Welcome to Four Daily Wins, your one stop reference for how to get the most bang for your buck in the Magic: The Gathering Arena Free to Play Experience.
The Anatomy of a Pack
The Bottom Line: Regular packs are guaranteed a Rare or Mythic. Mythic packs are guaranteed a Mythic. Golden Packs are guaranteed one Mythic and some combination of 5 Rares or Mythics. Don't buy packs unless they're from a Standard-legal set AND they're on discount in the Daily Deals.
The Facts
Play Booster contents vary slightly from set to set. For this guide, we'll be analyzing packs of Magic Foundations, the most recently released Standard set at time of writing.
One Foundations Play Booster in your inventory contains the following:
One slot with a 7/8 chance to be a Rare and a 1/8 chance to be a Mythic.
One slot with a 16.3% chance to be a Rare and a 2.6% chance to be a Mythic.
Another slot, also with a 16.3% chance to be a Rare and a 2.6% chance to be a Mythic.
Five other slots that will be Common or Uncommon.
With these percentages available, we can calculate the expected number of rares and mythics in a Play Booster to be 1.201 rares and .177 mythics. This will be helpful further down this entry.
A Mythic Booster is exactly the same, except the first slot is guaranteed to be Mythic.
A Golden Pack is earned by purchasing 10 Standard-legal packs from the Store. It contains the following:
One slot that is guaranteed to be a Mythic from a standard-legal set (not just Foundations).
Five slots each with a 7/8 chance to be a Rare and a 1/8 chance to be a Mythic.
How can we apply this information?
Breaking Things Down
It's difficult to calculate the exact value of cards and packs on Arena. The contents vary from set to set, any packs or cards that you acquire cannot be converted back into currency, and conversion rates between Arena's many different currencies are not consistent. This makes any attempted calculations imperfect at best.
We're not completely in the dark, though!
One Play Booster costs 200 Gems. One Mythic Booster (which is guaranteed to have a Mythic instead of a rare in the first slot) costs 260 gems.
This means we can say that the difference in the expected value of each type of booster is 60 gems. And since we know the number of expected rares and mythics in each pack, if we assume that commons and uncommons have no value (not technically true, but close enough), we can use a system of equations to figure out the exact value, in gems, of a Rare and of a Mythic:
1.201R + .177M = 200
.023R + 1.052M = 260
After solving for the variables, we can see that, based on Arena's own price calculation of store-bought packs, a rare is worth 136 gems and a Mythic is worth 204 gems (after rounding).
(Note that if this calculation doesn't sit right with you, we explore some other possible methods of assigning value to cards in the entry The True Value(s) of a Rare)
We can use that to determine the expected value of a Golden Pack:
204 + 5((7/8*136)+(1/8*204) = 926.5 Gems
It's not that simple, though, because Golden Packs don't cost you anything on their own, and instead are a bonus for purchasing Regular (or Mythic) packs.
This means that when you've bought 10 Play Boosters (of Standard-legal sets only), you're getting an expected value of 2,000 gems plus the 926.5 expected value of the Golden Pack, totaling 2,926.5 gems.
This also means that every Standard-legal pack you purchase could be considered to have a real expected value of 293 gems after rounding. However, the lack of ways to convert your cards back into currency means that you should NOT buy infinite packs. There are better things (such as event entry fees) to spend your currency on.
Check out the Online Store and Daily Deals entry for more ideas on how to apply this.