Hello and welcome to Daily Arena!

This week I ran a bunch of simulations of different scenarios, simulating attempts to collect different specific card pools in Arena under the current Wildcard/Vault system, under a tweaked version of the Wildcard/Vault system, and under a system using Generic Crafting Currency (i.e. “Dust”). I’m going to share my results here, along with my recommendation that WotC make similar changes in Arena to improve the player experience. I did this as a follow-up to my previous article (A Case for less RNG and Obfuscation) because it seemed like people were having trouble visualizing some of the issues I was pointing out, and why a Generic Crafting Currency is preferable to the WC/Vault system.

Okay, to get started, I’m going to include a chart, and then will explain what the chart shows.

So, what this chart shows is the number of boosters the simulation needed to open in order to acquire a playset of KLD cards under a few different crafting structures.

The horizontal axis is the number of boosters opened by the simulation, so as you move from left to right, more boosters were required to build the playset. The vertical axis is the number of simulation runs that required that number of boosters to collect the playset (I ran the simulation 11000 times for each chart, since I needed 10000+ to converge on consistent results, and running 20000 was too slow).

The Blue line represents the current WC/Vault system, characterized by:

Mythic Wildcards have a 3.(3)% random drop rate, with a pity timer ensuring you get at least one per 30 packs.

Rare Wildcards have a 6.(6)% random drop rate, with a pity timer ensuring you get at least one per 15 packs.

Common and Uncommon Wildcards both have a 20% random drop rate, with a pity timer ensuring you get at least one per 5 packs.

A booster pack contains 4 Commons, 3 Uncommons, and a Rare. The Rare has a 1-in-8 chance of being upgraded to a Mythic.

The Vault contains 1 Mythic Wildcard, 2 Rare Wildcards, and 3 Uncommon Wildcards.

Each booster you open adds 3.(3)% Vault Progress.

Each excess Mythic (copies beyond the first 4) you open adds 1.(1)% Vault Progress.

Each excess Rare (copies beyond the first 4) you open adds 0.(5)% Vault Progress.

Each excess Uncommon (copies beyond the first 4) you open adds 0.(3)% Vault Progress.

Each excess Common (copies beyond the first 4) you open adds 0.(1)% Vault Progress.

One quick note, since it came up in a comment: The actual drop rates for Wildcards generated by the simulation (which is a function of both random drop rate and pity timer) is roughly 5.2% for mythics, 10% for rares, and 30% each for commons and uncommons. This matches very closely to the nominal drop rate values I’ve seen pulled out via data mining. Once WotC publishes actual target drop rates I can re-run the simulations if my numbers are off.

The Black line represents a tweaked WC/Vault system, characterized by:

Wildcard drop rates are the same as in the current WC/Vault system.

Booster packs have the same content as the current WC/Vault system.

The Vault contains 3 Rare Wildcards, and 3 Uncommon Wildcards. One of the Rare Wildcards has a 1-in-2 chance to be upgraded to Mythic, and one of the Uncommon Wildcards has a 1-in-8 chance of being upgraded to Rare.

All Vault progress from the current WC/Vault system is multiplied by 1.87.

To arrive at these numbers, I started with the tweak to Vault contents to favor Rare WCs, which actually slows down overall progress, then bumped up the “Vault Progress Multiplier” until overall progression matched the current progression rate closely enough (a 1.9 multiplier was a bit too fast, but a 1.8 multiplier was way too slow). This might seem a little arbitrary (maybe it is), but I see a lot of people talking about the difficulty of collecting all of the cards in the game, so at least for some people it’s a real metric to look at (and try not to actually make worse).

The Green line represents a Generic Crafting Currency system, characterized by:

There are no Wildcards or Vault, all cards are instead crafted using a Generic Crafting Currency, I’m going to call ¢ here.

here. Any Common can be crafted for ¢50 .

. Any Uncommon can be crafted for ¢100 .

. Any Rare can be crafted for ¢800 .

. Any Mythic can be crafted for ¢3200 .

. Each booster pack contains cards with rarity distribution matching the current WC/Vault system, as well as ¢360 .

. Each excess Mythic (copies beyond the first 4) you open is converted to ¢110 .

. Each excess Rare (copies beyond the first 4) you open is converted to ¢30 .

. Each excess Uncommon (copies beyond the first 4) you open is converted to ¢20 .

. Each excess Common (copies beyond the first 4) you open is converted to ¢7.

The values used in the Generic Crafting Currency simulations were calculated to be as precise an “overall progression” match to the current WC/Vault system as I could get. The “low dust return” on excess cards mirrors the low Vault contribution in the current system. Part of what I’m trying to illustrate here is that even with numbers giving you an identical rate of resource collection the experience of collection changes drastically under a Generic Crafting Currency system.

NOTE : This simulation does not include “destroying” cards to create crafting currency, like you can do in HearthStone and Eternal. I want to make this very clear, that only excess copies of cards (beyond a playset) are being “dusted”. This is in line with WotC’s stated goals, and for the purposes of this article I am not making any commentary on whether I think that’s the best implementation.

Some Chart Analysis

So, let’s take a look at a few thing this chart shows us:

Under the three crafting systems I simulated, the average number of boosters a player needs to open to complete a playset of KLD, is the same (about 378).

The Generic Crafting System looks like a Normal Curve. Most of the players open around the average number of boosters to complete the playset, and it tails off in both directions.

Due to how WC distribution works in the current WC/Vault model, there are “peaks” where players finish the playset, corresponding to Vault openings. Notice there is a big peak near the average number of boosters, but there are also large peaks roughly 30 boosters in each direction. This is illustrative of the issue with the current system…it puts players in to “buckets” of “winners” and “losers”, meaning that the overall perception of progression from player to player can vary dramatically.

In the tweaked WC/Vault system, which is an attempt to reduce the “Rare Bottleneck”, there are still “peaks”, but they are quite a bit smaller, there are less pronounced “winner” and “loser” buckets, and it follows the normal curve more closely.

Okay, so this is interesting, and it highlights one of the issues with this current WC/Vault system, but you might argue that while both of the alternatives I show seem a bit “better” by some metric, it’s not so much of a difference to warrant making big changes in the game. After all, the “average” case is still the same, right?

That brings me to my next chart:

This chart shows the results of the same simulations, but in this case we are only trying to collect all of the cards for the Hazoret Aggro Deck Challenger Deck that was released by WotC with an MSRP of $29.99. There are a few reasons I looked at the Challenger Decks in this article: 1) They are not “Tier 1” decks; 2) They have overlapping cards between them; 3) They have a price set by WotC. One interesting thing is that these decks not being “Tier 1” doesn’t actually make that much of a difference, since the changed required to make them “Tier 1” (before DOM released) doesn’t change the rarity distribution all that much, and in Arena, Rarity distribution is the only thing that matters when trying to collect any subset of cards.

More Chart Analysis

So, let’s take a look at a few things this new chart shows us:

There are very pronounced “winner” and “loser” buckets in both WC/Vault models. The average number of boosters required to open to build this deck was 102 under the current WC/Vault system, but a large proportion of players collected it after opening just 90 boosters…while a large number of unlucky souls didn’t collect it until opening almost 120 boosters.

WotC’s price point per booster to buy them directly is about $1 in Arena. That sets this decks Arena price-to-buy at about $102 (remember, they sell this in cardboard at MSRP $29.99). If you make the (reasonable?) assumption that 2/3 of your boosters come from free play, you’re still talking about $4 higher than retail for this deck (and you can get it for less than that IRL, at least if you’re buying all four).

The tweaked WC/Vault system, even though it gives you the same average overall progression rate for a complete set, allows you to collect this deck opening 32 fewer boosters on average.

With a Generic Crafting Currency, the random cards you open in boosters make more of a difference, so the graph is a bit more messy, but you’re talking an average number of boosters to open that is close to the tweaked WC/Vault system (7 boosters less, on average), with more of the players concentrated close to the average number of boosters.

Anyway, probably nobody wants to only collect one deck, so I ran the same set of simulations for collecting all four of the Challenger Decks. My assumption is that this would result in a lower number of boosters required per deck, since 1) some of them contain overlapping cards; and 2) when opening boosters you are going to occasionally get random cards that fit into different decks.

This leads me to the final chart:

This chart shows the results of the same simulations, but in this case we are trying to collect all of the cards for each of the four Challenger Decks.

Even More Chart Analysis

Here’s what jumped out at me:

Under the current WC/Vault system, a player needs to open nearly as many boosters on average to build four decks as they would need to open to complete a playset of a large set (the number actually lies between the typical large and small set playset).

Both the tweaked WC/Vault system and the Generic Crafting system require opening a similar number of boosters, on average, to complete the four decks.

The WC/Vault systems still have the “winner” and “loser” bucket issue, while the Generic Crafting Currency system more closely follows a smooth Normal Curve, slightly favoring openign fewer boosters.

Under the current WC/Vault system, collecting all four Challenger Decks requires on average about 77 boosters per deck (just slightly more than the average for the Hazoret Aggro Deck under the more “generous” systems), putting each Challenger Deck price at about $77 in Arena, or about $25 assuming that you get 2/3 of your boosters via free play (so, roughly about the same price as cardboard).

The tweaked WC/Vault system and Generic Crafting Currency systems require about 55-57 boosters per deck, putting each Challenger Deck price at about $56 in Arena, or about $18 assuming that you get 2/3 of your boosters via free play.

Conclusion

My conclusion is that for various reasons, ranging from F2P and new user experience to value-per-dollar for paying players, the current WC/Vault system is…really bad. It obfuscates a bad pricing model behind a gambling system, and results in player progression experiences that can vary wildly from player to player, meaning some players have progression that seems fine, while for others it feels like it’s impossible to build a deck (or four) in a reasonable about of time/money.

I would advocate moving to a Generic Crafting Currency model, simply because it smooths every thing out, helping to normalize progression experience across players, and gives players more control over their collections while not speeding up overall progression. Tweaking the WC/Vault system in a way similar to what I simulated here would be a workable alternative, but still maintains some of the same issues as the current system (though it makes them less dramatic).

I’m very interested to see what they came up with in the upcoming Big Economy post.

For anyone who is interested, here are links to the charts for all of the simulations I ran:

Complete KLD Playset

Complete AER Playset

Complete AKH Playset

Complete HOU Playset

Complete XLN Playset

Complete RIX Playset

Hazoret Aggro Deck

Vehicle Rush Deck

Second Sun Control Deck

Counter Surge Deck

All Challenger Decks

Extra Charts

Some people have asked to see some additional simulation results. I’ve included those below:

Complete KLD Playset with Eternal Dust Rates

Hazoret Aggro Deck with Eternal Dust Rates

All Challenger Decks with Eternal Dust Rates

Hazoret Aggro Deck with Aggressive Dusting (My Dust Rates)

All Challenger Decks with Aggressive Dusting (My Dust Rates)

Hazoret Aggro Deck with Aggressive Dusting (Eternal Dust Rates)

All Challenger Decks with Aggressive Dusting (Eternal Dust Rates)

Thanks for reading. I’m really interested on input on this…do you think the current WC/Vault system is okay after looking over this analysis? Of the two alternatives I simulated, is there one that you’d prefer? Are there any specific simulation results you’d like to see that I don’t show here?

As always, feel free to contact me with questions, comments, criticisms or any other kind of input either here, on Reddit, via Twitter at @DailyArena, or on Facebook through 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.