Soulbound Rewards Cards - Expected # of Chests Required To Max Cards - by league, rarity, and foil | Splinterlands

TLDR; better start playing and earning chests, because it'll be a grind to get all those soulbound rewards cards maxxed. Also one more call-out is that the analysis does not assume potions are used (truth be told, that's an oversight on my part). I added a quick note at the end on how that adjusts the expected number of seasons required for different rarities.

We have details on the drop rates for chests now that the new soulbound rewards cards have been implemented into @Splinterlands. Here's the chart provided by the team:

The number shown next to RF and GF is the maximum number of RF or GF copies that can drop from a chest in that league, for that rarity. for example, in a Champion chest you may get up to 15 Regular Foil copies of a common card, but as few as 1. The actual number is random, according to @cryptomancer.

So now the fun part - let's check how many chests we'll need to max out a card, and to max out all cards.

First let's recap some data. Here's a table of the maximum number of cards earned by league, rarity, and foil, and just below the % chance of earning any of the combinations (noting from above that there's only a 33% chance of chests containing cards):

Now that we have the data above, and taking into account the # of variants per rarity (variant = # of different cards of a certain rarity, e.g. 12 for common, etc.), we can calculate the expected number of cards of each rarity and foil that will drop in each type of chest. A simple way to read the data below is "every Bronze chest will contain 0.021698 of every Regular Foil common card" or "every Champion chest will contain 0.03102 of every Regular Foil rare card". I.e. imagine that instead of containing a specific item, every chest contained a fraction of every possible item based on the probabilities above - that's the number you see in the table below. The number is calculated by taking the probability of getting a certain rarity/foil of card, dividing it by the number of variants, and then multiplying by the expected number of copies (which, since we were told it's random, I assumed would be the average between 1 and the max number of copies).

Now we can check how many chests it would take to max out a single card - an important note here is that this would assume that you ONLY ever get that specific card, which of course is very unlikely.

Now the most fun part... Since we can't expect to only get a specific card among all the variants, let's look at the expected number of chests required to max out ALL cards.

Now since here we're assuming fractional drops, you want to take the MAX of any two numbers to know how long it'll take to max a rarity/foil combination, not the sum. So for example if you're only getting Champion chests, it would take an expected 8,865 chests to max out ALL Legendary cards, and in those 8,865 chests you would also max out the epics, rares, and commons (in fact you'd max out the commons and rares more than twice each in that span).

So now let's assume you're in Champion, and you're receiving an average of 8 chests / day (that's roughly what I'm getting nowadays) and 60 chests at the end of the season, i.e. 172 chests / season. It would then take 51 seasons to max out every soulbound card, i.e. about 2 years. In other words, @yabapmatt nailed it.

One final note (thanks @xsuilx for the call-out) is that my analysis above does not include the use of potions. Those would double the chances of receiving legendary, epic, and Gold Foil cards, effectively halving the time required to max out those rarities. It would have no impact on rares as they're unaffected by potions, and would slightly lengthen the time required for commons.

Hope you found this helpful, let me know if you find any bugs in the analysis, and most importantly may the RNG be ever in your favor!

And now, here's a Coastal Sentry reimagined by Midjourney emerging out of a blank page. Because, why not.