# Booster Pack Math

May 5, 2012 Leave a comment

As a super casual Magic player, meaning that I don’t play in tournaments and I am on a rather tight budget, I have developed some specific guidelines about card acquisition. In theory, since I mostly only play against family members all drawing upon the same card pool, I could just proxy up whatever cards I want; but I recognize and respect the collectible aspect of a collectible card game–the challenge of procuring the cards you really want for your deck, and not always being able to get what you need/want.

ASIDE: Of course, that’s also one of the frustrating things about this game: Watching pros who essentially have no worries about getting any card, and so they just spend all their time working on and talking about decks with the assumption that they’ll get whatever they need when they figure out what it is they need; or worse, playing against people with bigger budgets and essentially dying to cards you couldn’t possibly own. I know that if I had been playing Friday Night Magic, for example, during the era of Jace the Mind Sculptor, and had seen them regularly, I would have packed my deck with some cheap specific hate–sure I’d lose to all sorts of other decks with a handful of dead cards, but at least I could have the satisfaction of shutting down some guy’s $100 card every time I saw it.

My current guidelines, therefore, are that I won’t spend more than $4 on a card, since that is the retail price of the booster pack the card would have originally come in. If the card is worth more than $1, then I will allow myself to proxy extra copies of the card. Frankly, having a one-of in a deck without tutoring is just plain lame, especially if the card is central to the deck’s game-plan. That’s been my beef with the Intro Decks, Duel Decks, and even some of the Event Decks: “Here’s the Elspeth Duel Deck, all designed to work and synergize with this powerful planeswalker, but, of course, you’ll be lucky to see her every three or four games, since there’s only one copy in the deck.” So, I try to balance the collectible aspect with the deck-building aspect. Once a card is $1 or less, then I’ll buy the full playset.

One of the implications of this system, though, is that any card over $4 is essentially out of my reach, unless I pull it straight from a $4 booster pack. I’ve ranted here before about the vagaries and frustrations of opening booster packs. Yet, I continue to buy booster packs, like some schmuck who keeps playing the lottery for years and years even though he never wins anything and the odds are always massively against him, just because of the off-chance of opening one of those cool out-of-reach cards (and admittedly there are some really cool cards out of my price range). But, in my favor, I have won the booster pack lottery from time to time–I opened a Huntmaster of the Fells not too long ago!

All this has raised some questions about my buying policies. Given the randomness of boosters, would I really be better off just raising my limits for card purchases and just never buying a booster pack again? Probably, but part of the problem is also my inherent sense that no little piece of cardboard should be worth *that* much! But where is the threshold of *that* much? I’m willing to pay $4 now for a card; so what about $5? or $8? and then $8 is not too much less than $10… and so it goes. $1000 for a Black Lotus, or whatever, is just ridiculous, right? But when compared to that, $15 for a Darkslick Shores doesn’t seem so bad anymore. Before I can make any real decision, it seems like I need some data to help me reason through this conundrum. So, let’s run some numbers…

## Large Set Numbers

I’m going to use Scars of Mirrodin to draw some concrete conclusions. I am assuming that SOM is a fairly typical large set. This set had 15 Mythic Rares, 53 Rares, 60 Uncommons, and 101 Commons. A booster pack contains 1 Rare, 3 Uncommons, and 10 Commons, with a Mythic Rare replacing the Rare in 1 out of 8 packs, or 12.5% of the time. I’m going to run some numbers assuming equal distribution, which obviously does not reflect the reality of opening booster packs, but does provide some sense of the odds at any rate. I’m also going to run two different booster pack rates: $4 per booster, the retail price (actually 3.95, but let’s make the math a little easier, and there’s always tax or shipping costs anyway, right?), and $2.50, the price per booster if you bought a whole box of them at $89.99, which seems to be a common enough low price.

So, assuming equal distribution, to guarantee yourself the Mythic Rare you really want, you would have to buy 120 booster packs – it’s always in the last pack, not the first 🙂 This would also net you 105 Rares (almost two of each), 360 Uncommons (six of each), and 1200 Commons (almost 12 of each). Those booster packs would cost between $480 and $300, depending on how much the boosters cost you. Now, if you were only buying those packs for the Mythic Rares, that would make each one worth $20 to $32. If you wanted just ONE of all the Rares and Mythic Rares, then each one would be worth $4.41 to $7.05 in this math.

Now, let’s look at the prices of the card singles. I’m going to use Channel Fireball prices here, because I like them and they usually have the cards in stock. The Mythic Rares from this set range from $.49 (Quicksilver Gargantuan) to $17.99 (Mox Opal). Of the fifteen **Mythics**, six are $6.99 or more, and nine are currently $3.99 or less, with five being $.99 or less. The total price to buy all fifteen Mythics would be $86.35, making an average price of $5.76. The **Rares** in this set range from $.25 to $14.99, with only six of them costing $5.99 or more, and only ten of them being more than $1. Of particular note is the fact that the five most expensive Rares from the set are the dual lands. And those prices will surely drop this fall when the set rotates out of Standard. The total cost to buy one of each Rare is $86.95, with an average of $1.64 per Rare. Thus, if we are only concerned with buying Rares and Mythic Rares, we could own one of each for a grand total of $173.30. Except for a handful of outliers, the **Uncommons** can be had for $.10 a piece, with just a few at $.25 or more. A playset of four of each Uncommon, not that we really want ALL of them anyway, would thus run us $24. The breakdown for the **Commons** is quite similar, although I also know that most of the Commons could be had for $.02 to $.05 elsewhere, with a playset of all the Commons (again – not that we even want all of the limited fodder they put into sets these days) thus running us $40.40. The grand total, then, for 1 of all the Mythics and Rares, and 4 of the Commons and Uncommons, would be $237.70, which is still quite a bit less than the $300 price to “guarantee” us these cards.

## Small Set Numbers

The numbers for a small middle set, in this case Mirrodin Besieged, are a little different. Mirrodin Besieged had 10 Mythic Rares, 35 Rares, 40 Uncommons, and 60 Commons. This means you would need to buy 80 packs to guarantee a copy of each Mythic under our assumptions. This would also net you 70 Rares (exactly 2 of each), 240 Uncommons (exactly 6 of each Uncommon), and 800 Commons (over 13 copies of each Common). This would cost you between $200 and $320 for the packs. So, if you were only buying those packs for the Mythic Rares, that would make each one worth $20 to $32. If you wanted just ONE of all the Rares and Mythic Rares, then each one would be worth $4.44 to $7.11 in this math. Thus, the theoretical values are roughly equivalent whether it’s a small set or a large set.

When we look at the going rate for the cards, however, a different math emerges. The Mythic Rares from this set range from $.99 (Praetor’s Counsel) to $24.99 (Sword of Feast and Famine). Of the ten **Mythics**, six are $4.99 or more, and only four are currently less than $4. The total price to buy all ten Mythics would be $81.90, making an average price of $8.19. The **Rares** in this set range from $.25 to $7.99, with only three of them costing $4.99 or more, and only seven of them being more than $1. The total cost to buy one of each Rare is $40.65, with an average of $1.16 per Rare. Thus, if we are only concerned with buying Rares and Mythic Rares, we could own one of each for a grand total of $122.55 (but we’re only getting 45 cards, not 68). The distribution for the **Uncommons** looks similar to a large set, except that many can be had for $.05 a piece. Even at the same price, a playset of four of each Uncommon would thus run us about $4. The **Commons** are almost all $.05, which makes $3 for a playset of all. The grand total, then, for 1 of all the Mythics and Rares, and 4 of the Commons and Uncommons, would be $129.55, which is definitely less than the $200 price to “guarantee” us these cards.

## Conclusions

Remember that these numbers were based on an assumed equal distribution that doesn’t really mirror reality. Also, the nature of Magic finance means there is some regular fluctuation in card prices including settling prices as the set shakes out over its life in Standard and then rotation. Even most cards that will continue to be played in eternal formats, tend to settle down a bit, especially with the most recent sets selling so well. Some old cards are just always going to be ridiculously rare and thus expensive. I would imagine that some Rares from earlier sets that were not opened in the same kinds of numbers as sets today are much rarer in terms of availability than Mythics from the most recent sets.

It looks like any Mythic less than **$20** is technically a reasonable buy, at least compared with having to open packs to get it. If you don’t have to have the card right now for a tournament, then you can usually wait things out and get it for much less (I say usually because there’s always the possibility of a Jace, the Mind Sculptor in a set, although that is operating under the constraints of a small middle set which wasn’t drafted all that much). I feel for people who may have pre-ordered Quicksilver Gargantuan for $4.00. If you are paying more than **$5** for a Mythic, then it better be an above average card because you are paying an above average price for it. My numbers also suggest that paying up to **$7** for a Rare or Mythic card is reasonable, again compared with having to open packs to get it.

These numbers are hardly definitive, but I have definitely learned something about Magic finance from writing this, that’s for sure. The moral of the story seems to be to wait on just about everything, if you can, and don’t buy booster packs (sorry Wizards of the Coast)!