Hi,

The excitement for the new splinterlands main set conclave arcane is growing by the day. A lot of players are preparing for the pre-sale. The three new pack types add a new dimension to the decision-making process.
Since I am an enthusiatic spreadsheet warrior, I have answered the question of which way and which combination is the cheapest to get a maxed Conclave Arcana set.

A little spoiler: Thanks to the different pack types, it gets cheaper!

<center>![CA_Packs.jpg](https://images.hive.blog/0x0/https://files.peakd.com/file/peakd-hive/splinterlands/23tS36MUgmXavybEcksb2AqgZKqJqD9KkVkcPQG5w6WTVKWfqtDXvkb4dU9txE9s25NX8.png)
These are the new packs. Choose wisely!
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Before we get to the comparison of packs, we need to talk about the probabilities of opening packs - including standard packs.
Splinterlands does give the odds for the rarity of a card. However, the guarantee of at least one rare card per standard pack results in different “real” odds. Legendary potions also influence the odds for the card types, because the bonus is deducted from the odds of the common cards.
I would also like to point out that according to the pre-sale post, the chance of epic cards can now also be doubled. This is new and is currently not yet in the description in the potion store.

To make clear what I mean with this, I want to give an example: If you open 100 Packs, the odd of getting a pack with only 5 common cards is 24 % (75.2 % x 75.2 % x 75.2 % x 75.2 % x 75.2 %). Here comes the guarantee and turns the 5th card into a random rare card. This results in the following probabilities when opening standard packs:

|Rarity|Common|Rare|Epic|Legendary
|-|-|-|-|-
|Base Odds|75.2 %|20 %|4%|0.8%
|Real Odds|70.4 %|24.8 %|4%|0.8%

As I said, using a Legendary Potion changes the odds again. I recommend always using potions! My further calculations then use the following odds:

|Rarity|Common|Rare|Epic|Legendary
|-|-|-|-|-
|Standard Pack + Legendary Potion|65.59 %|24.81 %|8 %|1.6 %
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---> EDIT
I mad a little mistake in the table above. Sorry! Here are the correct odds. Since the impact of the change isn't that big (1.35 % less rare Cards, that are already overprinted at the final result), the results below are not with this odds. But for your calculations please use the following:
|Rarity|Common|Rare|Epic|Legendary
|-|-|-|-|-
|Standard Pack + Legendary Potion|66.94 %|23.46 %|8 %|1.6 %
EDIT End <---

**Let's look at the new Packs:**

In contrast to the Standard Packs, Starter Packs and Legendary Packs consist of one card with a fixed rarity and 4 cards determined by the base odds. This leads to the following odds:

|Rarity|Common|Rare|Epic|Legendary
|-|-|-|-|-
|Starter Packs|64 %|36 %|-|-
|Legendary Packs|60.16 %|16 %|3.2 %|20.64 %
|Legendary Packs + Potion|56.32 %|16 %|6.4 %|21.28 %

<hr>

Now we have the numbers to do calculations on the Packs. Keep in mind, that all following calculations are based on the odd with Legendary Potion. For this mathematical consideration I also count all cards as regular foils and expact that cards of each rarity type are equally distributed. In reality you will be short on some cards, but theirfore you are able to trade those you have drawn more.

Before we look at the best combination of Pack types I want to show you the amount of Packs that is needed to get a maxed set of one specific rarity:

|Rarity|Common|Rare|Epic|Legendary
|-|-|-|-|-
|Individual Cards|24|29|14|15
|CC to max one Card|400|115|46|11
|Total CC needed|9,600|3,335|644|165
|Starter Packs needed|3,000|1,853|-|-
|Standard Packs|2,927|2,690|1,610|2,063
|Legendary Packs|3,409|4,169|2,013|155

Here is a short comparison to the Rebellion set at its launch:
|Rarity|Common|Rare|Epic|Legendary
|-|-|-|-|-
|Individual Cards|29|28|14|14
|Standard Packs|3,333|2,597|3,220|1,925

You can easily see that with the new sets and changes there are ways to get cards of a specific rarity easier than before. The magic number of the Rebellion set was 3333. You needed at least that much packs to get a maxed set. If you had used Vouchers this would have been 13,332,000 DEC.

<hr>

Even without the new pack types a maxed set could be build with less than 3000 standard packs. There are two reasons. First is the boost of Epic cards by the Legendary Potion. And the second is, that Rebellion as a "Summoner Set" had 5 additional common dual element Summoner or Archons, like they are called now.

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But let's come to the interesting part of my calculation now!
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**What is the smartest combination to get a maxed Conclave Arcana Set?**
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By using the calculated odds, I ran the amount of the three pack types and summed up the cards I would get.

>! [The optimum that was found is] <center>**1,584 Standard Packs + 36 Legendary Packs + 1,345 Starter Packs**</center>

|Rarity|Common|Rare|Epic|Legendary
|-|-|-|-|-
|Total CC needed|9,600|3,335|644|165
|CC from Starter Packs|4,304|2,421|-|-
|CC from Standard Packs|5,195.5|1,964.2|633.6|126.7
|CC from Legendary Packs|101.38|28.8|11.5|38.3
|Total CC|9,601|4,414|645|165

While it is possible to get three rarity types close to the value of needed CC, only the rare cards would be overprinted  by 32 %. But because of Archons and Gold Foils, this is no problem. (There is a high demand on rare Gold Foils, but I don't want to go into detail about this in this post)

The price of the optimal combination of packs would be 8,545,000 DEC. This is 36 % cheaper than Rebellion! Since Starter Packs don't count and are not available for the presale, 7,200,000 DEC would count to the Promo Card distribution and the Raffle. With 18 Legendary and 180 Rare Promo Cards you would also get these as a maxed version.
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**Concluding Remarks**

The different pack types help players to get a complete maxed Conclave Arcana Set easier than Rebellion and Chaos Legion. And also if you want to look for specific rarities, they are an improvement as well. Great job from the Splinterlands Team!

The 8,545 $ that I calculated here doesn't take Gold Foils and Black Foils into account. By selling these cards (4 % of them) you can lower the costs of a Conclave Arcane Set even more. For this I will do a separate calculation, because with the different price ratios of regular and gold foil for each rarity it is a complex topic for itself. A first rough calculation (all ratios 1:10) would lead to 1,130 Standard Packs + 26 Legendary Packs + 1,394 Starter Packs. The total costs would be 6,538,000 DEC.

A more accurate calculation would give us the absolute minimal combination of packs and the set value as well.

But for now I hope my post helps you prepare for the presale of Conclave Arcana. Thank you for reading. If you notice a miscalculation, please let me know.

Vonak!