An argument against the change of the merchant system

[janjetina]

It came to my attention that the merchant system was changed, limiting the supply of the singles, creating scarcity of the most demanding singles.

There are a few reasons why I think that this is not a move in the right direction.

1. It puts new players at a disadvantage, and gives those who have spent more time on the site and built their constructed decks (multiple decks!) with the help of the 'old' merchant the advantage over the new players who are at a significant disadvantage at building their first competitive deck (see point 2).


2. It is argued that the new players would be encouraged to build their constructed decks by opening the booster packs. What follows is the calculation that estimates the expected value of how many booster packs should be opened by the player to complete a playset of a card from a large edition (such as FOTR), which puts the lower bound on building the deck (lower bound results from the best case scenario when all other necessary cards have been collected in the process of collecting the playset).

Let's say, that a player is building a Moria deck, and wants to buy a playset of Goblin Armory, that is 4 copies of a Goblin Armory.

We observe opening of a booster pack as a binomial event, where success is defined as opening a booster pack and finding Goblin Armory in it.

The probability of getting a non-foil goblin armory in a booster pack is 1/121, as there is one non-foil rare per booster, and there is a total of 121 rares in FOTR.

The probability of getting a foil goblin armory in a booster pack is 1/(121*36), as there is one non-foil rare per booster box, and there is a total of 121 rare foils in FOTR, and there are 36 booster packs per box.

Probability of getting a goblin armory in a booster is the sum of the two probabilities above, i.e. 37/(121*36). I'll call that probability p.

So, p=37/4356. Conversely, q = 1-p = 4319/4356 is the probability of not opening a Goblin Armory in a booster pack.

Since the events are binomial, if we open n packs, we expect to find the following number of Goblin Armories:
m=n*p*q.

So, in order to obtain 4 copies of Goblin Armory (m=4), one expects to have to open n=m/(p*q)=4*(4356)^2/(37*4319) = 475 booster packs.

Let me reiterate: to get a playset of a FOTR rare single, like Goblin Armory, a player would have to open 475 booster packs on the average.

How much time does it take for an average player to get 475 booster packs? He gets 50 credits each week, which is sufficient for maybe 15 booster packs per month and one sealed event entry fee. During that month, a player may play a sealed league event and earn, say another 20 booster packs total (I'm not precise with numbers here, but the ballpark estimate is adequate I think, correct me if you have the exact data available) if he regularly plays in that tournament. So, that's 35 booster packs a month.

With that rate, it would take almost 14 months to obtain a playset of a rare card like Goblin Armory, and at the end of that, if the player is lucky, he would have completed just one constructed deck.


3. It is argued that the change was done to simulate realistic situation. However, the realistic situation differed in the following aspects:

- there was no monopoly; instead of one merchant, there were many available: Cobracards, Sorourke, eBay, etc. and each of them was quite well stocked (almost never missing any rare and frequently being stocked even with playable rare foils). Many people were selling singles locally as well (I used to be one of them).

- trading was available, both locally and over the internet (Mahasamatman). I understand that enabling trading would lead to potential abuse. Associating the accounts with confirmed e-mail addresses could probably alleviate that issue.

So, in a realistic situation, the supply of cards, viewed from a player standpoint, was practically unlimited.

There was also no scarcity of money in the realistic situation, such as there is in the Gemp.

That was the situation that enabled me to collect foils, so I still have my all-foil FOTR set and a few all-foil decks (or I would have if I hadn't lended someone my Servant of the Secret Fire foil playset to someone and in the meantime forgot who borrowed it and the guy hasn't returned the cards on his own).

[janjetina]

I need to correct the distribution of rare foils, as there was one rare foil per 66 packs, making the probability of opening a particular rare foil even lower (to 1/(66*121)), but it doesn't significantly affect the calculations. 

[bibfortuna25]

The best strategy for building decks in Gemp is to buy singles. You will often pull cards you don't want, but you can sell them back to the merchant to get some profit out of this. Now, cards like Goblin Armory are pretty expensive, but it still doesn't take over a year to acquire 4 of them if you want to.

[janjetina]

The best strategy for building decks in Gemp is to buy singles. You will often pull cards you don't want, but you can sell them back to the merchant to get some profit out of this. Now, cards like Goblin Armory are pretty expensive, but it still doesn't take over a year to acquire 4 of them if you want to.

The merchant system changed today. Most deck necessary singles are unavailable to buy. Artificial scarcity has been created. Hence my post.

[sgtdraino]

100% agree with you, janjetina.

[Nitsuj]

The only problem I see with Janjeta's math is that it assumes an even distribution of rares... which in the real world is true, because rare sheets had an even number of rares printed on them.  So theoretically, for every weight of a legacy, there is a goblin armory printed.

But gemp does not physically print sheets of rares.  I believe that each rare that is generated is simply a random choice from 121 cards.  Over time, law of averages says that you should pull as many Goblin Armories as you pull Weight of Legacies, but it needs to be an amazingly large sample set to guarantee that.

So, I argue that your 475 booster packs is actually low.

[MarcinS]

Ok, let me address your concerns one by one.

Concern 1: "To get a playset of a FOTR rare single, like Goblin Armory, a player would have to open 475 booster packs on the average."
Correct, incidentally - if a player buys 475 boosters, considering equal distribution of rares in a pack, this number of boosters will give that player a full playset of FotR rares (4*121 = 484 boosters).

Concern 2: "It would take almost 15 months to obtain a playset of a rare card like Goblin Armory (actually whole playset of FotR - see concern 1), and at the end of that, if the player is lucky, he would have completed just one constructed deck."
Correct, lets now try to get back to how this game was working on paper. How much money was an average player spending on LotR each month (not just boosters, but also singles)? Please keep in mind that very few players were buying cards by the boxes. My guess was $20 per week, which is enough to buy 6 boosters (at $3.29 retail price). This is how I came up with the 50 gold/per week scheme (=5 boosters). At this rate, an average LotR player in paper version would acquire a playset of FotR in 80 weeks (484/6) = 18 months.

I assume you are disappointed, because probably you were one of the players that was buying cards by boxes, and spending way more that $20/week on LotR (I know, I was), but I'm not sure if that is the kind of player behaviour I want to mimic in the online system. If I did, there would be almost no difference between Collector's and non-Collector's leagues/tournaments, as your expectation is, that player should be able to get all the cards he/she needs for his deck at a fast pace.

I think the main problem with Collector's league at the moment is, that there was a time, when Gemp-LotR was starting where first few sealed leagues were moving the cards from league collection to permanent one. This has put players that joined after, at a huge disadvantage. Unfortunately, I have no idea how to remedy this problem outside of resetting collections, which might make some people angry.

Concern 3: there was no monopoly; instead of one merchant, there were many available: Cobracards, Sorourke, eBay, etc. and each of them was quite well stocked (almost never missing any rare and frequently being stocked even with playable rare foils). Many people were selling singles locally as well (I used to be one of them)
Guess where these merchants were taking cards from? - They were buying them from other players (and to a much lesser extent - opening boosters, but if they did that, they were always losing value). Guess where were the players taking the cards from to sell to merchants? They were opening packs.

In other words - every card that was available at any of the merchants or on any other singles market, at one point or another came from a booster pack.

Now - tell me how is it different from the merchant system based on stock (as it is done now)? You are looking at the merchant now (3 hours after the change was made) - with several key cards being out of stock, and you assume these cards will never be restocked. What was real world merchant doing in that situation? It was increasing the "buy" price high enough to restock - this is exactly what this merchant will be doing. It will increase the "buy" price, until it will acquire one copy (or specific number - I can configure).

Possible changes
1. I may decide to adjust the weekly allowance, if it is indeed to low, and we want to have all players on average being more of a "power-gamer", compared to what was the situation in paper LotR, or if the average was mis-guessed.
2. I may change the pricing mechanism to fluctuate card price based on number of cards in stock, and for example - aggressively buy cards (increase price) the smaller the stock is.

As always, I accept any suggestions to the merchant mechanism (and game economy), both addressing the 2 possible changes above, or addressing anything in general. The only requirement is - it can't be something, someone came up with in 10 minutes, and provides no reason other than - "I can't get my [insert deck name] completed for the next league". Current system is a result of multiple hours of thinking, tinkering, data-mining and adjusting, so if you wish to challenge it, you better come prepared.

[bibfortuna25]

Since there is no finite supply of cards in Gemp, since it's all statistics in a computer, there is no incentive to simulate "running out of stock" for ANY cards. All cards should be available for purchase for every player, not just the ones who got there first. Sure, the prices will be high on some cards, but that's a much better alternative to making them unavailable entirely.

[sgtdraino]

100% agree with you, bibfortuna25

[hsiale]

I think the main problem with Collector's league at the moment is, that there was a time, when Gemp-LotR was starting where first few sealed leagues were moving the cards from league collection to permanent one. This has put players that joined after, at a huge disadvantage. Unfortunately, I have no idea how to remedy this problem outside of resetting collections, which might make some people angry.

I think with current player base this no longer is such a big problem. Leagues get big enough for prizes to overshadow what people got then.

Last Sealed league I finished second. Total prizes I got were way better than what I got for winning the first Sealed that was played a year ago.

An average player at that time got something like 20 packs out of such league (18 to build the deck, but prizes were low for middle of the table then IIRC). Currently and average player easily gets more out of a league. And I think the league size can increase even more.

Of course a player that plays just a few games or has really low win percentage currently won't take 18 booster packs out of a league. But there were only 3 leagues giving 18 boosters to everyone. That's 54 packs, even if you buy 5 a week you make up for it in 3 months.

[bibfortuna25]

What if new players who joined after that first few sealed leagues will automatically get that product added to their collection? That would put a lot of folks on more even ground.

[MarcinS]

What if new players who joined after that first few sealed leagues will automatically get that product added to their collection? That would put a lot of folks on more even ground.

That is a possibility. Though, I'd rather just increase the sign-up bonus from 200g it is at now, if it is indeed needed. Much simpler to do, and gives new players more choice of what they want to do with it.

[janjetina]

Concern 1: "To get a playset of a FOTR rare single, like Goblin Armory, a player would have to open 475 booster packs on the average."
Correct, incidentally - if a player buys 475 boosters, considering equal distribution of rares in a pack, this number of boosters will give that player a full playset of FotR rares (4*121 = 484 boosters).

Actually, the use of uniform distribution assumes a huge sample size. Nitsuj has mentioned this.

In my example the sample size is the total number of booster packs / rares. That is a huge number and for the practical purposes, I consider it infinite.

In your statement the sample size is only 484 booster packs / rares, and you are assuming uniform distribution over particular rares.

The assumption about the uniform distribution is not guaranteed to hold in that case.

The distribution in the sample can be arbitrarily skewed (see below) and no simple statement can be made about it (though you could make the statement that buying 484000 rares would give you about 1000 playset collections with high probability).

Clarification:

If there were only two types of rares, Hoeffding's inequality would apply, but this case is more complicated, still the way of thinking is the same.

Hoeffding inequality deals with the case when there is a huge number of red and green marbles in a bin.

If we assume uniform distribution inside the bin (i.e. number of green and red marbles being equal, analogous to the uniform distribution of rares over all the booster packs), and we take a finite sample with size N (e.g. N=484), we have a probabilistic guarantee that probability of picking a green marble in a sample will be close to the probability of picking a green marble from the bin, which is 0.5 (i.e. that the sample follows the same - uniform - distribution as the bin).

The guarantee in this, simple case, is given quantitatively by Hoeffding's inequality.

Let's say that we want the mean of the sample distribution to be within 0.05 of the mean of the uniform distribution. If we plug in N=484 and epsilon=0.05 into Hoeffding inequality, we get the probability of the sample distribution differing  from the bin distribution to be no more than 17.8%. If we want our mean sample distribution to be within 0.01, we get absolutely no guarantees (probability larger than 1).

However, our bin doesn't have 2, but 121 different colors, so the sample size has to be much larger in order for us to be able to have our guarantees about the sample distribution.

I'll try to address the rest of the response after my workout or tomorrow.

 

[bokizg]

I was thinking about to suggest a resetting all collections when I red Marcin's post. I would like to point out that even if system is slower then the current logic, that would bring great value to building up own collection. Players who started before and builded their collections to certain point might get furious but I'm curious what they would say about this option?
Having fresh start and much more competition might be healthy and fun. With new solid system that would slowly allow players to build up and improve decks over time and bring almost real feel of joy when adding cards to collection as they would be hard earned.

200g per league seems less choice from what we have now. Why would anyone want to have boosters chosen for him instead of buying them by him self. For example one might play ttt sealed league but needs king block cards for his collection deck and doesn't care about ents of fangorn boosters as those don't bring any cards that are wanted.

[sgtdraino]

If there were only two types of rares, Hoeffding's inequality would apply, but this case is more complicated, still the way of thinking is the same.

Hoeffding inequality deals with the case when there is a huge number of red and green marbles in a bin.

Is he an Elf?

Or maybe a Sword!

Hoeffding, The Equality Slayer!