Howdy, folks! Joe here with another installment of Daily Arena.

Lately I’ve been working an an engine to simulate collection building via buying/opening boosters under different scenarios (it has a lot of knobs to tweak to control how vault/wildcards/5th copies/etc. are handled).

I have a few things I want to use this to take a closer look at, but during the course of setting it up and testing things I have some initial results that I want to share pertaining to one specific area: Collection Strategy.

Once in a while I see posts show up in the Magic Arena subreddit asking questions like “What booster(s) should I buy?”, or “When should I spend my Wildcards?” I now have some simulation results that point toward what might be good strategies for both of those questions.

Say we have a list of four decks we’d like to build.

When you decide to buy a booster, here are a few ways you could decide which booster to buy:

Pick a Card – Look at the first card you don’t have in the first deck you want to collect, and buy a booster of the set that card is from.

– Look at the first card you don’t have in the first deck you want to collect, and buy a booster of the set that card is from. Optimize for Deck – Calculate* the best set for the first deck you want to collect, and buy a booster of a set that card is from.

– Calculate* the best set for the first deck you want to collect, and buy a booster of a set that card is from. Optimize for Collection – Calculate* the best set for the all of the decks you want to collect, and buy a booster of a set that card is from.

*I’ve tested many iterations of how to make the calculation for the “Optimize” strategies, and it appears that you get something close to an optimal strategy by looking at each card you want from a given set of cards, assigning a weight to each one based on rarity (needs to be a relative weight such that mythics are worth twice what rares are worth, and uncommons and commons are all zero), then adding up the totals for each set and picking a set with a maximum total. Example in the spoiler below.

Similarly, when you decide how to spend wildcards, you have a few options:

Redeem for Deck – Redeem your wildcards for cards in your first target deck as you collect them.

– Redeem your wildcards for cards in your first target deck as you collect them. Save for Deck – Save your wildcards until you have enough to “finish” your first target deck, then redeem them to finish the deck.

– Save your wildcards until you have enough to “finish” your first target deck, then redeem them to finish the deck. Save for Collection – Save your wildcards until you have enough to finish all four of your target decks, then redeem them to finish all of the decks.

I ran simulations for the current top four meta decks* from mtggoldfish.com for each combination of booster buying and wildcard redemption strategy, and came up with the matrix below for the average number of boosters you’d need to open to build all four decks given each combination of strategy:

*Decks in the spoiler below:



Pick a Card Optimize for Deck Optimize for Collection Redeem for Deck 344 337 335 Save for Deck 340 328 329 Save for Collection 324 329 316

The one seeming outlier here is the combination of Optimize for Deck and Save for Collection. After doing a lot of trials with different combinations of decks to collect, it seems that this number can vary wildly depending on things like how many cards overlap between decks, as well as the lists themselves. The takeaway here seems to be that if you are optimizing booster selection for one deck at a time, you should also redeem wildcards for one deck at a time.

Notice that the best strategy, always focusing on the entire collection when choosing boosters and when redeeming wildcards, gets you a nice 9% discount overall off this particular set of decks. Even the more realistic strategy of optimizing for one deck at a time along both booster collection and wildcard redemption axes gets you more than 5% savings, which may seems small, but in the long run I would consider worthwhile.

Another takeaway from this is that given the “middle ground” set of strategies, which seems realistic, at a nominal value of $1 per booster, these four decks cost (on average) about $424. The Jeskai Control deck on its own would cost almost $650 to collect in paper, and the entire collection of decks would be well north of $650 to buy on MTGO, as well…so for just a straight-up cost comparison between MTGA and other platforms for the game, you are saving money, especially if you can collect many of the boosters for free just by playing the game. (There is an argument to be made that you can recoup some of that value in other formats around Standard rotation time, though.) This should be taken with a grain of salt, though, since these numbers are only averages over 100,000 simulation runs.

Here’s a tool that allows you to input a list of cards in MTGA input format and will tell you what set you should buy a booster of for maximum value (only handles cards from XLN through GRN):



Anyway, today I just wanted to let you see what I’m up to and give some preliminary results. I’m going to use this tool to look into some things (like the “5th card problem”) and show how various versions of the “no-dupes” fix that WotC suggested might be coming will affect these numbers.

As always, if you have any comments, questions, or criticisms, please feel free to contact me here in the comments, on Reddit, on Twitter via @DailyArena, or on Facebook on the @DailyArenaMTG page.

Peace.

Joseph Eddy is a Father, Husband, Son, Brother, Software Developer, and Gamer. Magic is his favorite hobby, and he’s looking forward to seeing you all on Arena. He streams Magic Arena on a weekly basis (or more), but currently is unable to keep to a set schedule.