Hello Friends! I know I just wrote an Event primer last week, but something came up on Friday that made me want to write another article. There was some minor…debate I guess is the best word…. about the prize structure for the Event this weekend. I am going to go through the discussion for anyone that missed it, but the TLDR is the Event prize structure was really bad at first. When it became clear that this was the case I made a Reddit post to that effect, and DWD responded to the feedback in the thread by upping the prize support. There were actually a number of interesting points that came out in that discussion that I would like to explore, but there are a few things I want to make clear out the gate.
- This is an article that is not about playing Eternal in the way 99% of CCG articles discuss games. This is going to be a strange mix of math, game design and philosophy. If that is not your bag, no worries! I will see you again some time soon. If you like to look at games through a bigger lens, you might find this interesting.
- Although I made a Reddit post on this subject, and am now writing an article, I don’t think this is actually a big deal. In the grand scheme of the history of Eternal this weekend will be totally forgotten, and had DWD stuck with their original plans it would be unlikely to cause any noticeable long-term harm. I am anticipating someone responding to this article saying something like “Oh, this really wasn’t a big deal! Why are you bringing it up again?!?” Hopefully my purpose will be obvious by the end of the article, but I don’t want to make it seem that the prize structure of some one-off Event is a bigger deal than it is.
- I am not mad at DWD. I think they made an honest mistake, and they fixed that quickly, which should be commended. I am a very strong believer that when someone makes an error and correct it others should applaud them for the improvements. This creates an environment where people feel comfortable admitting problems and making the needed changes, rather than being defensive and stubborn. I would rather they do new and exciting things that occasionally need to be fixed rather than always taking the safest route. DWD has a lot on their plate right now, so I am inclined to be patient.
- My objective in this post is not to draw attention to some great accomplishment by me for the benefit of the community. Some of my critics, and the critics of RNG Eternal more broadly, say that we too often are looking for excuses to pat ourselves on the back. As you will hopefully see, I feel there are some broader lessons to be taken from this episode. My personal role involved speeding up the process marginally, and we would have likely reached the same eventual outcome whether I was involved or not.
So, with that, let’s launch into the discussion. To begin with, we need to talk about some cold hard numbers.
I need to give credit to mgoetze for pointing out the issues with the prize structure. My first impression was that the prize structure was unexciting, but you had a chance to do better than Ranked if you basically never lost. When he pressed me I realized I was wrong. He was also the first to publish the expected value calculations. I am going to go a little deeper on the math than he originally wrote about, but he deserves a good deal of the credit. So let’s go through the math!
First off, there are a few numbers we need to have for the purposes of our calculations. I used these before in another piece, but I am going to be using these same numbers (which were ultimately derived by early work from mgoetze as well!). Below is a table with the average value of all the chests in the game. There is a range of gold you can get from chests, but the averages are fairly well known at this point. You can see that below. We also know there is about a 10% chance of a chest upgrade. We have not had a confirmation from DWD that the chance of upgrade is exactly 10%, but it has been suggested that the rate is pretty close to that. This means that the value of a Gold Chest, for example, is 90% the average Gold from a Gold chest and 10% the Gold value of a Diamond chest. We also know that upgrade chains are possible, so the value of a Bronze chest is actually 90% the value from Bronze, 9% the value from Silver, .9% the value from Gold, and .1% the value from Diamond. After you crunch the numbers they come out to the following table.
|Chest||Average Gold||Upgrade Adjusted|
Sweet! Now that we have the basic units of the economy down, let’s compare the value of the Event to Ranked. I should note that I am ignoring the dust value of packs and individual cards that are being opened for the purpose of this discussion – I plan to return to this topic later. Now, it should be noted that the entrance fee to the Event was 1000 Gold, and you get 1 pack of Omens of the Past no matter where you finish. This basically means that you are just buying packs from the store 1-by-1 for every run you do. For the purposes of simplicity, we can just cancel that out as a “fair transaction”. We have no reason to believe that Omens of the Past packs will cost any more or less than Set 1, so we can say out entrance fee is functionally buying packs at market rate.
With that assumption out of the way, we need to discuss another element to the economy – game wins. This is a metric by which we measure the player’s input into the game. More time = more game wins. For the purpose of simplicity we will say a game win in Ranked is the same as a game win in the Event. This assumption is debatable, but I don’t feel this is the place to address that question. We want to figure out how much a game win is worth in Ranked and in the Event in terms of Gold. The value of a Ranked win is actually very simple to calculate. When we win a game of Ranked we have a 2/3 chance of getting a Bronze chest, and a 1/3 chance of a Silver chest. This comes out to approximately 148 Gold per win. The value of and Event game win are a little harder to compute, since the value is very dependent on how well you do. Someone who makes a deep run will get much better prizes than someone who does worse since the rewards are top heavy. First, lets take a look at the two different prize structures and see how they compare to Ranked. I give the upgrade adjusted value of the prizes for each record, and I have also color coded the results to indicate when Ranked versus Event is better/worse or roughly tied.
1st Prize Structure
2nd Prize Structure
There are a few important takeaways from here. In the 1st prize structure there is no point at which the Event is better than Ranked. Even with a 100% win rate you will never be able to break even with Ranked. This is not true for the second prize structure. A 4-win run is about equal to Ranked, while 5 wins run is significantly better. I would also like to note that the 2nd prize structure is actually strictly better than the 1st for the players. This is a term that is often misused in TCG circles, but in this case it is completely accurate, since the prizes are always equal or better.
Now, what win rates do we need to actually beat Ranked? Is it really possible to turn a profit on the Event relative to Ranked? Turns out it is! If your winrate is between 50-60% you are roughly breaking even, but once you pass 60% you are beginning to make a noticeable profit. I am not going to explain the math involved in any detail. It basically involves doing Event runs an infinite number of times with a uniform win rate. The real world is more complicated than this, but I promise that the math checks out.
So, hopefully this mathematical explanation convinces you that the original Event prize structure was worse than Ranked no matter what win rate, while revised prize structure is better if you are good. As I mentioned above, I ignored the dust value of cards in these calculations, but I should say that this is actually a relatively unfair assumption. When we are discussing Bronze and Silver chests, it is totally fair to ignore this since the commons and uncommons in chests are basically worthless, but things become more complicated when you talk about Gold chests. Since Gold chests give you a whole pack of Set 1 that is a good deal of value, but should we treat it as a hunk of Shiftstone, or should we treat the actual cards as worth anything beyond that. It is hard to make a set of assumptions that would be able to incorporate the intrinsic value of the cards, but we can include them in our calculations if we assume we are converting 100% of the cards to Shiftstone (this conversation is going to totally ignore the existence of premium cards). The Shiftstone value of a pack, including the 100 bonus Stone and a 10% chance of opening a Legend is around 398 Shiftstone. Now, if you wanted to use this value to make Omens of the Past cards then these Shiftstones would buy you about 21.6% of a Omens of the Past pack (I am adding up the cost to craft every card in a pack). If we translate that to gold, we could say 398 Shiftstone is worth about 216 Gold. If we were to add this into our model we get some slightly different numbers.
2nd Prize Structure (Counting Set 1 Packs)
I do not mention leaderboard packs or premiums anywhere in this article, and there is good reason for that – they make no real difference in your prize payouts! Such a small percentage of the population will actually receive these extra prizes that it is better to ignore them entirely.
I wanted to repeat this math incorporating the value of Set 1 packs because it moves the dial substantially. I see people saying “I don’t really need Set 1 cards, why value these packs?” all the time. Well, if I told you that each Set 1 pack is worth about 1/5 of a Set 2 pack, would that make you care a little bit more? Because that is roughly their value. This is even making some relatively uncharitable assumptions about Set 1 packs. I made a thread about a month ago to find out how many people are in the “100% Club” – people with a full 4x collection for every Set 1 card. Turns out it is probably less than a dozen people, which surprised me. There are a lot of people that could complete Set 1 if they wanted, but have instead invested in premiums, or are just sitting on hundreds of thousands of Shiftstones with no desire to finish collections until they are given a reason. Still, we are talking about a very small percentage of the population who honestly have no need for Set 1 cards, and even for them the Shiftstone value is close to 1/5 of an Omens pack.
So that concludes the mathematical section of our discussion. Our conclusions were that the original prize structure was worse than ladder no matter what, while the revised prize structure is better than Ranked if you can maintain a 60% win rate. Now I am going to move on to some of the bigger-picture questions that were raised in the thread.
The Ethical and Logical Philosophy of Designing Digital Card Games (AKA Overthinking Sh*t)
When I made the Reddit post I expected a quick reaction from the community. I will admit the title was moderately “click-baity”, but my purpose was to draw attention to the issue as soon as possible. There were some responses that surprised me, and warranted a full response even though the actual issue at hand was been resolved. I want to thank so many people who got involved in the thread, since so many people raised interesting arguments, and most did so in a respectful and thoughtful way. I can’t go through and acknowledge everyone unfortunately, but I wanted to specifically note kc_bandit’s articulate post that highlighted a number of points that should be clarified. I am going to be pulling a number of the arguments from that thread into this article in a distilled form, and attempt to give my response to each.
Why should Events have better EV than Ranked?
This was one of the most common responses, and there are a few elements to address. First, there is something I want to clarify. I do not believe that Events need to have similar average expected value to Ranked. In the case of our new event prize structure someone with a 50% win rate will make almost exactly the same as ladder if you use an adequately broad criteria for prizing. If you are focused on gold value you need roughly 60% win rate to break even with Ranked. I don’t think Events need payouts that are that flat or generous. I just want to make that clear.
What I think is important is that the top end prizes should be noticeably better than Ranked. I did a quick look for any DWD designated “purpose” for Events, and I didn’t come across any official statement to that effect. I would describe Events as pseudo-tournaments. They are an alternative to Ranked that rewards top players for clever deckbuilding and strong play in a competitive atmosphere. Shouldn’t they actually reward these players somehow? Outside of those who are able to hit things like top 10 on the leaderboard, the best players get “rewarded” by less gold than they would have received on ladder. That seems backwards to me.
Also, incentive structures in games should be aligned for people to do the things that are fun. This is something that Mark Rosewater (lead designer of Magic the Gathering, AKA MaRo) talks about a good deal. An important point that he raises focuses on supporting game elements with fun play patterns. If the winningest strategy for your game is unfun to play with/against your players will still play it anyway. Even if a fun strategy exists, players will generally stick to the winningest strategy, and then blame you for making a game that is unfun. Although it is possible to blame the players for refusing to play the fun strategy, MaRo says it is actually your fault for rewarding the wrong types of strategies. Whenever possible you should try and make the most fun and most winning strategy line up.
This way of thinking that MaRo advocates was originally applied to encouraging playstyles, cards and decks, but it applies here in a more “meta” sense. People tend to think about the “game” as being what happens when you get matched against an opponent. Some people recognize that the deckbuilding and deck selection component of Eternal is just as much a part of the “game” as in-game decisions. What is even more rare is an understanding that everything that happens once you enter the client is part of the game. The economy, the design of the different play modes, and even things like completing your collection is part of the “game”. By releasing a new play mode that you draw attention to as a special feature you are encouraging players to do it because you think it is fun. You put all that effort into implementing such a play mode, and enticing players to participate in something you think is fun, but someone who is trying to maximize value realizes that playing the Event can never beat their returns on playing Ranked. Huh? Why bother? As a game designer, if you truly believe that your players will enjoy your game more by playing an Event, you really should align your incentive structure in a way to encourage them to participate. Otherwise you put players in the awkward position of choosing between having fun and “playing optimally”. Why not give them at least a break-even prize structure, or the potential to “high-roll” and get a positive return if they do well? If you truly believe this Event is fun you should reward people for participating, to encourage that behavior.
It should be noted that some people will find there own way of playing the game that they think is the most fun aside from maximizing other elements of the game. By playing a jank deck on ladder you get a chance to maximize fun at the expense of wins, or play in some other game mode. There is nothing wrong with all of that, but that is probably closer to the exception than the rule. Your incentive structure should be designed to encourage the most people possible to have the most fun possible.
This general theme ties into one of my reasons for making the Reddit thread. New and intermediate players may have been planning to participate in the Event as a means to expand their collection. You are getting set 2 packs no matter how you finish, and some chests, and the cost is super cheap, so what could go wrong? In reality, there are a number of flaws with this line of thinking, and unless someone pointed it out as poor expected value, they may have spent their time and gold on the Event. I am a mathematically minded guy, and I was originally fooled by the first prize structure, so I expect many others would miss what was happening. I think these people have a right to make an informed decision before signing up for the Event, and posting an analysis of the prize structure assisted in this regard.
It’s a game isn’t it? Just do what is fun!
This is similar to the last question, but I am going to address it from a slightly different angle. Why do we have game rewards at all? If Eternal is a fun game, why does DWD decide to reward players (handsomely I might add) for just playing the game? You would probably need to talk to DWD for a full explanation on this, but I think the reason relates to creating a sense of progression. By giving you the chance to acquire new cards and decks you get the feeling of progress, and that drives you to push harder. I expect many people remember their first Legend they crafted, or their first tier 1 deck they completed. It is fun to build a collection and craft cards! By creating an Event with poor payouts you create a tension between the fun of the Event and the fun of improving your collection. Why do that? Can’t things be changed where the prize pool is closer to Ranked, or that you at least have the chance to “spike” a high value run? Don’t you think that people will have more fun if the prizes are higher?
Some might take to an extreme and think that I am advocating giving away the entire card collection for free, or having insanely high payouts, since having all the cards would be more fun. Right? Well, not exactly. I think the process of building a collection is interesting and fun in and of itself. If DWD just handed out 100% collections to everyone it would actually make the game less fun, and absurdly generous prizing would cheapen the experience of collection building. This is aside from business model stuff, which I will touch on later.
This leads to another point about why I made the Reddit thread. I thought there was a real chance DWD would increase the prize support. You can see this in a number of my comments. I honestly think they just kinda forgot to compare this to the value of regular Ranked. If someone pointed out their error in a clear and respectful way I truly thought there was a good chance they would amend the prize structure. This makes the Event more fun, and the game more fun as a whole!
I should also probably address another related topic about Eternal being “just a game”. This argument comes up a lot in different circumstances, but I figure this a good point to put my response down in writing. The argument that I am referring to runs something like the following: DWD doesn’t owe anyone anything. This is just a game, and you are free to just turn it off. Why make any demands at all? I would respond to this by saying that players do actually invest in the games that they play. Players invest their time and commitment in a game whenever they log in. They could log into different games, but they commit to this one on the condition that it continues to meet their expectations. Players can then make requests of the developer as a function of this commitment. You say “I want this, I want that” and the developer has the chance to meet those requests, or ignore them. Ignoring has a certain “commitment cost”, where the player needs to decide how important it is to them that their request be met. If the player feels they are making a realistic request of the company, and it is ignored, they have the freedom to stop committing to the game. This sort of informal exchange of requests and responses is the fundamental economy of any content creator. I generally feel that players are free to make any requests they like of a company (as long as they are articulated in a respectful tone) and the company is free to respond to them how they like. If the audience makes reasonable requests and the company complies, the game should grow as a result. If some make unreasonable requests and the company denies them, those members of the audience need to decide if they should either leave the game, or adjust their standards. (This “adjusting standards” part is important – if a player asks for something, and the company says “no”, that player should accept the fact that their request is not going to be met) If the audience makes a reasonable request, and the company fails to meet it, then there is a real chance that the game is harmed as a result. This is a long-winded way of saying that any member of the community has the right to make requests of the company, but the company has the option to ignore these requests at the potential cost of the commitment of members of their audience. Saying “it’s just a game” cheapens a very real exchange of commitment people “spend” on a game.
This is what a low entry fee Event looks like.
A number of people pointed out that this Event is lower entry fee, and therefore the prizes are not going to be as exciting. It is true that the entry fee is lower than the previous weeks, but I feel this loses sight of the conversion of entry fee to packs that happens. In my mathematical analysis I basically acknowledged this as a thing that was happening, but since it basically equated to a “fair exchange”. I just feel that top performers should be rewarded with payouts better than Ranked, and this Event fell short. As long as that criteria was met I think a wide range of possibilities are viable.
I’d also like to quickly address an ongoing conversation about Event payout structure. Should the payout be top heavy or flat? I actually think it should vary from Event to Event. Hopefully some day we can have high stakes tournaments with real-world top end prizes. In that case I don’t feel that “participation” rewards are necessary. I think the Event this weekend has the purpose of giving people something to do while waiting for Omens of the Past to be released. Given that, the relatively flat payout structure we have makes sense.
Spending gold on Event versus draft?
In my original argument of why the prize structure should be improved, I raised a point about spending gold on draft versus the Event. My point was basically as follows – the current Event structure forces us to basically buy a pack every run, meaning we can’t spend that gold on draft. As of right now we know that buying packs is worse value than draft, so simply being forced to buy packs is a cost in-and-off itself is problematic. In the original point I made a quick note that the 2-1-2-1 draft structure complicates the conventional wisdom that draft is better than buying packs, but some focused in on this note, and thought I was being unreasonable. Maybe buying packs was a better way to acquire cards for Set 2 given the 2-1-2-1 structure! That is a totally valid argument, but I feel that it is confused in the bigger picture for two reasons: confusing a sufficient argument with an ancillary argument, as well as ignoring opportunity costs.
Let’s start by talking about opportunity costs. It is hard to make a conclusive argument for everyone right on the value of buying packs versus playing draft. This will vary from person to person, depending on how much they enjoy draft, how much they need cards in Set 1, and many other factors. Even if someone can clearly be shown to have a better set of incentives to purchase Set 2 packs directly, the Event buying them through the Event is still a cost. You are actually giving up the opportunity to make that decision in the future. Set 2 packs will be on sale for 1000 gold (we expect) in the near future, and you will be able to buy as many packs as you like for 1000 gold each then. By being forced to buy them now for 1000 gold each you are giving up the opportunity to spend your gold differently later. You are also giving up your opportunity to play in Events next week or the week after that or the month after that. By being forced to buy packs at 1000 Gold a pop now you are incurring a real “opportunity cost”.
In the philosophical meaning of the word and “argument” is basically a logical structure that aims to prove a point. I am not going to bore you with introduction to logic 101, but it is important to understand the different between a sufficient argument and an ancillary argument. An argument that is sufficient means that it is all that is needed to prove a point, while an ancillary argument is something that is a supplement to the rest of the argument. If one argument is true and sufficient than the conclusion is completely true, and supporting arguments are essentially irrelevant. Take the following example.
Bob is bald, therefore he has no hair. In addition, Bob wears a hat, and men without hair tend to wear hats.
The first sentence is a sufficient argument. If Bob is bald then he has no hair, and that is all that is needed to make a conclusion about how much hair Bob has. It is true that men without hair are more likely to wear hats, but just because Bob wears a hat it is only a loose tool for guessing how much hair he has. Suppose someone said “Well, people wear hats for lots of reasons! Maybe Bob does have hair!” That first sentence if true, but Bob is still bald, so this secondary point about hats is essentially irrelevant in the grand scheme of things.
In the case of the prize structure thread, I think people got distracted by the secondary point about draft versus buying packs. Although I stand by my “opportunity cost” argument above, the core of the thread was really about the expected value of Ranked versus the Event. In my opinion this is an entirely sufficient argument to justify improving the prize strcture. Although there is an important conversation to be had about buying packs versus drafting as a method for acquiring Omens of the Past, this in no way contradicts my core argument about the expected value of Ranked versus the Event. Some people seemed to get caught up in this, which ended up being a distraction. If I had to go back, though, I would remove any mention about draft since it was less important than the core mathematics.
Just let them make money! They are running a company aren’t they?
Yes, DWD is running a business. They have a right to decide how they want to make money, but I don’t really think the original Event prize structure is the best way to do this. The amount of money they are going to bring in from doing an Event like this is probably close to inconsequential. Although it is interesting to play in an alternative metagame, the mono-faction metagame is not particularly compelling. Compare it to last weekend where we got to play with new cards and had a real diversity of archetypes. The mono-faction metagame is less interesting than the 2 faction metagame almost by definition. Do you think people are going to be buying gems to play piles of mono-factions Events? Seems unlikely to me. You know what would be a great way to make a lot of money? Release Omens of the Past. Create a more interesting Event with Gem only entry fee. Create more exclusive content for players that pay like premium Sigils or premium avatars. They could recalibrate the in-game economy to make it less generous to “Free-to-play” players, or more generous to those that spend cash. There are about a million ways to improve revenue, and almost every single one sound more effective than charging 100 gems for an Event with medium replay value. Although it is true that they could be making some money from this Event, if this is their true intention, I feel this is a relatively feeble attempt.
I should also briefly respond to the “DWD is trying to drain our Gold reserves before Omens release” theories. Both this week and last week we have been able to convert our gold to Omens of the Past packs at the same ratio we will be able to spend when the set is actually released. Lets say you had 100,000 gold right now, and spent it all on Events this week and never win a single game. You get 100 Omens of the Past packs. Instead imagine you spent it all on packs when Set 2 is arrives. You get 100 Omens of the Past packs. There might be an argument to be made once we learn more about the prizing once we move into Set 2, but for now it seems like they are “tricking” us into spending the Gold in exactly the same way as we might spend it in 2 weeks time.
Beyond all this, I don’t think harvesting gems off an Event like this is really “in the spirit” of DWD’s business model based on what we have seen. I should emphasize that I don’t know anything about the details of their chequebook, but it seems to me that they make a lot more of their dough from deeply enfranchised players compared to those who are struggling to pay for Event entrance fees. League of Legends is the most profitable game in the world, but it is possible to become a top player without paying a dime. In fact, as I understand it, most players pay essentially nothing. You can spend money to accelerate your collection of heros, or you can buy special aesthetic treatments that are only available through the use of real money. Does that model sound familiar? It should, because Eternal (and many other games) have embraced it to varying degrees. I think that DWD wants to make the game entirely accessible through “F2P” means for devoted fans. These players are likely to drop money (if they can) on content like special Totems or other treatments just as a mechanism to support the game they love. DWD has (so-far) positioned itself as being extremely accessible to F2P, easily beating Hearthstone and Magic Online in its accessibility to F2P players. Although I fully believe DWD has every right to make money of their content, I don’t really think they see this as a mechanism to that end.
This ended up being even longer and muddier than I originally imagined, so hopefully some of that was coherent. This piece obviously is talking about more than just the prize structure of this one Event, and applies more broadly to the way people approach video gaming and video gaming companies. My brain is a little fried from going through all that, so I will leave things there, but if you were able to make it to the end of this rambling mess, be sure to share your thoughts on the Reddit thread! Anything I missed? Take care everyone!