How much Collection Power does a Splinterlands Chaos Legion pack give, on average?

I did the math, so you don't have to :)

As someone relatively new to Splinterlands and looking to get a higher collection power for my account, I was curious on a couple questions given the new Chaos Legion launch:

• How much power does a Chaos Legion pack give, on average?
• How would potions affect how much power I get per pack?
• Is it better to buy packs or buy cards on market, for maximum collection power?

Read on to find out!

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How much power per Chaos Legion pack, on average?

We have Chaos Legion collection power information from previous PeakD announcements, and we also have rarity drop chances on the official Splinterlands docs. It works out to be:

On top of this, there is a 2% chance a card will turn gold. Gold cards have different collection power values:

We can use the trusty expected value equation to turn our odds and values into a concrete number:

This might look scary - but simply says that the average collection power you get in a card will be the sum of all odds multiplied by their collection power values.

By using this equation and the above facts, we can calculate that a card should, on average, give you 23.32 power.

But wait!

There is an extra piece of information to consider. We know that each pack has 5 cards, and 1 card is guaranteed to be rare or higher. This means that 4 cards in the pack will have a certain average collection power (no guarantees), and 1 card will have a different average collection power (guaranteed rare or higher).

To calculate the average collection power when there is a guarantee, we need to create a new rarity table:

• The usual chance of getting a rare or higher drop is 24.8% (0.8% legendary, 4% epic, 20% rare)
• Now, the chance is 100%
• Therefore, to normalise, we need to multiply odds by 100% / 24.8% = 4.032

Using these numbers, we can calculate an expected collection power of 71.61 for the guaranteed rare or higher card.

Therefore, each Chaos Legion pack will provide 164.91 collection power (on average).

(Note: during presale, there is a 2% chance to get a promo card. We don't know how much CP this might give, but will add to the benefit).

This means, to get 15,000 power (the threshold for Silver III) you need to buy 91 packs, assuming you're averagely lucky.

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How would potions affect how much power I get per pack?

Legendary potions double the legendary chances per card, from 0.8% to 1.6%. Gold potions double the chances of a gold card, from 2% to 4%.
This naturally raises our collection power per pack, but by how much?

Here's the math:

For legendary potions, we can construct a new rarity table:

Note: I've made an assumption here that the odds of getting a non-legendary have been reduced proportionately to their previous weights. There is nothing I can find on official docs / Discord that actually explains the logic here (if anyone knows, please leave a comment!)

Again, using the expected value equation we find that:

• The collection power of a card using a legendary potion is 29.11.
• The collection power of a card using a legendary potion, where rare or higher is guaranteed, is 89.36.
• Therefore, the collection power of a pack where you use legendary potions on all 5 cards is 205.78.

Another note: it is not super clear whether your "rare or higher" card is affected by a potion, but I have just assumed it applies as normal.

Repeating the analysis for gold potions:

• The collection power of a card using a gold potion is 30.89.
• The collection power of a card using a gold potion, where rare or higher is guaranteed, is 94.84.
• Therefore, the collection power of a pack where you use gold potions on all 5 cards is 218.4.

So for collection power maximisation purposes, gold potions are better than legendary potions.

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Is it better to buy packs or buy cards on the market, for maximum collection power?

It is hard to calculate this. For pre-sale, it entirely depends on the price of VOUCHER which we must consider as part of the pack cost.

After pre-sale, looking at Peakmonsters today (16 Oct 2021) shows the best CP per USD cards going for ~30-32 CP per USD. Seeing as each Chaos Legion pack will be $4 USD pack, and gives us an average collection power of 164.9 CP, this means the pack gives 41.2CP per USD. This is better than the market today, which indicate to buy Chaos Legion packs.

Of course, we don't know what will happen to the market after Chaos Legion launches though.

Common wisdom from card games suggests that if you really want to maximize CP, you should probably wait to buy cards on the market - opening packs will always be a gamble where you slightly lose in the long run (on average). It's still fun though!

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All of my calculations were done on Google Sheets, feel free to DM me if you'd like to take a closer look:

Hope you enjoyed and learnt something that can help you with your Chaos Legion strategy! This is my first post on PeakD so apologies if I messed up somewhere.

@yoog