Tuesday, 19 April 2016

Sealed vs Draft vs Add-A-Pack Sealed

Let's cover some Magic fundamentals. It's well known that draft decks are, almost always, better than draft decks. I'm going to talk a bit about why here, and then apply those lessons to figure out how much adding packs to a sealed pool is going to improve the quality of the deck you can build - this is particularly important given the new "friendly" sealed leagues starting now on Magic Online. Let's jump in.

In Sealed Deck (for several years now), you get six packs of product. The big difference is that in draft, you're selecting cards that are best for your deck and passing around, while in Sealed, you are stuck with those cards you open. So in one sense, in a normal Booster Draft, you get to see 252 cards, whereas in Sealed, you are seeing only 84. Does this mean draft decks are 3 times better than sealed? No, of course not - even with selection, and seeing all those cards, you still end up with only 42 of them - half as much as in a Sealed Deck. Moreover, the other players are going to be taking a lot of the good ones, so it's not like you're getting all the best set of cards from a draft pool.

So how much better are draft decks than sealed? Well it's a little hard to quantify exactly, but the method I like to use to get in the ballpark starts with the color pie. In most formats, you want to stick to playing two colors of spells (this goes back to how you build mana bases - 3 colors are very hard to pull off without lots of fixing, and the math simply dictates your consistency is too low most of the time). What this means is that you're only playing about 40% of your colored spells in a typical Sealed format. In draft on the other hand, you get to draft to your two colors, by-and-large. You rarely actually get to the best case of all of your picks being in those colors (at the end of packs, you're stuck with whatever is left, and early in the draft, you may end up jumping around a bit before figuring out what your colors actually are). Still, this best-case-scenario gives us some rough guideline, which we can adjust later.

If we assume that everyone in the draft is on 2 colors, then that works out to 16 color-drafters, or about 3.2 drafters per color. This leads us to getting about 31.25% of the cards in each of our colors. We can easily round this down to 30% as a nice ballpark number (and because of the reasons listed above about jumping around colors, as well as splashing against us). You're also getting 12.5% of the colorless cards (generally artifacts and lands) as opposed to the 100% in Sealed (so this is one place Sealed has the edge).

Now you have to add in that you generally play 23 spells, and the rest of your deck is generally basic lands (obviously, some formats are exceptions to this). Maybe you add in a couple sideboard cards to the count - it doesn't make a massive difference. How much of the format is that? I'm going to use SOI numbers here, as it seems fairly typical - your mileage will vary a bit, but again, we are just ballparking here. Roughly 8.5% of the set are the colorless cards, which leaves about 18.3% for each individual color. So in a draft, you're getting about 30% of two of those colors, and 12.5% of the colorless.

23 out of 42 cards gets you to 55%. One of those cards is, on average, a land, and a couple more or probably in other colors, which means the real percentage of cards in your colors is going to be closer to 60%, or even a bit higher. 60% of 30% is 18%. So you're looking at getting about 18% of your colors' cards in a draft., and about 7% of the lands and artifacts.

Of course, this is a lot of assumptions - both the 60% and the 30% are going to be a little high, I think, but only by a couple percentage points - so maybe you're really looking at 17%. And beyond that, you get to take into account that you're making a deck - which means that archetype considerations might come in, and mana curve considerations definitely will. But again, this is a ballpark number. If we multiply this out by our 3.2 drafters, this means that we're peeling off the top 55-60% of cards in every color, and it's more or less only those cards which are making their way into draft decks.

In sealed, we still usually play 23 cards, but now we have to pull them from from 2 colors of the pool. So we have that 18.3% of cards in a color twice, plus 100% of the colorless buddies. This works out to around 37.9 cards, rather than 42 in a draft. If we exclude lands, we get to 35.5 cards instead of 40.8. 23 divided by 37.9 gets us to pulling from the top 65%, which means we have to dig about 10% lower than we did on the draft side.

Now, there are of course a lot more differences - on the plus side for draft, we noted that we can play more to archetypal synergies, and have a better curve. On the sealed side, colors are probably not split 100% exactly 5 ways, and this is especially going to be more true of bombs (higher rarities -> fewer cards -> variance is more of a factor, and you still get to choose).

So we can expect draft to be a higher margin better than sealed the more two-colorness matters, the less high-rarity cards matter (i.e. the flatter the power level between cards), and the less good colorless cards (artifacts and lands) are.

Okay, great, Sealed is very roughly 10% worse than draft, I have no idea what that means for win-rate, and there are a whole bunch of caveats. What did I mean when I was talking about the Friendly Sealed then?

Well, you get the option to add in a 7th and later an 8th pack. How much of a difference does that make? Well, it's 1/6th better, then an additional 1/7th better, which works out to 1/3 better by the end? But in more relate-able terms, using the methodology described above, which takes into account the realities of color limits,  7 pack sealed is slightly stronger than draft on average (much closer to draft than 6 pack sealed), and 8 pack sealed is a good bit stronger still (roughly as much better than Draft than Draft is to normal 6-pack sealed). This is without taking into lands, which mostly means extra fixing, which means splashing and/or 3 colors is more likely with more packs, which means... well something, but I assume that the extra pack sealeds are even stronger.

Long story short, adding packs makes a big difference in deck quality, and I would expect you to not be able to compete very well without doing so (when faced against people who are).

Friday, 15 April 2016

Chess Tactic of the Day #1

A few days ago, I was playing a 1-minute game with the black pieces. After white's 36th move in this Dutch Defense, the following position arose:

Black to play and win.






(In future I will try to come up with a better way of doing this).
If I had found 36...Nh3! I would have won on the spot. The point is that this cuts off the g1 square from white's king, and sets up the irresistible threat of 37...Qh6 followed by 38...Nxf2+. Despite having a couple moves, white is helpless to wriggle out of this, OR to create fast enough counterplay to distract black's pieces from the attack.

In the actual game, I had about 25 seconds left, and spent about 5 of them trying to make Qh6 work immediately. When that wasn't working out, I played the lemon 36...Ne4 and went on to lose.

Thursday, 14 April 2016

Making Luck Episode 5: Pregame Analysis

This week, Adam and I take a long look at how we approach analysing a board before the game starts - how to pick a strategy, what to look for, etc. We also look at a few 'bonus' example boards before diving into the next Kingdom of the Week!

Making Luck Episode 4: I Got You Saying the Previous Thing (City)

Last week, Adam and I took a bit of a goofy look at everyone's (okay, not everyone) improving Kingdom card: City.

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!


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 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.


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.

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.

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 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 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 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.

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.

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.