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Trinket Mage

While I usually have some snarky or trying-to-hard-to-be-clever leadoff for these card reviews, I will instead concede to my own inadequacies and leverage dialogue between two genuine, bona-fide master wordsmiths:

Yep, that’s Zac Hill (of StarCityGames, Huffington Post, Pro Tour, and Wizards of the Coast R&D fame, to name a few names) citing what may be the most obvious, but easily understated, fact of Magic effects. Tutors are the backbone of Eternal formats, like Legacy and Commander, and when they get the chance to rear their heads in Standard the power is only magnified by the intentional (And generally well-sculpted!) balance found there.

During the first trip to Mirrodin, Fifth Dawn brought us this card as a common:

Of course, that was also the time of Skullclamp and the Affinity archetype breaking the game. The version of Trinket Mage above is from Scars of Mirrodin when it returned as an uncommon, one of the few cards to move up from the lowest rarity in modern Magic.

One of the themes in Fifth Dawn, the originating set for Trinket Mage, was “cogs”:  one- or zero-mana artifacts that provide some modest utility or natural synergy with something else, particularly those that are sacrificed to do so (citing Aaron Forsythe citing Mark Rosewaker in the aforementioned Fifth Dawn themes article). While Fifth Dawn itself featured only a small handful of artifacts that cost one mana, the whole of the Mirrodin Block and Magic itself was littered with such cards.

And it’s only grown since.

But What Does it Do?

Trinket Mage is one of a handful of tutor effects at common, after excluding all cards that seek out basic lands. At a glance it seems superficially similar to Totem-Guide Hartebeest, only with a converted mana cost rider. I decided to add the “murder-beest” to the cube after significant positive feedback from other cubes. So why haven’t I tried out Mage here yet?

Let’s talk numbers.

According to the Gatherer, there are currently 79 total artifacts that have been printed at common (or published as common through a Master’s Edition release in Magic Online) and have a converted mana cost less than or equal to one (which includes the one in the upcoming set, New Phyrexia). While I could go through in detail, describing each one in relation to pauper cubes, I’ll instead leave that review exercise up to you. Take a look at the breakdown and compare it to the few that net out into my cube.

Which is why we’re looking at Trinket Mage and the idea of including it in the cube, rather than cogs we’d need with it.

There are currently eight targets for Trinket Mage in the cube. The question I wrestled with was how to understand what critical mass of cogs is required to make Trinket Mage really appealing. My first thought was to compare it directly to the Hartebeest. There are 18 aura targets, and I’ve generally found I always have at least one great target to fetch if I’ve picked up the Antelope. Is this the critical mass?

No. The comparison is flawed.

There’s a fundamental, contextual difference in what Trinket Mage and Totem-Guide Hartebeest  can tutor up. The latter grabs one of 11 different removal spells, or 9 different, assorted spells. The former can grab one of six pieces of equipment (including the ‘creature’ Flayer Husk), a colorless Rampant Growth, or a removal spell.

Hartebeest tutors for removal at least half time, with almost twice to total number of available removal spells than equipment for Trinket Mage. And if you’re in Hartebeest’s color (white) you’re almost certainly prioriting grabbing many of those aura removal spells anyway. (To wit, that’s where the lion’s share exists.)

Trinket Mage doesn’t have this type of underlying redundancy in it’s tutor targets. Equipment are colorless artifacts and are often snapped up earlier, even as first picks, because they are safe (and powerful) utility spells. You’ll almost always run any reasonable piece of equipment given the choice, and the pauper cube has nothing but excellent equipment that cost one mana. Pyrite Spellbomb, the removal spell, is slightly inefficient but provides a cycling-like flexibility.

And that’s the ultimate conundrum of dealing with Trinket Mage: if we see it early in a draft it’s a potentially rewarding pick we can reasonably supply picks for, but if we see it late it may be a relatively dead pick thanks to the natural distribution of cheap equipment among all drafters that aren’t you.

This leads me back to the earlier question regarding the threshold of cogs needed to make Trinket Mage work consistently. Does Trinket Mage even need to work consistently?

Mostly yes.

Totem-Guide Hartebeest has so many more targets to grab, with a more powerful selection of targets that aren’t drafted universally, that it fits just right. Trinket Mage would be a Gray Ogre far too often to feel good of including.

Bonus: Real Maths

Let’s look at this another way: assume we want Trinket Mage is in my cube (Reminder: it isn’t), and we want it more than any other potential first pick in a draft. What are the odds we will be able to pick it as the first pick from one of our packs?

First, see this outline for translating my notation below, and an online calcuator for these problems is found here. Together, you should be able to easily replicate solutions and adapt these questions to your cube. I’m glossing over setting and making the calculations manually (it’s not useful or illustrative here).

Now, using my cube, let’s see the odds of Trinket Mage being part of an eight player draft:

  • Total Population = 368 = N (The population here is the total number of cards in the cube)
  • Population Successes = 1 = k (There is one Trinket Mage in the cube population)
  • Sample from Population = 360 = n (8 sets of 3 sets of 15 random sample cards; the 360 total cards to be drafted by eight players)
  • Sample Successes = 1 = x (Exactly one Trinket Mage is in one of our packs; exactly one success in the draft of our sample of 360)

The result of h(x; N,n,k) is approximately 98% (0.9783). This means that we can count on Trinket Mage being present in all but 2% of drafts. Pretty good, and finally quantities the odds that any specific card isn’t in a draft.

While we can’t model how people draft (or, rather, I don’t have the necessary knowledge bases to appropriately model an eight player draft of 360 unique cards) we can look at some simple odds on seeing Trinket Mage in our opening packs:

  • N = 360 (The population here is the total number of cards in draft)
  • k = 1 (There is one Trinket Mage in the draft population)
  • n = 45 (3 sets of 15 random sample cards; the 45 cards we see as potential first picks)
  • x = 1 (Exactly one Trinket Mage is in one of our packs; exactly one success in seeing a target in our sample of 45)

The result of h(xN,n,k) is 12.5% exactly. That’s pretty bad, but at least the numbers work out reasonably thanks to divisibility.

Similarly, what are the odds that a tutor target for Trinket Mage is in our opening packs, assuming all eight targets are present in the draft packs?

  • N = 360 (The population here is the total number of cards in draft)
  • k = 8 (There are eight Trinket Mage targets in the draft population)
  • n = 45 (3 sets of 15 random sample cards; the 45 cards we see as potential first picks)
  • x > 0  (There is at at least one Trinket Mage target in one of our packs; more than zero successes in seeing a target in our sample of 45)

Here we calculate the odds that we see something other than zero targets via the result of h(x>0; N,n,k), which is approximately 66% (0.6602). This isn’t bad,  but you’re still out of being able to grab a tutor target as your first pick in any of your packs about a third of the time.

To be fair, the odds of having all eight targets in your opening 45 is a solid 0.000003% compared to the almost 40% (0.3971) of seeing exactly one of the eight (and since we’re picking without replacement, we can add the odds for seeing exactly two, three, and so on up to reach eight). Basically, you should see something worthwhile for Trinket Mage but potentially not actually see the Mage himself.

Our initial justification to dumping the Mage in was that it’s powerful to draft around but without an eligible pick becomes worth much less, and your odds to being able to first pick something eligible isn’t great either.

Bonus Bonus: Antelope of Doom

So how about Totem-Guide Hartebeest? Well, the odds of being in the draft and available as your first pick are the same as Trinket Mage would be. But recall that Hartebeest has 18 tutor targets, most of which is removal (which you’d be picking anyway).

  • N = 360 (The population here is the total number of cards in draft)
  • k = 18 (There are 18 Hartebeest targets in the draft population)
  • n = 45 (3 sets of 15 random sample cards; the 45 cards we see as potential first picks)
  • x >0 (There is at at least one Hartebeest target in one of our packs; more than zero successes in seeing a target in our sample of 45)

The result of h(x>0; N,n,k) is approximately 91% (0.9151). This the final evidence that should solidify why I decided to put the Hartebeest in: your odds are extremely good to see a tutor target (which dips to a still-better-than-for-Trinket Mage 77% (0.7749) if you consider just removal spells) as a first pick.

All this mathematical arm-waving said, there is a slight issue of context (the colors of the removal spells seen, though the majority are indeed white) as well as other unique cards seen through pick 2 through pick 8 (Note: Your 9th pick is where you start wheeling packs you’ve already seen and, therefore, the cards are no longer unique). Solving for the average cases would require defining what the average case is, and that challenge isn’t something I can tackle quickly. The pure numbers shared today help illustrate the differences experienced.

Bonus Bonus Bonus: Subtypes

Manually scouring my cube data to find all of the Aura spells was error laden and time consuming. I’ll be adding a ‘Subtype’ field to the cube spreadsheet to compensate for this frustrating oversight. My bad.

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  1. Richard Maurer
    May 6, 2011 at 10:44 AM

    Glad someone’s done the maths. I’ve been umm-ing and aahh-ing over trinket mage for a while now. Good blog.

    Incidentally, can’t wait to see your take on possible Pauper Cube additions from New Phyrexia. Some of them are absurd!

    • May 6, 2011 at 11:44 AM

      I have a review in the docket, with changes proposed to follow thereafter! Thanks!

  1. May 6, 2011 at 11:42 PM
  2. June 1, 2011 at 11:14 PM
  3. June 28, 2011 at 2:34 AM

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