-6 cards for which you can be very confident to draw it all. That means you are going to be somewhat inconsistent unless you're significantly over-drawing. And well, you can usually just overdraw a bit, but that leads to inefficiency, which costs you time. And if the thinning isn't fast, you can have some real problems - even something pretty quick like Steward will take a couple of shuffles before you're reaping real benefits, and if it's slower like Trade Route? Yeah, good luck with that. So it turns out, even with trashing, you want something more....
  4. Sifting
    Really? I know that's what you're asking. Yes. Sifting is amazing. It doesn't help you get to the point where you can draw your deck - in fact, a lot of what is traditionally considered sifting hurts you there - but once you are there, it starts becoming very, very valuable. The thing is, how are you dudding out? You draw all of your dead cards together, without having the cards you need to kick off. Sifting cards let you see LOTS more cards to get to your key starters. And when you are engine building, to get your consistency up, you would otherwise need to buy lots of extra draw cards anyway, for redundancy (a la point 1). This would lead to you overdrawing anyway, at which point it's just much more efficient to get some sifters instead of pure draw-more. The big thing to note here is that we are traditionally thinking of cards like Warehouse, Cellar, and Dungeon, but something like Cartographer, Journeyman, or Catacombs can fill this role as well. It's just worth noting that for these, they don't really help you find that first village. Even more important, cards that let you mess with the random draw of 5 cards to start your hand work here, too - Scheme, Guide, and even top-deckers like Watchtower and Royal Seal.

Of course, the real thing that you need in an engine is a good payload and enough time to effectively deploy it. Consistency helps you here, because it speeds you up through the late game. Thinning also speeds you up through the early game. In general, though, this won't be enough. Gainers which are cost-limited (e.g. Workshop) are going to help you through the midgame, because they let you grab more components to get your draw going or stabilize it somewhat (a la point 1).

But in general, +buy is going to be superior, and quite necessary. Why? You will need to be able to string together multiple big things at once - usually victory cards, really, but frequently some more expensive economic bonuses and/or engine components as well. Let's look a little more in depth at this. Getting one Province per turn is going to be too slow might be your first thought. And that's generally true. But even when you can get to this point pretty quickly, you are still going to have a problem: if you are only buying one card a turn, your engine is going to be consistently degrading as you get that Province - and as we saw, this is actually even true if you can add a Smithy and a Village with the Province. So unless your deck will be inconsistent as you continue down that green path. And really, who is going to be duchy-dancing better, your engine, or the opponent's money deck? If you are doing this in a protracted fashion, it's the money deck; it just degrades a lot less. So, instead, you want to plan to have the game end before this breakdown happens. This leads to a guiding principle of engine play which I'll cover more in a later article: Don't green until you have a way to end the game in sight. There are a number of exceptions to this, of course, with the biggest one being (unless you need the points to not immediately lose).

The concept of time is the most important thing here. It's a shifting scale with multiple axes. In general, in a non-mirror, the Engine will be playing the role of Chaser, whilst its opponent will be the Pace-Setter. But that will be in another article!

Thursday, 21 May 2015

Opening Probabilities: Hitting 3P

Similar to the last post, here I am looking at your chances of hitting 3+P on turns 3 or 4. I am borrowing heavily from this post.

Potion/Nothing: 60.61%
Potion/Silver: 65.40%
Potion/Poor House: 65.66%
Potion/Lighthouse (or Fishing Village):  65.78%
Potion/Sage: 66.92%
Potion/Oasis (I'm only about 90% I calculated this right): 71.97%
Potion/Moat (or Shanty Town, any draw 2): 77.02%
Potion/Great Hall (Trashing Hovel): 83.33%

The key insight here is that not drawing your potion is actually MORE important than the nightmare of 2+p. So cycling goes a long ways - which is good, because that also synergizes with what you want to do with the potion-costing cards anyway, whether at 2p or 3p. This changes, of course, once you start needing 4p, though the potentially bigger issue there is that you don't really want Golem before you have actions to go with it.

Wednesday, 20 May 2015

Dominion Opening Theory: Money Matters

This post pulls heavily from sources here and here with some math of my own as well (but it's all the same, pretty elementary combinatorics).

Here, I am just going to look at chances of hitting 5 and 6 coins from various openings. Knowing these can really help to inform how you want to open the game quite a bit, as you plan out your turns 3 and 4. Hitting high coin amounts are definitely not the only factor you should consider - but it is an important one.

The following probabilities assume no funny business or interference from opponents.

(Silver/Terminal Silver is Equivalent)
Chance of hitting 6+: 42.4%
Chance of hitting 5+: 91.2%
Chance of hitting two 5+: 14.9%

Terminal Silver/Terminal Silver
Chance of hitting 6+: 17.7%
Chance of hitting 5+: 72.2%
Chance of hitting two 5+: 12.6%
Terminal Collision: 30.3%

Chance of hitting 6+: 67.7%
Chance of hitting two 6+:   5.1%
Chance of hitting 5+: 87.4%
Chance of hitting two 5+: 29.0%
Baron drawn and whiffs:  17.7%

Chance of hitting 6+: 24.7%
Chance of hitting 5+: 78.3%
Chance of hitting two 5+: 13.6%
Salvager drawn and whiffs:  17.7%

Chance of hitting 6+:   8.8%
Chance of hitting 5+: 94.9%
Chance of hitting two 5+: 34.1%
Chance of 5+5+3:   6.3%

Horse Traders/Silver
Chance of hitting 6+: 38.7%
Chance of hitting 5+: 94.9%
Chance of hitting two 5+: 27.2%

(Equivalent to Shanty Town or any other draw 2)
Chance of hitting 6+: 24.6%
Chance of hitting 5+: 94.9%
Chance of hitting two 5+:   0.0%

Chance of hitting 6+: 32.2%
Chance of hitting 5+: 91.8%
Chance of hitting two 5+:   8.2%

(Or any other Peddler variant)
Chance of hitting 6+: 36.0%
Chance of hitting 5+: 91.8%
Chance of hitting two 5+:   8.2%

(Any Non-economic card)
Chance of hitting 6+:   8.8%
Chance of hitting 5+: 49.4%
Chance of hitting two 5+:   0.0%

(Or with any cantrip that does actual nothing - Pearl Diver is better)
Chance of hitting 6+: 15.2%
Chance of hitting 5+: 60.6%
Chance of hitting two 5+:   0.0%

(Or any other Peddler variant)
Chance of hitting 6+:   7.6%
Chance of hitting 5+: 54.5%
Chance of hitting two 5+:   0.0%

Silver/Great Hall (trashing Hovel)
Chance of hitting 6+: 27.8%
Chance of hitting 5+:  100%
Chance of hitting two 5+:   0.0%

Engines' Economic Explosiveness

A point that I think a lot of players get to – and I know I certainly did – is to look at the world of Dominion in a Big Money Paradigm. What I’m talking about, in my case at least, is a concept I call “money density”. Basically, a rough measure of quality for a BM deck is something like “take your average coin production per card, multiply that by your average hand-size, and that gives you your average economic capacity per turn.”

This is perhaps a bit simplistic, but it really does give you a rough assessment of the capabilities of a big money deck. I will note that even when you are playing big money, there are lots of imprecisions to modelling things this way: card efficacy doesn’t, in general, scale linearly, unused money has no value, turn-to-turn variations are quite important, ancillary benefits of cards beyond coin-value are real, etc. Even within this Big Money Paradigm, there are lots of nuanced decisions to make.

When you are stuck in this mindset, it can be hard to think of why you would add “do-nothing” cards – a la Village – to your deck. Sure, the cantrip makes it not hurt so much, but it doesn’t actually help your money density, and you are potentially missing out on getting a better card – silver, at least, will do more for you. And in a Big Money deck, the extra action usually doesn’t do a lot for you – if you get to the point you’re needing one very often, you probably should have just bought fewer terminal actions. Or not play Big Money at all.

This is where the Engine Paradigm (or draw-your-deck if you want slightly less pithy but arguably more descriptive names) comes in. If you can get to the point where you are drawing every card in your deck every turn, the way you look at your economic output on a turn changes completely. Now, you don’t need to look at average coin per card; you can actually just add up the sum total of all economic production in your whole deck.

To illustrate this, let’s look at an example of adding a Gold (which is not what you want to do terribly often in engines, but is always available and gets the point across). Adding the gold in a Big Money Paradigm will increase your money density by the difference between $3 and your old average value, divided by the number of cards in your deck. So if you had a starting deck plus five silvers, your old density was 17/15 = 1.133, and you increase by (3-1.133)/16 = 0.117. Multiply that by 5 cards per hand, and you get .583 coin per turn on average. This is pretty good for a Big Money deck. It’s worth noting here that each successive gold will do less though – the next one only adds .103 per card, or .515 per hand. This is because the difference between where you were and the $3 of the Gold continues to shrink, and the impact of each card is less as your deck gets bigger.

If you’re drawing your deck, on the other hand, you simply get to add the full $3 to your ever-turn spending power. The next gold just adds $3 again, too. This is a lot more, and it gets to be a progressively bigger gap over time. So you can see that even treasures can get leveraged more if you are drawing your deck.

Now, there are reasons why it’s not quite so rosy for engines as the above might make it sound. As it relates to the discussion above, the most notable thing is that if you are adding payload cards which don’t help you to draw (like Gold), you will have to get more pieces that do so you can continue to draw your deck every turn (terminal payload also requires getting more villages). This diminishes the ability to really add as much economy as you might otherwise be able to. On the other hand, being able to add to your per-turn payload so quickly self-synergizes, exploding in on itself in a chain reaction – getting that extra $3 now means I have more that I’m able to spend next turn to keep increasing my economic capabilities without falling behind on draw. This ramping effect virtually always more than compensates for the need to get extra pieces to keep drawing, at least if you have the capability to get extra buys – otherwise making $30 on a turn doesn’t do much for me. On top of that, there are ancillary benefits – if there are cards which are much better in combination or in multiples, you get to reliably do that, and you get to hit them with your attacks every turn. Engines also give you better control of ending the game just when you want.

The real downside of engines, which might make you not want to go for one, is that they can be slow to set up. This, along with increasing the reliability of the engine, is why trashing and/or sifting is such a boon to the engine. It’s all about getting to that point where you are drawing your deck as quickly as possible, because once you are there, even if it takes a long time, even if you are forced in to buying victory points in less efficient chunks, the raw power of an engine’s chaining buildup, if one is possible on the board, is usually enough to overcome the potential speed deficit.

Theory: Engine Draw Basics

I have written elsewhere about the benefits of Engine Economies (and I will probably port that over here at some point). But in order for all that to work, you actually need to draw your deck consistently. Given this, a good question to ask is, how consistent is it?

Fortunately, we have mathematics. The first thing to note are some very basic statistics. How many cards can your deck draw? Seriously, this is as easy as totaling up the number of +cards on all your cards, and adding five for your initial hand. Obviously you need to subtract out cards you discard (e.g. Embassy counts for 2, not 5), and cards like Journeyman which don't technically draw cards should still count for their obvious number (in this case, 3). Obviously variable-drawers like Scrying Pool will make things trickier, but for now I'm going to focus on your more basic engines. You can compare your total draw to the number of cards in your deck, and this will tell you whether it's even possible to draw your deck. Consistency, however, is another question, and it requires math that's a bit more advanced.

The specific math we're going to be leaning on here is a mainstay of card games, the Hypergeometric Distribution. There are a number of Hypergeometric Calculators available on line, such as this one. I do most of my work in Excel, which has this stuff built in, of course. The biggest reasons for this are that it's easy to generalize doing a lot of similar calculations across a spreadsheet, and I almost always have at least one Excel tab open anyways.

I'm not going to walk through all the mechanics here, but I will outline you through how to calculate the basics for the first scenario I'm looking at. That scenario is 12 "dead" cards (anything that doesn't draw, from Curse to Goons), which is going to be reasonably common, as you start with 10 and often have to add about 2 payload cards to get your economy going, along with 4 Villages and 4 Smithies. Ok, this means 20 cards in our deck total, and we start with 5. The Villages each draw a card, and the Smithies each draw 3, so 5 + 4*1 + 4*3 = 21, or actually one more card than we have in our deck. Great. So we should be able to draw our deck pretty reliably, right? Let's see.

The first thing we need to get going on our turn is a village. So we use our hypergeometric calculator to come up with the chance of getting zero of those out of 5 cards. You should come up with 28.17%. Then, we need a Smithy. Of course, we can play any number of Villages before that Smithy. So the way to model this is, we need to see the chance of drawing none of 4 Smithies in a hand of 5 cards, from a total of 16 cards, where the 16 is the size of our deck minus the Villages, since we can just cycle through those. We should come up with 18.13% here. Okay, so now we've hit at least one Village and a Smithy. To continue, we need another Village. The key thing here is that it doesn't actually matter whether we found one before the Smithy or after, the overall chances of getting at least one remain the same - we just need to check for having none in our hand, which is now 7 cards, from our deck, which now has 3 Villages left out of 18 total cards. We get a 20.22% chance of missing now. Same thing for hitting the next Smithy - 3 left out of a deck of effectively 15 cards, and a 7-card hand. That's a 12.31% chance to whiff.

Continue that pattern down the line until the deck is drawn. Remember that what we've been calculating are the chances to miss. To get from this to the chance to draw our deck, we first need to turn them into chances to succeed by subtracting them from 1 (=100%). This gets us the chance of e.g. drawing AT LEAST one Village. Then, because we need ALL of them to succeed, we need to multiply those chances together to get the chance we draw our deck. When we do that, for our example, we get... a whopping 20.08% chance to draw the deck on any given turn, starting from a fresh shuffle. It's worth noting that if we only hit 3 Smithies, we will have drawn all but 1 payload card - the chance of doing this with an action live is not much better, though, at only around 30%.

As we move to bigger decks and adding more cards, it's important to note that, as we get to the point we're over-drawing our decks, we don't necessarily need to hit EVERY village and smithy - at a certain point, the deck is drawn, and the superfluous drawing components do nothing (except, perhaps, give us enough actions to complete all our payload).

I'll wrap up this post by noting some general trends. With 12 dead cards, you don't reach a 50% chance of drawing your deck until you are at 6 Villages and 5 Smithies. Adding in even a single extra dead card starts hurting your chances pretty significantly. If we're limited to a single pile of Villages and Smithies to draw with, we can't do better than 77.64% to draw our deck with 12 dead cards, which we reach at 10 Village and 8 Smithies. After a point, adding extra superfluous Villages is the best way to get your deck drawn. Non-drawing Villages are way worse for our consistency, even if we compensate by making our drawing cards better - Festival + Hunting Grounds is quite a bit less consistent than Village + Smithy on the same number of each pair, generally leading to deck drawing itself between one-third and two-thirds as often as the traditional Village-Smithy roles. It's also worth noting that the "more villages after a point" advice from the Village-Smithy framework does NOT translate to the Festival-Hunting Grounds one - you want a balance here.

As for the strategic implications of what all this means, I'm going to leave that for a different post. For now, let's just say to not be too surprised or upset when you get those dud hands - they're most likely more common than you think.

Saturday, 9 May 2015

Instructional Game #6: Empty the Treasure Maps

Game Log

...with Shelters.

My opponent opens Minstrel/Silver, gets a pair of Maps on turns 3 and 4, and collides them pretty quickly. I go for Silver/Silver into a Count and start trashing down. After turn 9, our decks look as follows:

The battle lines are drawn: he's attempting to use his quick map activations to power through Provinces and lock the game up. I'm trying to build more of an engine and... wait and see what to do. I have some options: just get some treasures and be able to single Province more consistently; use Stonemason to grab tons of components, probably to Graverob lots of things over a couple turns; use Bishop to score tons of points. I feel that probably any of these would actually work, but as the game state progressed in this particular game, I like the options progressively more as you got through that list. The reason for this is that the later ones give me increasingly more time before the game ends, and extra time should help me with my superior deck, as what I really need is to survive long enough for that quality to shine through. The key point here is that I expect my opponent's deck to break down if I give it long enough to do so.

At the time of the game, though, I was a bit wishy-washy, and my natural instincts of taking the points lead when it seems to be enough caught on for a moment, leading to my buying a Province on turn 14. This is a pretty bad play, as it just speeds up his win condition (empty the Provinces), while not really advancing my own thing at all. Soon after this, I strike on the optimal plan: Bishop golds for points, Stonemason overpay for more components, Stonemason Golds/Catacombs for components as well, loading up on more Maps to refuel. And it works like a thing of beauty. The other nice thing about this deck (besides being a strong, resilient way to gain a zillion points) is that it gives me a lot of control over when the game ends. I can always buy another Province to lock the game out, or I can also smash lots of things and make a pile ending happen, but either way, it will be on my terms.

As we finally round the bend on turn 18, I see an opening, using the on-trash ability of Catacombs, and pile out on Stonemason, Wandering Minstrel, and... Treasure Map!

Thursday, 7 May 2015

FPS: KISS (Fancy-Play Syndrome: Keep It Simple, Stupid)

Game Log

I go for a big engine here - Lookout to trash down, Armory gains things, Throne Room for Shenanigans. It's a strong deck.

My opponent goes for Scavenger+HP.

On his 9th turn (he's first player here), he gets the final Hunting Party, his 6th. At this point, our decks look like this:

At this point, we're off to the races. By the middle of turn 13, our decks look like this:
Unfortunately for me, I have a dud here, and I can only Mine up a Silver to Platinum and buy a Duchy. But the thing is, this just ends the game. Yup.

Let's break this down a little more. On that turn 9, I have a little more power than him, I can gain a bit more stuff, thanks to Throne Room and Armory. Island can mitigate the deleterious deck-bloat aspect I run into to some extent. In exchange for this, my opponent's deck is nigh-unbreakable. The key thing to note is, as long as he can get to $11 without drawing ALL of his Hunting Parties, he can Scavenger right then to seed his next hand with a Hunting Party. This gives him tremendous reliability. His deck will not break - if mine does, I'm dead. And though I am a pretty good favorite to not dud out on any given turn, I'm not terribly likely to make it through ALL of them, especially given that I need to make some magic happen with my Islands, and I'm somewhat limited on actions.

Now, part of me wants to cry "first player advantage", and indeed, though I lost by 20, I did have to turn for Province a bit early, and more importantly, that 1st-turn lets him get the 6-4 HP split here, which is pretty big. The problem with taking this mindset, though, is that even though I may be favored were I first player here, I would always be in a *better* position if I just play the simpler strategy. It doesn't blow my bigger engine entirely out of the water, and first-player might be a bigger deal, but it does have some advantage everywhere.

Moment: Door-Slam

Game Log

...with Shelters.

We both go for Scrying Pool engines. My opponent gets an early Mountebank, I get more trashing via extra Foragers. The game remains fairly close, until I break through on turn 11. I'm thinner, I have more actions, I have more money - my thinning has, after some eventuality, paid off. Going into my turn 12, our decks are:

...with 3 curses, 10 coppers, 5 shelters, and 2 Embargoes in the trash.

On my turn, I win 4 prizes (thanks, thin deck, sorry Bag of Gold), and... well, look for my play. Answer is in white text below, highlight this paragraph to see it. I bought the last Scrying Pool, the last five Market Squares, and the last three curses. Princess really did some work here.

Wednesday, 6 May 2015

Practical Advice: Playing From Behind

Game Log

...with Shelters. Witch into Rebuild seems pretty clear here.

My opponent gets a 5/2, opens Witch/Estate.

I have 3/4 and get Silver/Feast. Tuns 3 and 4, my Feast becomes a Witch, and I get another feast and a Silver. Going into turn 6, my Feast and Witch are colliding in my hand, and the decks look like this:

At this point, I feel very far behind. I hit $4, and I make what I feel is a pretty bold choice: (with hovel in hand) I buy a Silk Road. What?! Well, tactically, I'm not sure the time is right. But the idea, the strategic thought, is something I am very much on board with.

The concept here is that, though I am very far behind in any case, I'm especially down in the long game. So I make the decision to try to turn the game as short as possible, such that there is more randomness and luck (or less time for the overall quality of his deck to shine through). This should be really losing, but on the other hand, I think everything is really losing, this gives me better random chances, and most importantly, it gives my opponent the chance to make mistakes.

The first of these comes on turn 13, when he buys a Duchy. This is a classic trap in 2 ways: "I'm playing Rebuild, better get Duchies pretty soon" (which is often not true in non-mirrors, Colony games, and various odd scenarios), and "my opponent is playing to end the game quickly, better get points soon in case that happens" (you're often better served by not helping them end things). At that point in the game, he had 3 Rebuild, 1 Estate, 1 Province, and 1 Duchy. If he just focuses on getting those cards up to colony, he's going to have a near-insurmountable lead. He can then finish off by grabbing 1 more green card LATE. As is, the Duchy both slows him down, and it helps me get the piles empty to end the game sooner. This should have been a Rebuild. A similar situation occurs on turn 15, except at that point, he's also locking in one of his own Estates by emptying the LAST Duchy.

He follows this up by grabbing Silvers, in a game where he has very little chance of actually making $8 (though to be fair, actually buying Province would essentially seal the game). By his turn 19, through some luck as well as my mad greening and his missteps, he is actually down by one point, with $6 in hand. He makes a final mistake by buying the last Silk Road, which is only worth 1 point to him. I have one of my Rebuilds, Duchy->Province, and buy the final curse to win.

Let's dig a little as to why this Silk Road is a mistake. There is first of all the general principle of him wanting the game to go long, and this helping me close it out. But specifically here, if I have Rebuild, I can upgrade Duchy into Province or Province into Colony and just win; also, if I have Witch at all, I win immediately - and I am about even money to have at least one of these things happen for me (I also have some very small chance of being able to buy Province). Beyond that, I will probably buy an Estate. If I do that, my one point lead would let him win if: he Rebuilds a Duchy or Province (which requires him both drawing Rebuild and nabbing the correct hit off of its play) OR he has his only Witch AND (in either case) can buy Estate (or, of course, having enough money to buy Province - really unlikely considering he's just seen 3 Silvers). Note that he can't really buy an Estate that turn himself, since even if I were to whiff AGAIN the next turn, one more Estate from me would end the game. But even not buying that Estate, an extra one from me the following turn is worth 6 for me, really putting the squeeze on him (though he would indeed have some chance).

Alternatively, if he doesn't get the Silk Road (instead getting... I'll get to this in a second - for now, let's assume nothing, though that's obviously not strictly best), then what? Ok, well, I can win my next turn if I get Rebuild AND Witch. If I only get Rebuild, turning Estate into the last Silk Road and buying Curse would let me win by a point, but more likely I would upgrade an expensive green card, and then buy the best green card I could afford. If I get only Witch, I win if I can also hit $4. Failing this, I just buy the best green card I can, which gives him a turn to score some points (but he most likely NEEDS to do so right then). Alright, so what should he buy? Estate. It gives me no new wins, scores as many points as Silk Road, doesn't hurt his deck (as he'll never see it again), and there are some scenarios where I can't buy the last Curse, or he can GIVE me the last curse with Witch on his next turn, where it actually turns a loss into a win. Would it have changed the outcome of the game? As it turns out, almost certainly no (I would have been able to buy the last SR instead of curse on my turn 20, which gives him another turn, but he needs to Shanty Town into Witch into a good Rebuild, or ST into two good Rebuilds, which is very very unlikely). And in general, it's very unlikely to. But playing the slim percentages is something you have to do. More to the point, without the earlier too-soon-duchies, I probably would have simply had not enough time to get all the gains I need, he would have been able to get his Rebuilds going to the point where he has a few more points, and then I'd be locked out. These kinds of situations don't come up often, because I put myself into a position where I'm likely to lose, and quickly, which is something people don't like to do. But the volatility turns out to be my best chance, and as the player in the lead, you really need to be vigilant and know which way to turn, because if you aren't precise, you really can open up the door.

Instructional Game #5: Maximizing Draws

Game Log

So there's a lot of Trash-for-benefit to note here, between Stonemason, Salvager, and Forge, with both Border Village and Cultist to enable that. The Tactician + Forge combo means that you should be able to clean your deck up - and this is important. You still need to go for Cultist here, for two reasons: First, getting too far behind in the Ruins split is going to be problematic, as though you can eventually clean up, it's going to take a lot more time. Second, the deck does need draw, and Cultist is by far the most efficient way to get it here (well, one could argue Tactician, but that's not repeatable).

With that layout, we enter the game. I open Salvager/Silver. You might be tempted by Spice Merchant here, but I want more money early, to get my Cultist, have a chance at double Cultist by spiking 7, and have decent chances at hitting 6 for Border Village into Cultist. Further, the Copper trashing may be less important here than normal, given that Forge will hopefully clean that up anyway.

I want to loop back to Border Village here for a second. Normally, the card is something you actually wouldn't want in your Cultist decks, as it can be drawn dead, you aren't very likely to draw them in the right order, and especially important for cultist, it hurts the chaining aspect. Here, though, I am planning on cleaning up, and especially, there's lots of Trash for Benefit.

The game progresses smoothly - my opponent is clearly on the same basic plan as me. I don't get to my Cultists at very nice points in the shuffle, and it might be easy to think I am falling behind for that reason. But on the other hand, I am hitting my money slots pretty well, gaining better cards. This is easy to underestimate, particularly by feel in-game, but in reality, my draws are really just exceptional. After my opponent's seventh turn, our decks look as follows:

We can see that I've just been drawing better than my opponent here. It's somewhat slow for me to get my Cultists online, but he's hardly been better, and to compensate, I have trashed an extra Estate, and more importantly, I have the next turn. With that turn, I get three Cultists fired off, making $7. I am significantly ahead, but it's really important to play precisely in these cases, to maximize your chances, as the luck can turn at any point. And there are lots of options. The main ones here are Forge, Border Village + 5-cost, or Stonemason into two 5-costs. I go for Stonemason-Cultist-Tactician. There are 6 ruins left at this point, so I don't want to abandon that split and pressure entirely. I also don't want to go double Cultist though, because 6 Ruins isn't so many, and I want to start setting up for clearing out. Finally, extra Border Village just doesn't do enough for me here.

The Ruins split ends up at 5-5, and my draws are good for the next couple turns. More importantly, my opponent, who is still playing quite well, misses his Forge on his Tactician turn. Thus, I have used my superior draws to set myself up that, even when I whiff on turns 13 and 14, by my next Tactician turn, on 15, I still have an advantage. And given my thin deck, and all the trash-for-benefit, I am on the prowl, and find the winning cascade of gains that Stonemason so often engenders. This is one last point of precision - just gaining some points would probably put me in very good position, but given the explosiveness of the board, there is some chance that my opponent could make some play making mid-turn gains and pull out some incredible comeback. Slamming the door when possible is something you always need to be on the lookout for, and take when you can get.

Tuesday, 5 May 2015

MTG Standard Deck: RG Dinosaurs

This is the deck I have been brewing/playing for the past 10 days or so in the current Standard format. The idea was to come up with a deck which would have good game against both Esper Dragons and Red Aggro. Basically, I've combined the Deathmist Raptor/Den Protector Engine with a RG Dragons shell, and added Goblin Rabblemaster, giving it an aggressive bent, with a "Bees" package out of the sideboard for decks with lots of ground creatures. The following is a list with which I 4-0d a daily event on MTGO last Saturday:

24 Land:
8 Forest
1 Haven of the Spirit Dragon
5 Mountain
4 Wooded Foothills
4 Temple of Abandon
2 Rugged Highlands

2 Instant:
2 Lightning Strike

1 Planeswalker:
1 Chandra, Pyromaster

33 Creature:
1 Elvish Mystic
3 Avatar of the Resolute
4 Scaleguard Sentinels
4 Den Protector
4 Goblin Rabblemaster
1 Boon Satyr
3 Courser of Kruphix
4 Deathmist Raptor
2 Ashcloud Phoenix
4 Thunderbreak Regent
3 Stormbreath Dragon

2 Roast
2 Scouring Sands
1 Heir of the Wilds
1 Setessan Tactics
4 Hornet Nest
1 Boon Satyr
1 Collected Company
2 Destructive Revelry
1 Tormod's Crypt

 Since then I've made some updates:

24 Land:
8 Forest
1 Haven of the Spirit Dragon
4 Mountain
4 Wooded Foothills
4 Temple of Abandon
3 Rugged Highlands

3 Instant:
3 Draconic Roar

1 Planeswalker:
1 Chandra, Pyromaster

32 Creature:
1 Heir of the Wilds
3 Avatar of the Resolute
4 Scaleguard Sentinels
4 Den Protector
4 Goblin Rabblemaster
3 Courser of Kruphix
4 Deathmist Raptor
2 Ashcloud Phoenix
4 Thunderbreak Regent
3 Stormbreath Dragon

3 Roast
1 Scouring Sands
1 Setessan Tactics
4 Hornet Nest
2 Boon Satyr
1 Collected Company
2 Destructive Revelry
1 Harness by Force

I think I achieved my goal of having good matchups vs Red and Control, though I do think I have an unfavourable matchup vs the other big deck in the format, Abzan Aggro. The deck is still a work in progress, and I hope to go in some more depth soon.

Monday, 4 May 2015

A Tale of Traps

Game Log


First of all, I want to say I don't actually think this game was played particularly well, by any stretch, by either player. Indeed, the reason I'm posting this is that there were a number of errors being made which I see as fairly common even for players who are pretty strong. As such, I'm going to refrain from posting any images here which would show my opponent's name, as the point really isn't to shame him, but rather to try to point out these pitfalls so that you, the reader, will be able to avoid them. Obviously, you can figure out who it is if you really want to.

Trap 1: University
The University trap is very easy to fall into. There are lots of good and shiny 5-cost cards, and you want lots of them, so you go for it. The problem is, this is incredibly slow. You have to buy a Potion, buy a University, and only then can you start getting those 5s to pour in. A player who just went straightforwardly for buying those 5s the old-fashioned way is just going to be 5s ahead for several shuffles, and particularly if those 5s have an effect of improving your deck's ability to build itself (as is often true), perhaps just indefinitely. On top of this, as a village, University is a Necropolis - and that's card-negative, generally not where you want to be. Given all this, in order to make University worth it, you usually want some plan to make the game go late (often extra points) and/or ways to see those reshuffles quickly (i.e. deck-thinning). You do have some of that here (Tunnel and Island give more points, Spice Merchant thins a bit, Embassy and Margrave can help you draw). But the draw is pretty weak - only Margrave can combine with University to actually increase your hand-size, and then you are not doing it in a very potent way - the draw power is equivalent to Village-Moat. Yeah. So I really don't believe in University or the Engine here.

Trap 2: Opening Potion
This trap is a bit tough, and perhaps I shouldn't call it a trap, because it's very often correct. The thought is 'if I want cards that cost 2p or 3p, I should open potion'. And because you typically want those cards as soon as possible, this is indeed most of the time correct. But there are lots of exceptions. And I think this is likely one of those exceptions - if you want to go for the engine, I think you want to open Spice Merchant and defer those Universities for a while, as getting your deck thinned and spinning a bit is more important than loading up on those 5-costs super-fast (and indeed, you aren't so much slower anyway, as you are more likely to be able to just buy some 5s). A good example of delayed potion happened in a game this morning on Adam Horton's stream which can be found here.

Trap 3: Tunnel
People often like to rush for Tunnel+Enabler, thinking they'll gain lots of golds and get way ahead. This can sometimes be good, but generally it's quite mediocre, even with fairly decent enablers. More importantly, in doing this, you're playing a deck that is more like a slog than anything else - it takes an awful long time for you to get a decent number of golds out of this, and in the meantime, you have added a nothing card to your deck (and this is even assuming you do hit your collisions pretty well). In the long run, you do have a gold-heavy, fairly robust deck, and some extra points to boot. So it is generally like a slog, and not necessarily a great one. Of course, there are other ways to play the card. What doesn't make sense, though, is trying to get this to work in an engine. You're adding lots of non-draw cards to your deck, which makes it exceptionally difficult to draw your deck. Of course, the enablers usually sift you, so you may well still be able to have some ability to draw your important cards, but the point still remains that as you increase the number of cards you have in your deck, you decrease the chances of getting everything you need to come together. In this game, your draw isn't great, and especially given your few villages and mostly needing Embassy over Margrave to enable, you're eventually turning yourself into something near Province-per-turn mode. And keep in mind, you were pretty slow to get there. This really lowers your ability to reap the benefits of an engine.

Trap 4: One Copper Trasher
I have to give credit here for pointing this one out to Stef, the longtime top player in the game. Here's the deal: usually, you only want one copy of a copper trasher (Moneylender or especially Spice Merchant, as here). This is because you're going to run out of fuel for them fairly quickly, and there's diminishing returns on these cards, as you get to trash a lot fewer cards per trasher with each successive one. However, in games where there is some trash-for-benefit card, getting the second one gets much, much better, and is very often the thing you want to do. Here, I was the player who overlooked this: I slam lots of silvers and only one Spice Merchant. This is fine, but given my Butcher strategy, getting the second SM just seems a good bit better.

As for how the actual board goes? Well, in the game, my SM+2 Butchers was fine enought o overcome the wonky kind-of-engine from my opponent. In general, though, I am not sure which way to turn between Margrave-based BM, Embassy-based BM (picking up tunnels at the right moment), or 2SM+1-3Butcher BM.

Friday, 1 May 2015

Know Your Basics #1: Ironworks Rush

Game Log


...with Shelters.

Despite the Shelters and the Colonies, this game has to be an Ironworks/Silk Road rush. The problem is, there just isn't anything else to do. You can play for Stables, but this is just too slow. And you can play for a mix of that with Herald, but lowering the Herald pile actually speeds the Rush up even more than you in that case (as the Rush player is pretty happy with Heralds, but really really happy with the easily-empty-able pile). Adding Doctor to your Stables engine doesn't help too much on average (though I guess you can give it a whirl on 5/2 exactly - I don't *think* it's enough even there). It helps a Herald engine a good bit more, as those cards work synergystically, but again, the Herald engine just has NO time, and you have to look to Navigator as your payload or give in and get Platinum anyway.

In the actual game, my opponent goes for Doctor/Ironworks into... some kind of Herald thing where he prefers Golds to Stables for a while. I flounder around a bit trying to keep my options open and figure out what he's doing, oscillating a bit between playing to be able to go a bit long (probably close to just being wrong) with some Duchies and just ramming home the piles. In any case, I am able to close it out on turn 14, and it wasn't as close as the 32-10 final score would make it look.

In cases like this, it's important to note that the Rush player is going to have both the point lead and all the control over how the game is being steered, and that is not something you want to go up against - you need a LOT of raw power to overcome it.

Anyway, it's important to know a few of these basic concepts, like a rush, not so much because they will always be right (it took the rest of the board being fairly weak here, given the Shelters and Colonies), but because you need to have some plan that doesn't just roll over to them.

Instructional Game #4 Clean, Clear Subtleties

Game Log


The first thing that jumps out at me here is Ironworks/Highway. Of course, in retrospect, there isn't that much support for it. In order for that to be a key or even significant part of your strategy, you need to be drawing good chunks of your deck pretty reliably. The only draw here is Torturer (a terminal with no village) and Vagrant (which doesn't help get the components together). The other way you can get to drawing that much is by thinning, but the only thinning is Counterfeit. It's possible to try to get Counterfeit to work, but it's pretty slow - and your opponent probably WILL be contesting you on Highways. So at best, that's a friendly interaction that can come up.

My opponent - again, a strong player - opened Ironworks/Silver. I actually think this is just a mistake here. Counterfeit/Highway probably should be a pretty central part of your plan, because Counterfeit thins and gives buys, and Highway leverages that pretty nicely. Perhaps more important, if you let one player get too many Highways, they might actually be able to do some pretty degenerate things. In any case, the important thing to note is that 5s are key. And Ironworks here, without a Highway in play, pretty much just grabs Silver. Now Silver is probably a reasonable card on this board, but here's where we look at the percentages: Silver/Silver is about 91% to hit at least one 5, including about 15% to get two. Ironworks/Silver is about 73% to get at least one 5, including about 1% to get two. Furthermore, if you use IW to grab a Silver in order to hit your $5, then you're not up anything over what Silver/Silver would have done unless you hit that 1% (in which case you've got an extra Ironworks). So where your real advantage lies, after the second shuffle, is in that, if you miss with your Ironworks hand in a way that you hit exactly $3 after gaining Silver, you end up with an extra Silver after that shuffle. (There's also some weird cases where your Ironworks misses the shuffle and then collides well, but these are really really fringe, and require getting Highway before Ironworks, and I really don't think you can bank on that). I in no way believe that that extra Silver can compensate for the lowered chance at hitting 5s. This thought process is what was going through my mind (not the exact percentages, mind, just the generalities) when I deferred my Ironworks until later - I want it to gain 5s, it can't do that soon, so I'd rather start my decks rolling.

Okay, so the game proceeds such that he does actually get that Ironworks leading him to $3, also hitting $5 on the other turn, equal spot, so that after the 4th turn, he straight up has an extra Ironworks compared to me. But the next shuffle is unkind to him (at this point, our shuffles become highly uncoupled due to the differing number of cards in our decks). By the end of turn 7, our decks look like this:
I have an extra Counterfeit. He has an extra Silver, Copper, and Ironworks. It looks at first blush that I might be a little ahead. But looks can be misleading - this advantage is already quite large, and he's going to need some good draws (more realistically, for me to have bad draws) in order to come back.

Over the next four turns, we can see how easy it is for an advantage like this to snowball: My deck is slightly trimmer, more efficient, and this compounds in on itself to get even sleeker (the extra Counterfeit is very nice for this as well), while picking up significant payload in a non-fattening way: the Card-neutral Highway. Thus, by turn 11, we are looking at:
I want to point out that my opponent has, given his situation, played very well here over the past few turns! His deck has lots of high-quality treasures and is set up like a quite decent Big Money deck ready for a healthy greening phase. Of course, the sleekness of my deck *ought* to leave me ahead here, but... over the next few turns, I play rather badly: I get a third Counterfeit (which I cannot support), and load up on Vagrants over Silvers. This is based on me still thinking of getting nice Highway chains capped off by Ironworks, but this is really an unrealistic pipe dream. My opponent keeps playing cleanly and hangs in the game the whole time. I make just one more good play, buying an Estate for effective $4 on turn 15 with 4 Provinces left - I am at the top of a shuffle and know I will never meaningfully see the next one, and given that the score is at all close, the point is absolutely worth it. Fortunately for me, my big early lead combines with a touch of first player advantage to overcome my later attempts to throw the game away, and I win on the 17th turn of the game.

Card Studies: Governor #1

One of the things I would like to do on the blog is take more in-depth looks at certain cards. This is probably based more about what I'm learning myself (and I feel like it's fairly often that I will 'level up' on a card) than on what I feel like I have some kind of mastery over. Anyway, I'd like to do this by looking at some game logs I think are instructive, one-at-a-time and then hopefully with some compilation pages for those different key cards. Over time, we can hopefully build up a pretty good repository.

Anyway, I'm going to start with Governor, which is a card I didn't feel like I had a very good feel for only a short time ago, but which I feel I've made a huge leap forward with in order to get to... mediocre with it.

Game Log


Some notes on the opening here: Looking at it now, I kind of like double Silver. Priority number one is to get Governors ASAP. It's also somewhat important, though, to ease your burden in drawing through your deck. I actually don't think that's super important, but it's nice if you can get it done.

I actually opened Wishing Well/Silver, but I think that's not the greatest, since I want to be able to multi-Governor quickly. Buying multiple Governors in a shuffle is going to be facilitated by getting the second silver, and the Wishing well cycles you to playing those Governors faster, it's true, but not by THAT much. The other thing to note is that Governor trashing a 3 into a Governor can be a real way of upping your Governor count fast, but if that silver is such a huge part of your economic output, that becomes less of a possibility. I get a second Silver on turn 4, which I need to do at some point, but I think it's just better to do this sooner rather than later.

My opponent went for a Loan, which is the other thing to consider here, but I don't really like it. You have to get treasures at some point fairly soon, and you take a pretty significant hit to your chances to hit 5 - I don't think the bit of trashing is worth it. And specifically he pairs it with Wishing Well, which I like even less, as it will crimp is ability to Governor up reliably. Of course, in this case, it works out okay, as he gets a 3/5, which puts him 'in the game', but I don't think the reward for this justifies the 25-30% (not an exact number) of the time you are WAY behind.

As the game progresses, I get more Wishing Wells, and he gets quite a bit more in the way of actions.

He gets a huge turn 9, which lets him triple Governor and win the split 6-4. I gain a couple Golds and buy a Province (trashing Hovel) on my own 9th turn. I think the most critical turn of the game is turn 10: My opponent draws a lot of cards and then... does nothing but build a lot. He gets a Prince, two Embassies, a Storeroom, and a Throne Room. The problem with this is that it just doesn't work very well in the style of Governor. At the end of it all, he only has $8 in his deck (Storeroom notwithstanding), including just one Silver and one Gold. Of course, all this building would be great in a lot of situations, but with Governor around, he is simply not going to have the time with those cards in his deck for it to pay off.

On my turn 10, I only have to use one Governor for draw, and I'm still able to double Province and pick up an Expand (which has a little bit of extra value here by virtue of its $7 cost - can be defensively upgraded into Province).

My opponent's turn 11 he really goes off with his engine, but in the end, he picks up no points, and another Prince. And he's drawn me 4 cards in the process. This lets me choose my time and 'go for it', double Provincing while using Expand to mill another. This gets us to this point:
And while I don't technically have 50% of the VP here, it really is a hard lock - he needs the last Province and 7 Duchies, which will take him a couple turns at least - and in the meantime, I will get some more points, which means he'll need basically all the rest of the estates, which will simply take him too long.

Governor games end quickly - don't spend too long building.
Winning the split is big, but having an eye on what to do afterwards is also important.
Be cognizant of when you need to start greening - it's usually pretty quickly.