Analysing Card Rarity Probabilities In Chest Rewards With 400 Cards

I have reached 400 cards obtained from chest rewards!

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.

Previously, I reported the statistics every 100 cards. In this post, I will be sharing the statistics after 400 cards. Let's see if the deviations are reduced with a bigger sample size.

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

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.

Recently, they have been some changes to the ranked rewards such that the Legendary and Gold Foil probabilities are different across the leagues. For Silver chests, which I am playing for, the probabilities remain the same, i.e. 0.8% for Legendary and 2% for Gold Foil. This means I can continue to track my rewards without any additional tweaks to the percentages. However, the card chance has dropped from 50% to 38%, so it might take longer for me to accumulate cards going forward.

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So here's what I have gotten so far:

Cards	Common	Rare	Epic	Legendary	Gold Foil
1-100	72	25	2	1	2
101-200	76	21	3	0	2
201-300	73	23	3	1	2
301-400	77	17	5	1	3
Total	298	86	13	3	9

Rarity	Actual Cards	Actual %	Expected %	Deviation
Common	298	74.5%	75.2%	-0.7%
Rare	86	21.5%	20.0%	+1.5%
Epic	13	3.3%	4.0%	-0.7%
Legendary	3	0.8%	0.8%	-
Total	400	100%	100%	-

Foil	Actual Cards	Actual %	Expected %	Deviation
Regular	391	97.7%	98.0%	-0.3%
Gold	9	2.3%	2.0%	+0.3%
Total	400	100%	100%	-

Some observations after 400 cards:

• For the latest batch, I have the received the most Common (77) and Epic (5) cards, and the least Rare (17) cards when compared to earlier batches.
• Fortunately, I still managed to get a Legendary card within this batch of 100 cards.
• Overall, the deviations to the expected probabilities have dropped but am still receiving more Rare cards than expected, and less Common and Epic cards than expected.
• For Gold Foil, I have gotten 1 more than expected, so that's a slight positive.

Some final notes/remarks:

• These cards were solely obtained from chest rewards, i.e. I did not include cards from Chaos Legion/Gladius packs for this analysis because the use of potions and/or the guaranteed rare card would skew the %.
• Also, given that the chance of getting a card from chests varies from league to league, I have excluded that for this analysis because I wanted to focus on the distribution between the rarity tiers and foils.

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Overall, I would rate my luck for card rewards so far as close to average even though I am still missing a Djinn Oshannus from the chests to complete my Rewards collection of the old series. Hopefully I can get it soon because that's my favourite card so far. Let's see what happens after 500 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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