Sunday, 3 April 2016

SOI Math-y Limited Set Review

It's that time again. The prerelease of another Magic: The Gathering set... has come and gone (ok, I'm a little late in getting this out). The full spoiler was put out Friday before last, and it's time to get cranking in on the numbers to see what will and won't be true about the format from the point of view of pure Math Math Math Math Maths.

For this set, I had to do a little legwork to figure out how often each card will show up, because Double-Faced Cards (hereafter DFC) change the normal pack breakdown. I am not actually 100% sure how this shakes out, but following the best information I could find (hat tip to the kind people in this reddit thread), it seems like every pack will have either 1 Common OR Uncommon DFC (each common will be in 5/80 of packs and each uncommon in 3/80), and 1/8 packs will have a Rare OR Mythic DFC (of those, each mythic will be in 1/15 of packs, and each rare in 2/15). Those packs with 2 DFC will only have 8 'normal' commons, whereas the rest will have 9. And every pack, per normal, will have 3 'regular' uncommons and 1 rare or mythic (in a 7:1 ratio there). All of this is still ignoring foils, but I still don't know how often those pop up, and anyway I'm pretty sure they rarity-match fairly well, so in the end you only get a very slight drop in commons and a very, very slight raise in everything else.

Beyond this, for most of my analysis here, except where it's incredibly obvious to do otherwise (or where I specify), I only looked at the front half of DFC. The big shakeouts of this are going to be that there are a little fewer humans than what I suggest (lots of them transform into werewolves), and creatures will generally be very slightly bigger than I suggest. However, since I think you're going to expect ot see front faces most of the time, this is a reasonable simplification. If you really want to know something specific about how back-sides affect something, you can ping me; if you want lots of things, you are of course free to analyze that yourself :P

Having gotten all that boringness out of the way, let's begin!


Madness

Most of what I've seen discussed is assuming that Madness will be a huge influence on the limited format. People are talking about the ability to discard things at will being a big benefit on cards, just for the sake of having that cost of "discard a card". And the justification is, of course, that "it enables Madness". And indeed, if you get to flash in a 3/5 for 3 mana, that's a big game. However, in order for "discard a card" to be something you actively seek out, you would need to have lots of Madness in your deck. Is that a realistic thing?

Well, Madness appears on 18 cards, (along with a 19th, a rare, giving Madness to all of your vampires) - 4 rares, 6 uncommons, and 8 commons. Not worrying for a moment about playability, this comes to an average of 23.6 Madness cards per draft - that's just under 3 per drafter. Now, it is worth noting that these are compressed into the Grixis trio of colours, meaning that you're going to get these cards disproportionately often when you're in a combination of those colours. What does that amount to? Well, if you're just one of the colors, it doesn't help much - you expect to get maybe 3-4 Madness cards in a draft. If you're in two, it can go up to 7-8, but I think even in these cases, and you're prioritizing Madness, you're not going to get more than 8 very often (and indeed, I'd expect you usually to have fewer Madness cards than this, especially in a 'normal' deck).

We also need to look at the other side of the equation: Discard outlets. There are a bit more of these than actual Madness cards - 30.7 per draft - though that includes a number which are very limited in what they can discard, or how often they can. So in terms of actual enablers, we're looking at roughly the same number as we have of actual Madness cards.

The next thing we want to do is consider what those numbers mean for gameplay. On the one side, if you have an enabler, you usually are pretty happy with as many madness spells as possible. So we don't need so much of a calculation here, but how many madness spells can we expect to cast? If our deck has 6 madness spells (I think this will be a reasonably typical number), then we're fairly likely to have at least one to go with our enabler in our opening hand (66%), and by the time we get to the point we could madness it, it's quite likely. We start to get better than an even chance of getting a second Madness card once we're maybe four turns into the game. But you need the game to go very long (or have lots of draw) to get to a third - we're talking 10+ turns for any kind of reliability.

At this point, I think it's worth noting that, not only do you need to assemble your Madness combo, but you also need for it to be relevant. Madness costs tend to get you two things: a discount on mana, and/or instant speed. You probably aren't going to hold spells to play them at instant speed, at least once you've played everything out. And once you're far enough into the game, the mana discount isn't doing much either. So all told, I think you can expect to get one to two benefits from just being able to madness things.

Because of all this, I think that what you're really looking for are cards where you'd more or less be happy playing otherwise. For instance, a looting effect will get a card of value out of the discard anyway, so it's a really optimal case. And a card like Elusive Tormentor gives you a very good rate, so the cost of discarding a card isn't a bad deal there, either.

Delirium

Delirium is another one of the major mechanics of the set. We'll look at how important it is, and how easy it is to turn on.

In terms of sheer frequency, cards with Delirium are slightly more numerous than those with Madness - an average of 24.8 per draft. Of course, the size of the bonus Delirium gives you varies quite widely. I'm not going to try to get into how important it is just yet, because I think that's something you have to worry about on a card-to-card basis, draft by draft. However, I think it's fair to say that it will be highly infrequent that going very far out of your way in a draft to enable Delirium is worth it: there simply aren't that many cards which care about it, and from looking at them, on many it doesn't make that huge of a difference. Still, it's a significant benefit in many cases, and it's worth looking at seeing how easy it is to turn on.

First, let's look at the 'natural' case. Creatures are going to trade pretty naturally. And instants and sorceries naturally go into the graveyard. Obviously there are enough creatures in the set to have more or less as many as you want. How about instants and sorceries? At 53.8 and 47.9 per draft, respectively, the answer is a pretty definitive yes. The limiting factor therefore seems to then be how many of these cards you can stuff in your deck - you usually need to have a pretty decent number of creatures, which limits your room for these other cards.

In order to get Delirium ion, you'll need one of each, which means you're going to have chances maximized by having equal numbers in your deck. With 4 instants, and 4 sorceries, you'll have drawn enough to have at least one of each with at least 50% probability by about turn 5, but you won't get up to being very likely until about 10 turns later. The thing to note here, though is that you still need to be able to play both of these, plus that's assuming a creature for free, AND you still need another type in yard! This leads us to a couple of other things you can do to help you out. First, there are self-mill cards (looters can jump in here in a pinch). Milling 2-3 cards is usually going to be enough to get you a land, plus shore up percentages on one of the types you were potentially hoping to get otherwise (Creature, Sorcery, Instant). There are a number of mill outlets (more on that later). Second, artifacts. There are a handful of artifact creatures, as well as another graveyardable artifact or two in the set, and that can be an extra type also. (If you're lucky enough to get a planeswalker, having it be another type in your yard is... probably not a great consolation for it having died, but it's not nothing I guess).

However, all of that isn't enough to really get Delirium reliably early - at best, you're looking at having it pretty often in the late game, and if you get very lucky, you'll get it midgame sometimes. This is where the serious enablers jump in - and they're mostly enchantments, which are often self-sacrificing. The Vessel cycle is the key here, with the Blue and Green ones the best for Delirium purposes, getting you most of the way to your threshold by themselves. Overall, I count about 13.2 cards per draft that have enchantments go to the yard for Delirium, to go with 11.6 cards for lands and a bit under 9 for Artifacts (depending on how much you count artifact creatures). The UG vessels are absolutely the key cards here, but other than them, a good combination of other cards can get you there in the midgame. I want to stress that you need a mix, because at the end of the day, you need at least a few of several types in order to check four boxes. Counting on your one sorcery is going to be sketchy, no matter how many other enablers you have.


Other Graveyard Effects

So I talked a bit ago about mill effects. There are 16.6 per draft, or enough for everyone to get a couple - probably for everyone who wants them to get a few. Delirium is one obvious reason you would want them, but it's not the only one - there are a number of cards that either care about graveyards, or have some effect (usually an activated ability) while in the graveyard. 7.2 of the former plus 11.4 of the latter comes, overall per draft, to 18.6, or a bit over two per player. When you're milling these, it's pure value - which mostly means that you should be fairly wary of milling your opponents, and a bit eager to mill yourself - but it's not a huge bonus, just a nice value bump.

Investigate

As we make our way through the mechanics of the set, our next stop is Investigate. There's less of a numbers problem - the mechanic is a lot more about card advantage and format speed than anything else - but it's still something to be aware of. In particular, there are 32.2 cards per draft that investigate, which on average is going to work out to about 4 per drafter (though some aren't playable), which means roughly 1-2 clues per game, which is probably a very good amount. There are also 8.6 cards which care about clues per draft. These cards are disproportionately in Green and Blue, which means it's probably possible to draft some kind of "Clue deck", getting a couple build-arounds and a number of Investigators. I don't know that this will be particularly viable, because it's very durdly, but it should at least be sweet.


Tribal synergies

There are several tribes worth talking about here.

Vampires
21.7 vampires per draft, but only 4.9 cards that care about that creature type. I think what this means is that you aren't really going to get much of a "Vampire" deck almost ever, though BR is probably going to have a good number of these, and there's some mechanical overlap with Madness as well.

(Were)Wolves
Wolves and werewolves more or less always get lumped together in terms of what cares about them, so I am counting them together here. We get 25.3 per draft, and 6.2 cards that care about the type. It's also worth noting that the flipping of the werewolves all dealing with the same mechanic leads to some synergy there, as well. This means you can make a deck built on the synergies, but I think mostly it will be down to "big creature beatdown".

Spirits
Spirits are even less cohesive than Vampires, with 22.6 cards per draft and only 4.7 cards caring about the type. It is a little worth noting that a number of these cards make multiple spirits, so that's somewhat of a plus. I suspect this will play more like a stereotypical UW fliers deck most of the time, and not be terribly concerned with the creature type.

Zombies
Zombies are once again in the ballpark of many of these other tribes - 25.5 cards per draft (gain some token makers mean the total number of zombies will be higher), and 4.5 cards that care about the type. Actually, because so many of these cards make 2/2s exactly, and a number of them, I think you will want some way to take advantage of that - unfortunately, UB doesn't seem to have terribly many of those...

Humans
Humans definitely look to be the premier tribal archetype, clocking in with not only 57.0 per draft, but also 11.1 cards which care about the type. It's worth noting that while these are centered in GW, there are quite a number in other colors as well. This means you're less likely to get as big of a percentage of those 57 creatures as you are in other tribes, but it's also possible to play some of the 'lord' kind of card to good effect in other color combinations. 


There are a few other tribes that show up in decent numbers (Horrors, Angels, etc.), but none with enough rules baggage to worry about.


Skulk and Creature Size

The last mechanic to talk about is Skulk. I think this is one which is very easy to underrate. If you think about it, if you have a 3/3 with Skulk, it can't be blocked by higher-power creatures, but you also need to consider that lower-power creatures naturally have a hard time blocking it. This means you either need multiple small creatures to gang-block - at which point any effects you have become very powerful - or a 'good blocker' (high toughness low power creature). Either way, you can choose to not attack, effectively occupying those blockers for the turn while you look for more pressure to apply. The big benefit is that these cards are really hard to 'eat' - you need a creature with power higher than their toughness, but not more than their power, AND toughness higher than their power.

Feeding into that, several people have noted that there are more creatures in the set with power higher than toughness than vice versa. I want to stress that this is actually NOT true when you account for rarity - there are 50.3 creatures per draft with power> toughness, 62.5 with 'square stats', and 56.3 with toughness>power. Still, this is a higher power to toughness ratio than we've had in most sets recently.


As for the actual size of creatures, let's start with power:
At 1 power, we have 33.3 creatures per draft, or 19.8% of the format.
2 power:  56.7 creatures = 33.7%
3 power: 48.4 creatures = 28.7%
4 power: 11.8 creatures = 7.0%
5 power: 8.1 creatures = 4.8%
6+ power: 5.4 creatures = 3.2%

In terms of toughness:
1 toughness: 40.0 creatures, 23.8%
2 toughness: 44.0 creatures, 26.1%
3 toughness: 45.7 creatures, 27.1%
4 toughness: 16.7 creatures, 9.9%
5 toughness: 14.2 creatures, 8.4%
6+ toughness: 6.6 creatures, 3.9%

In both cases, we see a big drop-off from 3 to 4. In particular, this makes 2/4 and 3/4 pretty excellent defensive sizes, as they normally are - most opponents will only have a few creatures that can punch through in their whole deck. When we throw in Converted mana cost, we see that there are significant jumps in size once we hit 5 and 6 mana - 5 gives you some 3/5s, 4/5s, 5/4s, and the common 6/6 for 6 (along with the uncommon 7/7 at that cost) rules the roost.



Miscellany
Over 42 enchantments per draft, together with 19 plus artifacts might make it seem like Root Out, the set's Naturalize effect, would be main-deckable. And that might be fine, in a pinch, but you have to realize that a good chunk of these are unplayable, and perhaps more importantly, a big percentage have sacrifice effects - which mean that they aren't really going to be sitting around in play for you to take out. The big number of build-around enchantments mean that you should still like to have this in your sideboard, but I would try not to maindeck the card.

There is very little fixing in the format - 15.3 cards per draft. A lot of this comes from lands at higher rarities, where it's very hard to line them up with the color combination you want. Most of the rest is in some mediocre green cards. Don't play three colors, and don't try to splash without a very, very good reason.

The number of mana sinks is WAY down from OGW - 40.2 per draft to 19.8 per draft. That, together with fewer 7 drops et al, is going to be a big reason to cut down to 17 lands from the 18 you were often running before. Now, if you have enough discard outlets, that could still be a reason to run 18, so I don't expect 17 to be as ubiquitous as it is in some formats, but I do expect it to be the norm.




Cards
This is not meant to be an exhaustive list, but rather just a smattering of cards I find interesting, especially that I think are being largely misevaluated.

Mad Prophet
I think this card is being significantly overrated. In most sets, I would guess I wouldn't want to play it at all (though probably it' would be fringe playable, depending on format speed). Between Madness and Delirium, this set has enough going on that I think I'll usually play it - and indeed, it's the kind of Madness enabler I'm looking for. But it's not going to be great, the 'it draws a card every turn' feeling I've been getting from many people.

Angelic Purge (And Sinister Concoction)
I'm not big fans of these cards either. Certainly I expect to play one, if I get it, in most decks, but I certainly wouldn't call them premium removal - they are far, far worse than Oblivion Strike, I think.Having to sac a permanent is too big a cost, and while Concoction is probably better than Purge, I still think discarding is a net negative, and by a non-trivial amount.

Skin Invasion
I get that most people are reasonably high on the card, but I think it's even better. A low-average case scenario is that you stick this on an opponent's creature you then trade for, and get a 1-mana 3/4. 3/4 are quite good stats in the format, and that's a very, very efficient price. But we also got to force an attack, so likely a favorable trade. Also, there are going to be a lot of cases where you can actually eat a creature out of it - not a particularly big one very often, but when you do get a 2-for-1 with the efficient creature attached, it's going to be close to the best card in the set.

Thraben Gargoyle
This card seems good to me. It trades with a decent amount of stuff for just 1 mana, and then later in the game, it's a 6 mana 4 power flier. Neither of those cards is particularly good, but the combination of them is enough to make this above-average.

Declaration in Stone
Much like Angelic Purge, I don't think this card is all that great. The comparison that comes to mind is Reality Shift, from Fate Reforged - and that card wasn't particularly playable. Now, I do think that this card is better - a bear is enough better than a clue to overcome the sorcery vs instant thing by a significant amount, I think - but that's only enough to make this playable, not great.

Grotesque Mutation
Keep in mind on this one that firing it off on an unblocked creature is basically just Alms of the Vein, which I think is quite bad. Of course this card is a good bit better than that overall, but you really need the +3/+1 to do work in winning a fight for that to be the case, and this being 2 mana and only +1 toughness keeps it from being great in my eyes. Playable, sure, but one of the worse tricks, not one of the better. Worth noting that the green pseudo-fight cards probably make this card in that color combo than elsewhere.

Indulgent Aristocrat
I don't think this card is very good at all. You need probably 2 other vampires in play, plus some fodder, for it to really be worth it? This sounds like too much set-up for probably not all that hot of a pay-off. There aren't that many vampires, and I don't think boards will stall that much, either.

Dual Shot
I'm going to guess this is probably main-deckable. There are lots and lots of 1 toughness creatures to take out. Of course, most of those aren't all that great, but this is only 1 mana. Plus, let's not forget you can use it as a pseudo-trick to trade a 3 power for a 4 toughness creature. Between all that, I think it will work out most of the time - though it probably won't be great all that often.

Malevolent Whispers
This card seems very good to me. Let's ignore that it can be Ray of Command for a second. Just as a sorcery, it compares reasonably well to the last Threaten effect we saw, Press Into Service. +2/+0 is worse than Support 2, to be sure (though not strictly worse, since it's easier to top-deck this for a win). But given the main use of these kinds of cards - namely, to kill - I think being 1 less mana probably makes up for that? It's comparable, anyway, and I thought that card was quite powerful already (in the right deck of course). Adding the possibility of Ray of Command is a BIG game.

Confront the Unknown
I actually like this trick pretty darn well. Early game +1/+1 is often enough to win combat, and then getting another card makes this a cheap 2-for-1. Later on, you're more likely to have multiple clues. Worst case 3 mana to cycle isn't that bad anyway, but I really like the trick - it's excellent if you can ever get the pump to be a card for you.

Runaway Carriage
Card seems perfectly playable to me. Not good, mind you, but enough that I could see it being your 23rd card reasonably often. In aggressive decks/situations, it's a pseudo-Lava Axe for 4 mana. Lava Axe isn't very good very often, but 4 mana is ok, and though they can soak up damage by blocking... you're generally not too upset about that - it's not down cards then. And defensively... well, it can trade for almost any ground creature. Sure, you don't really want it to be your only blocker, but even the bad case of stopping their big things from attacking and then being forced to trade for a smaller thing isn't too terrible. Obviously you can construct scenarios where it's pretty bad, but I think most of the time, it's perfectly fine, though not great, out of the 4-drop slot. Plus it's 2 types for Delirium, small bonus that is.


Monday, 28 March 2016

Making Luck, A Dominion Podcast

 My good friend Adam Horton and I have started doing a weekly(...ish) Dominion Podcast entitled "Making Luck". We're covering a variety of Dominion topics, mostly strategic, of course. Every week, we'll end the show with a kingdom to discuss and analyze, and then the next week we'll go over conclusions we've drawn from playing some games in the meantime at the beginning of the show. You can find the 'casts on Adam's YouTube page (I might add them to mine at some point, if I can get find myself enough time to do so), or wherever you like to get your podcasts. If there's some way you consume podcasts that it ISN'T available, please let us know.

We also really look forward to interaction and comments from our listeners. We're working out exactly where best to do that (maybe someday we'll have a website?), but for now, you can comment on the YouTube pages, or on the posts on this blog (in future, each episode will be getting its own blog post), or you can email me through the "Contact" link at the bottom of the blog.

Anyway, here are the episodes so far:


Episode 1: I Touch You and Instantly the Purring (delaying or skipping Potion)


Episode 2: I'm Disappointed (Forager)


Episode 2.5: Hermit/Market Square Com-BO (Adam only)


Episode 3: Curses Are Better Than Silvers (Draw-to-X Engine)

Thursday, 24 March 2016

Swindler

Swindler is a card which I've long rated very highly. It is cheap, and in the best case, incredibly devastating. However, recently it has lost a lot of its luster in my eyes. Let's break it down.

Starting Off
Swindler is terminal. This should give you some amount of hesitancy in opening Swindler/Swindler. On the other hand, the attack can be very powerful, so it's not crazy to think that it might be worth risking the collision. There are 2 main general factors here: how much does the collision hurt you, and how good is the attack?

Checking the opening percentages, we can see that compared to Swindler/Silver, by opening double Swindler you're losing 19% chance to hit 5 at least once, and a couple percent to go 5/5. You're also nearly 25% less likely to hit $6 (all of these figures are for turns 3/4 and assume no funny business from opponent giving you cards or stealing them from your deck, or spy attacking you, etc. - though it's important to note that without some kind of spy effect, their Swindler attack doesn't change these numbers for turns 3 and 4). You have a 37.9% chance to attack them twice, and a 98.5% chance to attack them at least once, up from 0% and 83.3% respectively. This means that by opening double Swindler, you get slightly more than .2 fewer 5-costs and slightly less than .25 fewer 6-costs (if you want those), and in return, you get .53 more Swindler plays.

To figure out whether or not that's worth it, you need to gauge how important hitting 5 (or 6) is, and how much the attack is worth. Let's go after the attack first: 7/12 (58%) of the time, you're hitting a Copper, which you will always be turning into curse. Copper into Curse is very good in the early game, because coppers are a huge part of the economy. 1/4 of the time, you're hitting Estate. This is really bad - worse than silver since it skips their estate for them. Indeed, you're always cycling early game, which is not good for you, though the appeal of the good cases is definitely enough to overcome that. Still, a quarter of the time it's actively bad. The last 1/6 of games, we are hitting their buys. How good this is varies a LOT from board to board, as when there's something really bad (used to be true more than it is now, but note that it's effectively always true for 5-costs by going into Duchy), this is very good. But sometimes you're e.g. turning Swindler into Silver, which is a downgrade, but a minor one.


Money Paragraph
So though I've gone for double Swindler in a huge percentage of games I've played where that was an option, I now think that this is usually incorrect, that Swindler/Silver is often better. The cases for this are when there's a key 5 or 6 you want to get early. The cases where doubling down on terminals is better include those times where there's something bad at every price point, and of course when the 4s are not much worse than the 5s. I also want to note here that Swindler/Swindler is a decent amount better (in a relative sense) 'on the draw' (i.e. as 2nd player), since you are more likely to hit a key card (on turn 4, your opponent has more total bought cards in their deck). Since hitting these cards is the best thing you can  usually do, that is a noteworthy if not huge boost.


Later On
Swindler is a fine card later in the game, but it tends to not be special. Hitting estates is still bad. Hitting Copper turns from being very good (denying a good fraction of economy) to being very mediocre, as one copper into a curse doesn't matter so much at the mid-stage, and the fact that you skip the copper for them starts being a non-negligible fraction of that penalty. The simple way to look at it is, there are just fewer shuffles left for the junk to be junk, so one shuffle of skipping the junk is a bigger fraction of the total times that your opponent has to draw it for the remainder of the game.

Hitting important cards can still be quite good, but very often the opponent's deck has a lot of redundancy, so that messing one thing up is not too terribly difficult to correct with future buys. This is particularly true of a well-established engine, where they can just re-buy whatever component you're denying, and given that they're drawing lots of cards almost every turn, they get to do so quite quickly. If you play many Swindlers in a turn, it can still be very good, since it's much harder to deal with something like 4 extra terminals all-of-a-sudden, but if you are really having the chance to play 4 of a terminal payload card in a turn, there's often going to be an alternative that's better.


Strategically
Swindler is a card which really wants you to be keeping track of knowing your opponent's deck. Knowing what you're going to hit can be very nice at times (though unless you have a Spy effect, you usually only have some probability cloud of a guess). More importantly, though,you want to know what card is going to be worst for their deck. Do they have too many terminals? Not enough payload? Are they lacking +buy? Something I don't see often enough from other players, but which I feel like I do often, is giving my opponent a card and then buying the exact same card. Sure, sometimes there's a Thief on the board, and you just give them that every time because it's terrible, but especially as with more expansions we've had fewer 'bad' cards, it's more often the case that you want to give them a marginal card, and you want to make sure it's the most marginal one for their specific deck.

One place where a Swindler-heavy strategy can really work out is in an Aggro Pile deck. It's a disruptive card that slows the opponent down, and it can also take chunks out of piles. It's usually pretty hard to make this your game plan from the start, because you have little control over what you hit, but it's something to be aware of as the course of the game progresses. If piles get low enough, especially depending on your position in terms of luck and deck quality has unfolded, you might want to start angling to get that pile ending, applying pressure to either seal up a short-term advantage (most likely in points) or hoping to get lucky because you're in a very bad spot. If you get in this situation, you need to be very careful about how much you lower piles and what you do in terms of points. If you start spinning the points angle too early, then your opponent's better deck will have time to crush you. But if you continue to slam your opponent with Duchies as you are also depleting piles, this may well turn out poorly for you as well.....


Defenses
The most obvious defense you can take is to buy cards only on values where there's nothing really bad to Swindle into. You usually can't/shouldn't really make a go of this, as 5 always has Duchy, but 5-costs also tend to be really good and important to get. You should not take a big hit in card quality just to try to avoid something getting swindled, especially since it's far more likely for you to draw and use the card than for the card to get swindled. What you should do, though, is be willing to take some very marginal downgrades. The obvious kinds of examples here are something like Village over Walled Village when Thief is on the board and you aren't relying on the Walled bonus (which you almost never are). In general, 3s tend to be safer, as there aren't tons of very bad 3s, though 4s, 7s, and potion-costs are potentially actually the safest, in those cases where they're the only card at that price point available (though you do have to worry about running the pile out). Super marginal cantrips are things you can think about avoiding altogether. Pearl Diver is really the poster boy here - the chance to get turned into Estate is sometimes quite bad. On the other hand, having these means other things are less likely to get hit, so you need to figure out whether you're more in need of protecting your few key cards ("Good Stuff" decks often fall here) or staying clean and not getting yourself junked up (engines hate having an extra estate).

More importantly as defenses come other cursing attacks. It's certainly possible to get both these AND Swindler, but when the curses run out, you risk turning them back into coppers, which is very bad - at this point in the game you usually would much prefer Silver to Swindler, and because this point will come, you need to seriously consider whether the early spurt of attacking effectiveness from a 0th shuffle Swindler is worth it.

There are a number of other minor defenses. Moat and Lighthouse work about as well as they ever do (though they can get turned into Estates I suppose - this usually isn't a deciding factor though). Silver flood decks shrug Swindler off fairly well - often they give you a silver back, and worst case you're getting like a Chancellor, which really isn't that bad when you're silver-flooding. Jack of All Trades and Hermit are particularly good, since getting Coppers turned into Curses actually makes them trashable, when otherwise they wouldn't be. Against those cards, you usually skip Swindler, though I will note that if you do Swindle a copper in those cases, you should almost certainly go ahead and give the Curse. Cards with on-trash benefits help defend a fair amount (usually), but it's quite a situational thing. Be on the lookout for them, though.



Overall:
Swindler is a strong card. When cheap options are good compared to expensive ones, and especially when there are bad things to stick people with, going for multiples can be good. This can lead to pile outs, but you need to have lots of game awareness.

More often, you will get one as an annoying attack that helps you ramp up early on. There's quite a bit of variance in the card, but that doesn't mean it's bad.


Wednesday, 10 February 2016

Gardens: An Introduction and Dominion Theory

Ah, Gardens. For a long time, you were my favorite card.
At some point, I determined to not lose to this card - which is probably how I got the itch for all the alternate VP that came later. It's true, though, that mastery over it is not a simple thing. I have learned an awful lot, and I think there's still a chunk out there that I have yet to bite off. But let's dive in.

Running in head-long
The most naive strategy in "going for Gardens" is to just buy as many as possible as soon as possible. People don't stay on that for very long, because it doesn't take much to figure out that your deck gets so bad, you actually have to build more to be able to afford all the Gardens. But it's not too uncommon to see players who do only a few turns of preparation before starting their charge into Gardens, buying every card possible as soon as possible (i.e. maximally jamming coppers into their decks), and trying to get lots of Gardens and lots of cards more or less ASAP. Let's take a look at a couple of examples to demonstrate this kind of approach.

Candlestick Maker
I have recently seen it floating around that Candlestick Maker is one of the better "Gardens enablers", with the implication that a headlong strategy here could make real strides. The idea was to end the game around turn 17, by which point it was supposed to be not uncommon to have 6 point Gardens. Memories can apparently be faulty: In order to get to 6 point Gardens, you need to add 50 cards to your starting deck. Turn 17 means 17 natural buys, which means you need 33 additional buys from CSMs. Work out the example yourself, and you'll see that even if you stack your deck, you can't get that many - indeed, you max out at 55 if my memory serves right. However, having a best-case-scenario mentality isn't very useful anyway, so what I'm going to do here is look more at an average case. Examples like the following can show the power of theory-crafting in planning out many kinds of strategies, broadly.

Turns 1-2 you are buying CSM. Turns 3-4 you are getting, most likely 3 more. How did I come up with 3? Well, the maximum possible is 4, but to get that, you need a CSM turn 3 with at least $4, another one turn 4 with at least $4. And you can float a token, potentially. However your deck is only capable of producing $9, and 2 cards miss the shuffle. If either of those is a CSM, you're done. If they're both coppers, you once again can't get there. If both CSMs fall in the same turn, you're once again hung out to dry. There are a lot of fail cases, and indeed it's not crazy unlucky to only get 2 more (though it is fairly unlucky). So 3 is a reasonable guess. Then turns 5,6,7 will be a single shuffle, in which you are pretty likely to get the remaining 5 CSMs. At this point, you are likely to have played CSM about 6 times. Assuming you're using all your spare buys for coppers, this means you're looking at somewhere around a 23 card deck. That means you're looking at a 4 turn shuffle next, and 1-2 CSMs, on average, missing that shuffle, with it being more likely for more to miss if you have been luckier earlier and have more cards now. 4 natural buys plus 9 CSM buys gets you 13 more cards, taking you after turn 11 to around a 36 card deck. This gives you a 7 turn shuffle, in which 0-1 CSMs will miss, most likely. Thus, after turn 18, you're looking at 53 cards.

Here is where we need to start looking at what exactly we're buying on these turns. Surely lots of the buys are heading to coppers. But we're also obviously going to want to buy actual things, too. And especially with the coin tokens to smooth us out, we don't want to waste any of the 'real' money we are producing. If we're playing this headlong rush, that means we will be buying Gardens. If we go back to the point at which we're anticipating the CSMs running out, at the end of a shuffle on turn 7, we see a 23 card deck with 3 Estates, 10 CSMs, and 10 Coppers. The money density of this deck is 20/23 or about 4.35 per hand. We can also anticipate having 1-2 tokens left when we enter this stage. Given that, it seems very likely that we'll be able to buy Gardens on each of these 4 turns, along with our 9 coppers. We're likely to pick up another couple tokens as well. This means that at the start of the shuffle on turn 12, our money density will be 29/36, which is a hair over 4 per turn. Thus, we can still Gardens-per-turn for the next 4. Following this, though, we're dropping off a bit, so by the time we go for Estates, we won't be able to double consistently. Overall, then, we're looking at 20-21 turns to be able to empty our 3 piles. If we look back, this is most likely going to leave us just shy of hitting 60 cards (which would take 1-2 additional turns, average case).

So what we end up with is: 20-21 turns to empty piles and end the game, 8 5-point Gardens, and 11 Estates, for a total of 51 points. This equals the number of points from a player who is able to empty all the Provinces without trashing their Estates or touching Duchies. Of course, the problem is that this simply isn't good enough. I'm not sure if this is even good enough to be straight-up Big Money. Probably yes, but only barely. Of course, they are almost always going to have some improvement on straight money, so you'd better have an improvement on straight CSM/Gardens if this is what you want to do.

Workshop
Workshop plays out in some ways very similarly to CSM. Gain a bunch of them, buy out of the Gardens, empty the Estates. It's the most classic rush strategy in the game. In this case, we are even Workshopping the Workshops (which is not great if you're contested, but as I often say, you want to consider non-mirrors when picking strategy, and only consider mirrors when implementing). Of course, Workshop is also terminal, which means you are going to be a little bit slower to empty them, but also means you want to stop 'shopping 'shops a bit before you actually empty them (buying the last 1 or 2 when you have exactly $3, or if it gets late enough, gaining them later on). The terminal-ness of the Workshop is a pretty big downside in comparison, but this is more than compensated for by the increased economic upside. When I gain Gardens, Workshop made $4. Even when I gain Workshop, it made $3, and $2 for Estate is still better than the $1 from a CSM. Of course, collisions happen, and without tokens, you probably aren't going to be able to use all of your $$ efficiently, providing some waste. This means you won't see the full benefit of the $4 economic potential.

Still, the games will start out playing more or less the same. Then, because you're worried about collision, you start gaining Gardens a turn or two faster. The key point is that throughout the period you are gaining Gardens, you're also buying other cards which actually help you end the game (mostly Estates), as opposed to just picking up coppers. 7 turns before you start greening, into about 9 turns of gaining Gardens+Estate, plus an extra turn to finish off stragglers means you are going to be finishing somewhere around turn 7. Of course, you're going to have gained way fewer cards in that time-span - we're looking at barely 4 point Gardens as opposed to almost 6 - but the increase in speed is a big deal. 43 points is enough to outlast 6 Provinces, which in all honesty is still not all that special, but it's quite a lot better.


Some Fundamental Concepts
There are two main approaches you can take with this kind of head-first charge for Gardens. One is to try to rush down and end the game. This is great if you can actually end things fast enough, but most often, that's just not going to be possible (the major exception, of course, is the card Ironworks). The other is to try to score incredibly large numbers of points. This also tends to not be great most of the time (Beggar is, once again, a very large exception).

Does that mean that the card isn't good? No, not at all. Does it mean it's doomed to be merely an alternative to Duchy as a means for getting a few extra points at the end of a game? Sometimes, but not always. It can still be the star of the show. How? Well, headlong rushes can still happen sometimes with multiple enablers. More to the point, if you build just long enough to be getting 1-2 Provinces and THEN dive for the Gardens, things can turn out well. But most often there are one of two strategies with which this card can get you there:

Aggro Pile
If you haven't checked it out, I might suggest my previous blog post to familiarize yourself with what this deck is all about. But how Gardens comes in is, if you add some kind of attack, particularly a junker, to the Headlong rush mix, then suddenly you are in business. You're emptying piles slower, but only slightly slower. More importantly, you are slowing your opponent down quite a lot, and while you certainly aren't shrugging the junk off yourself, it doesn't hurt you nearly as badly. This thus gives you enough time to finish up piling out without getting horribly outscored by an opponent going after the big cards.

Engine
I know, it might seem crazy. But in all honesty, engines tend to be the ways to maximize Gardens. Engines love Gardens. After I made that determination to not lose to Gardens, the way I most often did was when I went head-long, and my opponent opened Chapel... and then went for Gardens.

The thing to understand here is that engines are better suited to gain more cards over the long term than virtually any other deck. Once you get a running engine, it's very common to be gaining 3,4,5, even more cards every turn, as you add a little bit of payload and maintain your draw apparatus. Going straight for enablers doesn't permit that, and over a time-span of almost any length (look at the CSM as an example), you really aren't going to be doing better than 2 cards per turn that way. The fundamental problem is that as your deck gets bigger, your shuffles get longer, and you see your enabling cards less often. In contrast, as engines get bigger, they continue to see every enabling card nearly every turn - so even though they have fewer overall, they see them much more often.

Because of this, Engine decks routinely end up to be nearly the size of your more 'traditional' Gardens decks, and especially with the help of wasting a bunch of extra final-turn buys, they can often actually end up largely, sometimes by quite a substantial margin. Chapel-ing away ten cards is insignificant against an extra card or three per turn across the remainder of the game.




As an example of this, I would like to point to this game. Of course, this isn't a comparison to a head-long rush - my opponent didn't go for Gardens, and indeed this would have been a clobbering regardless. But the point is that, in 13 turns, I was able to gain 8 Gardens and have them all be worth 5 points, and you don't do that by rushing them, you do it by building an engine. The reason why this is so powerful in an engine is that it gives you a lot of flexibility, because it's a massive well of points which you can 'float'. If your opponent goes straight for Gardens, you clean up by just taking down all the Provinces. If, though, they go for Provinces, then you have a massive reserve of points waiting for you in the form of Gardens, which means you don't really need to worry about losing a Province split by any margin other than 8-0.


Of course, there's a lot more to the card than this, but I hope this introduction has been helpful.

Saturday, 6 February 2016

Dominion: The Aggro Pile Deck

Aggro Pile:

One of my favourite strategies is to go for speed. To end the game on my terms. To take hold and bring it to an end before the opponent can really deploy their long-term strategy. Speed, not power.

This means three-piling. You need a few things for this to go right: the ability to get piles out, the ability to control when they empty, score enough points (and know how many that is), in the process. Usually, it also means doing something to slow your opponent down, as even mediocre Big Money decks are capable of scoring a reasonable number of points fairly quickly.

But WW, isn't this just a slog?
No. In a slog, at least how I'm thinking about it, you’re trying to get a matrix of VP points that is insurmountable. Your win condition is to get so many VP the opponent can never come back. In, contrast, aggro-pile decks aim to get the piles out and end the game before your opponent’s (typically superior) deck can get going enough to catch up with you. Your deck is not about scoring all the points possible, but rather about having all the pile control you can get, and having just enough pop to score a little more than the opponent.

Typically, you’re going to want your opponent to help you out in emptying at least one of the piles. Most often this comes from junking attacks (where, if they skip it, you’re going to crush them anyway - this is weakened significantly by the very strongest thinning). However, there are also some piles that just naturally you want to empty pretty fast - Fishing Village is a classic example.

Indeed, you generally need a combination of 2 enablers and/or naturally-emptying piles, and you will have time to knock the last one out by yourself. So Ruins AND curses works well, or a card like Fishing Village with either kind of junk, or some decent to nice gainer with a fast-emptying pile or junk.

Most often, you’ll be piling out with Duchies as that third pile. And you tend to start just hacking away at them near when there are a few gains left to 2 empty piles, and simply ride them hard until they’re gone.

















It’s also possible to actually just blitz out piles, though this is quite a bit rarer. Ironworks is a key enabler for the rush, particularly with some Kingdom VP pile it can gain, since actually having 2 of your 3 piles be VP gives you obviously more points, which translates to a little more time. Stonemason is another big card here, as it can get rid of piles very fast. Same goes with Procession.







When playing against this kind of strategy, you typically want to not do something too fancy - that tends to be the number one way that Aggro Piles actually gets the time it needs. At the same time, you don’t want to touch Duchies at all, unless you’re either winning on the spot, completely locking them out (e.g. taking the penultimate Duchy with a substantial lead), or just contesting full bore in a mirror. 

Big Money tends to be a pretty bad matchup for this kind of deck, so you need to have a plan of defeating that as well. Indeed, Aggro Pile is a deck style which must always be very reactive to what your opponent is doing, and in most cases actually needs to have some kind of bailout plan as well - either you are an engine with an eye towards clamping down on the piles, or you have some kind of reasonable Big Money/Slog game-plan in case they go for points straightforwardly. It tends to be important to develop these fallback plans before comitting too hard to Aggro Pile.












Key Enablers in rough order from best to worst:
Junk: Ill-Gotten Gains (two piles by itself), Marauder, Young Witch, Cultist (which can sometimes be a second pile, but being this expensive is very risky), Mountebank, Sea Hag, Familiar, Soothsayer (though this is often more suited to Slogs)

Gainers: Stonemason, Procession, Ironworks, Border Village, Armory, Death Cart, Squire, Salvager, Workshop, etc. I want to point out City, as well, because if you can turn the corner on them at the right moment, it's often possible to slam down e.g. the Estate pile.

Empty-able Piles: Ruin, Curse, Stonemason, Fool's Gold, Squire, Hamlet, Duchess, Pawn, Pearl Diver (etc), often board-dependent, but things like Fishing Village, Ironmonger, etc that people just snap up at every chance because the cost is so low (and they’re so good)....







Example Games:
http://gokosalvager.com/static/logprettifier.html?http://dominion-game-logs.s3.amazonaws.com/game_logs/20151124/log.0.1448393618472.txt
Marauder, Cultist, Familiar - junk is flowing, you have multiple piles that are going to fall, so you can really start playing for the 3rd pile. I think Marauder over Cultist is very important here, since the spoils are good, drawing is less good (with a deck full of junk), and chaining is quite unlikely (and also has a chance to skip your Familiars. The important point is that treasures are good, which is very common in these kinds of games. My opponent shouldn't have bought the Duchy, but it's very unlikely they can get to 2 Colony and a Province in time, anyway.

http://gokosalvager.com/static/logprettifier.html?https://dominion-game-logs.s3.amazonaws.com/game_logs/20151127/log.0.1448643955753.txt
Here we have IGG. Trader provides some defense, but also a combo. Jester helps, and FV isn't too bad, either. Notably, Duchess provides a great 3rd pile as well.
  
http://gokosalvager.com/static/logprettifier.html?https://dominion-game-logs.s3.amazonaws.com/game_logs/20151127/log.0.1448655452593.txt
Young Witch can make both Curses and Banes empty, and with Familiar available, this is a good bit more likely. Hamlet is another third pile, and so some jockeying for positions should have happened. Pile awareness here allowed me to steal this one.

http://gokosalvager.com/static/logprettifier.html?https://dominion-game-logs.s3.amazonaws.com/game_logs/20151208/log.0.1449533322065.txt
Again, Curses and Ruins both running, Hunting Party is one of those stacks that tend to run, and we even have Stonemason for more shenanigans. 

http://gokosalvager.com/static/logprettifier.html?https://dominion-game-logs.s3.amazonaws.com/game_logs/20151230/log.0.1451490645872.txt
This one is all about piles that want to run (Highway, Market Square, Minion), plus the obscene power of Stonemason. In these kinds of games, you need to be very aware of what you need to do to run the game out, as well as what your opponents can do for the same.

http://gokosalvager.com/static/logprettifier.html?https://dominion-game-logs.s3.amazonaws.com/game_logs/20160107/log.0.1452205936848.txt 
Another example in the same vein as the previous.

http://gokosalvager.com/static/logprettifier.html?https://dominion-game-logs.s3.amazonaws.com/game_logs/20160107/log.0.1452191577234.txt
An example of the Procession style here. Very often you can process into process into mroe stuff into more stuff, emptying out LOTS of cards in a single turn. Note that you need to green pretty early to defend against your opponent doing do.

http://gokosalvager.com/static/logprettifier.html?http://dominion-game-logs.s3.amazonaws.com/game_logs/20151119/log.0.1447972595341.txt
You didn't expect me to leave you without an example of a classic Ironworks rush, did you? The raw speed and power is on display here, since even facing down Goons on a Colony board, and totally uncontested (which is correct unless you want to mirror and contest fully), I'm able to knock out all the piles (and even nab a duchy) for a blistering 54 points and end the game in a mere 16 turns.