Analysing Card Rarity Probabilities In Chest Rewards With 100 Cards

How often have you read posts about people sharing how lucky or unlucky they have been when it comes to chest rewards?

For me, I like to analyse stuff objectively using data, so I actually kept track of the cards that I have received from chest rewards to check if I am more lucky or unlucky compared to the official data.

A few weeks back, I actually got my 100th card from chests and I thought it would be a large enough sample size to analyse this more meaningfully.

Before we jump into that, in case you didn't know, these are the official card probabilities:

Rarity: Common: 75.2% | Rare: 20% | Epic: 4% | Legendary: 0.8%
Foil: Regular: 98% | Gold: 2%

This means if you have gotten 100 cards, on average, you will likely have about 75 Common cards, 20 Rare cards, 4 Epic cards, and maybe 1 Legendary card. 2 of them on average will be Gold Foil, while the rest are likely not.

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So here's what I have gotten:

Rarity	Actual Cards	Actual %	Expected %	Deviation
Common	72	72%	75.2%	-3.2%
Rare	25	25%	20%	+5.0%
Epic	2	2%	4%	-2.0%
Legendary	1	1%	0.8%	+0.2%
Total	100	100%	100%	-

Foil	Actual Cards	Actual %	Expected %	Deviation
Regular	98	98%	98%	-
Gold	2	2%	2%	-
Total	100	100%	100%	-

Some observations:

• My overall numbers are relatively close to the official expectations
• The biggest deviation lies with Epic cards where I should have gotten 4 cards on average but only received 2
• The gap was filled by Rare cards where I should have gotten 20 cards on average but received 25 instead
• Thankfully I managed to get 1 Legendary card among the 100 cards
• Nothing much to comment on Goil Foil as it was right on point with the official expectations

For interest, these were the cards I have gotten:

• Legendary: Djinn Biljka
• Epic: Djinn Renova, Lava Launcher
• Rare: Venari Bonesmith (8), Exploding Rats (4), Gargoya Devil (3), Twilight Basilisk (2), Venari Crystalsmith (2), Venari Wavesmith (2), Naga Assassin (2), Venari Seedsmith (2)
• Common: Pelacor Conjurer (18), Gargoya Lion (15), Pelacor Deceiver (11), Pelacor Mercenary (11), Pelacor Bandit (9), Venari Heatsmith (8).

Some final notes/remarks:

• These cards were solely obtained from chest rewards, i.e. I did not include cards from Chaos Legion packs for this analysis because the use of potions and the guaranteed rare card would skew the %.
• Also, given that the chance of getting a card from chests varies from league to league (e.g. 50% chance for Silver and above), I have excluded that for this analysis because I wanted to focus on the distribution between the rarity tiers and foils. This means you probably need to open at least 200 chests in order to get 100 cards.

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Overall, I would rate my luck for card rewards so far as close to average even though I would have liked to have more Epic cards (hopefully a Djinn Chwala!). Let's see what happens after 200 cards.

If you like reading this post, do appreciate an upvote to support my work too! As always, thanks for reading and have a pleasant day ahead!

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