Saturday, 27 June 2015

MtG Math: Timberpack Wolf cycle

There are a lot of previews coming in fast and furious for Magic Origins, and I would like to devote  some time to the larger set (though I am not sure I will really get the chance to until the whole thing is spoiled). For now, though, I want to focus on a cycle of commons for limited which were spoiled in this week's Limited Information column, which can be found here:

I want to start with the blue entry in the cycle, Faerie Miscreant. A 1/1 flier for 1 just doesn't cut it as a playable card (at least in modern limited formats), so we need to look to the rest of the card to make up for this deficit. And each one past the first you cast - assuming you have one which survived - draws a card. Drawing a card is a good upside, but of course the first thing isn't getting you any value at all, so we need to spread that benefit out. Effectively, with 2, you've spent 2 cards and UU to get 2 1/1 fliers and 1 card back. So net, we've spent 1 card and gotten 2 1/1 fliers for UU. If we add in a 3rd, we've spent UUU and 3 cards for 3 1/1 fliers and 2 cards back. So we can see pretty quickly how this scales - we're always putting 1 card in, net. That's the cost in cards, 1 net card. In terms of tempo and board impact, we're spending N blue mana for N 1/1 fliers. That's a really bad deal at N = 1, a good deal at N=2 (I've seen a comparison to Raise the Alarm panning this; of course being an instant is nice there, but here we get fliers, and I think that's significantly more important), excellent at N=3 (Spectral Procession), and it starts to get bonkers with higher N.

(Technically, this is a little bit different from that, since netting 1 card in isn't the same as actually just casting one card - the two big differences are that you can do this on the installment plan, i.e. across multiple different turns, and that  drawing extra cards effectively makes your deck smaller - both of these are generally small plusses).

Okay, that's all well and good, but you actually need to draw that many copies of the card for it to be worth it. So here's where the math comes in: How many are we actually going to draw? I'm glad you asked. Here's a chart describing how many you would expect to have drawn in your top 15 cards - that's through turn 9 on the play, or turn 8 on the draw (or a bit sooner when you start talking about chaining lots, since they will be drawing for you). Given that you may have some card draw, this is, very roughly, how long you would expect an average limited game to last. Of course, that will depend on the speed of the format, and it actually looks to me like this is being a bit generous to this card, as you probably won't quite have this much time. Anyway, the chart:

The thing to realize is that it doesn't actually hurt you if you don't draw any. So it actually looks like 3 may well be the worst place to be. But realistically, I don't think you can even consider playing any of these things until you hit 4, and you don't really want to play them until you have 5. Of course, once you have more than 5, they actually start to be pretty good cards - and with this many, you have cantrips, which means you can start thinking about shaving a land.

Of course, this begs the question, how realistic is it for me to actually get that many? And you might think, nobody will want this card, my chances are actually pretty good. While the beginning of that premise isn't so bad, the problem once again comes with numbers. In any given draft (just forget about sealed, it's a pipe dream), there will be 24 packs opened. There are 101 commons in the set. If we ignore foils, there are 10 commons in every pack (if I understand how foils work right, then there will, in reality, be slightly less than this on average, but the difference will be small). So every pack has a 10/101 or 9.9% chance of having any particular common - in this case, our Faerie friend. It doesn't take much work to figure out that, on average, there are going to be a bit more than 2.3 opened per draft. Ok, but there's some variation, right? Yes. Assuming each pack has 10 distinct-but-otherwise-random commons, here's the likelihood of having every given number of a particular common opened in the draft:

So 2 is most likely, with 3 slightly more likely than 1. To have 5 or more? We're looking at just over 8%. And you actually have to get all of these cards, which is certainly not a given. So okay, it will be rare. But 8% is like 1 in 12 drafts, if you can get them all. Of course, you still don't want to spend high picks on these - you really want to wheel them. And you need them to be in-color. Realistically, going into a draft, you are just going to pass these around all the time, unless you happen to see several fairly early on. By the time you see 3 in pack 1, you actually have pretty reasonable chances to have enough get opened (even here, you're just under 50% to have at least 2 more opened, so you don't want to give anything significant up).

So to sum up for the card, look for lots of them, and you can take a chance. You want at least 5 to play any. But if you just treat it as totally unplayable, you're missing very little equity.

Okay, great. This card is part of a cycle, though, and this second chart will really help us figure out the value of the others.

Let's go to black next, with Undead Servant. Again, a 3/2 for 4 doesn't really cut it. So you need to have multiples of this thing. The subtle difference here is that you get a 2/2 for *each* card in the graveyard with this name, so the upside on getting lots is bigger. 1 is a 3/2, 2 is 2 3/2s and a 2/2 for 2 cards, 3 is 3 3/2s and 3 2/2s for 3 cards. The second is makes the card decent (and good enough to play), but it takes the third to make it really good. This is going to obey the same math as we saw above, and I think in this case, we can get away with a bit fewer, since we're closer to being a real card to start with, but it seems like we're still going to want at least 4 to play any, and that is still pretty unlikely. But if you notice a few early on and can wheel them all out of your first pack, you can set yourself up - it's something to watch out for.

The red one, Infectious Bloodlust, is perhaps both the most interesting and the most difficult to evaluate. Someone has remarked that Goblin War-paint wasn't particularly playable even in its archetype in MM2. That's true, but MM2 is a format with a very high power level, so I imagine the bar will be significantly lower in this set. And while this card does force you to attack, and give 1 less toughness, being able to search up another copy is pretty real upside. Ok, I don't think this card is going to be very good at all if you only get one copy. But you don't actually want to draw more copies really - you want them to be in your deck in order to get your value. Indeed, probably the optimal number of this card is 2-3, which is a very reasonable number to have opened. Of course, you do have to potentially worry about competition for them. And you probably don't want to grab your first in pack 3, or even late in pack 2. If you have an aggressive deck with lots of 2-drops, though, this seems quite playable at 2-3 copies.

The green one, Timberpack Wolf, is the reprint of the set. Now, I haven't played with the card before, so you all may have a better feel for it than me. But I think this card, like classic slivers, is going to be pretty prone to being overrated. Okay, it's a 2/2 for 2, so the downside is really not bad - Grizzly Bears are probably totally playable, if not exciting. But if you only have one in your deck, it's just not that exciting. If you have two, you're only 4.6% to have both on curve on the play, 5.8% on the draw. Once you get to three, you're up to 12.1% on the play, 14.9% on the draw, to have two of them by turn 3. And this is assuming that you haven't mulliganed and can cast them (and keep in mind that any hand with 2 of these in it is significantly more likely than normal to be short of lands). You're very unlikely to get more than 3, considering there probably won't be that many opened, and you're going to have to fight people for this more than the previous cards in the cycle, I would guess. Once you get to a board stall, multiple of these are better than Bears, certainly, but they're not tons better. The big thing is that they are more able to hold off a big creature. But they can't exactly attack through. And they're still quite a bit worse than Watchwolves, as killing one cascades into shrinking the rest - which is something you'll need to watch out for. All in all, the upside you're getting over bears is quite tiny until you start to get a lot - and I wouldn't anticipate that being super likely.

Finally, we have the white entry, Cleric of the Forward Order. I've actually been progressing through these from what I think is worst to best, in order (as well as being a WUBRG which is offset by one). And I do indeed think this is the best of the bunch. This is largely because it's the best card when it's all by its lonesome self. It is just a bear, but it gains a little life. 2 life really isn't nothing. And then it stacks, so the second gains 4, the third gains 6, etc. Okay, life-gain is often derided as not being worth very much, but it really does have a pretty significant impact in a lot of cases. Of course, board presence is quite a bit more important in most limited games. So why do I think this is better than the wolf? Well, mostly because this card is better when you aren't curving out with multiples perfectly - which is the vast majority of the time - and not that much worse when you are getting a lot. I mean, I would rather have 3 4/4s than 3 2/2s, for sure, but 12 life isn't nothing. Okay, if you are getting 3, you definitely take the wolves. If you are only having 2, you probably take the wolves, but it's slight. And with just 1, you clearly take the Cleric. The bigger point is, you are unlikely to have enough in your deck to get 2+ with good consistency, and very unlikely to get 3+. Cleric of the Forward Order is probably still only a mediocre card - a middle pick, though it could be better if the format is pretty aggressive, and you need 2 drops. The life gain is better there, too.

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