Card pack statistics

Statistics for card packs are a means of observing the rarity drop rates for cards from card packs, determining the opportunity cost of whether a player should continue to buy or not buy packs.

NB: For inclusion into this article, studies recording the rarity drops of card packs should have a reasonably large sample size and should have a citable reference from a reputable source.

Pity Timer
"Pity Timers" exist, which define the maximum number of packs that a player opens before guaranteeing the next Rare/Epic/Legendary card. Pity Timer counters are tracked individually for each store-bought expansion set, including the Classic set. However, no Pity Timers are applied to Golden Classic packs.

A translation of the announcement Blizzard made in complying with China's "disclose odds" law stated:

"In adherence to new laws, Hearthstone is hereby declaring the probabilities of getting specific card rarities from packs, with details as below. Note: Each Hearthstone pack contains cards of 4 different rarities. In addition, please note that as players open more packs, the actual probability of opening cards of a higher quality increases in tandem."
 * RARE - At least 1 rare or better in each pack
 * EPIC - Average of 1 every 5 packs
 * LEGENDARY - Average of 1 every 20 packs

The statement that the probability increases as more packs are opened may be a reference to the (otherwise-unannounced) pity timer.

Actually statistical studies have shown the following:
 * An Epic card will be opened within 10 packs of the last opened Epic, for that set.
 * A Legendary card will be opened within 40 packs of the last opened Legendary, for that set.

Pitytracker.com has also compiled their own card pack opening statistics for each expansion: pitytracker.com/insights.

In addition, Blizzard announced that beginning with Knights of the Frozen Throne, players are guaranteed at least one legendary card in their first 10 packs from any given expansion. This, however, does not apply to Golden Classic packs. Combined with the usual 40-pack pity timer, this implies that if a player buys a 50-pack bundle (of packs of a never-before-opened type), they're guaranteed at least 2 legendaries, and can reasonably expect 3 or more.

Expected dust value
According to the below meta-study's data tabulated under the "Golden cards" section, the average card pack has a disenchanting value of 102.71 Arcane Dust. Each card has an average disenchanting value of 20.54 Arcane Dust.

Meta-study
The following numbers combine data from several other studies on this page. Since it has at times been suggested that the distribution of cards has changed over time or is different for different expansions, the numbers are shown per expansion. Note that all data collection has been done for each expansion when it was the most recent expansion, so there is for example no data available for card distribution in Classic packs that were opened after the release of Goblins vs Gnomes.

Currently included studies:


 * June 5, 2014: Steve Marinconz (1,000 Classic Packs)
 * August 2014: E. R. Kjellgren (11,359 Classic Packs)
 * February 12, 2015: Amaz (400 GvG Packs)
 * August 29, 2015: HearthSim (15,109 TGT Packs)
 * April 28, 2016: Kripparian (713 Old Gods Packs)
 * April 28, 2016: Amaz (413 Old Gods Packs)
 * December 1, 2016: Kripparian (896 Gadgetzan Packs, Before Tri-Class Bug Hotfix)
 * December 1-2, 2016: Kripparian (450 Gadgetzan Packs, After Tri-Class Bug Hotfix)
 * April 6, 2017: Kripparian (1,101 Journey to Un'Goro Packs)
 * April 8, 2017: N. Millar (1,256 Journey to Un'Goro Packs)

This produces a total sample size of 32,697 card packs, describing 163,485 cards in total.


 * September 13, 2017: Joe Tweak (380 Knights of the Frozen Throne Packs)

Rarity distribution
This table shows the likelihood of any single card being of a given rarity. The differences in the percentages appear to be all within the boundaries of statistical variance. This suggests that, at least up to and including the Un'Goro expansion, there have been no changes in the distribution of cards per rarity.

* Note that the sample size for Goblins vs Gnomes & Knights of the Frozen Throne are probably too small to be statistically relevant.

Due to how cards are generated (with the guarantee of at least one Rare or better in any pack, plus the existence of a "Pity timer" for Epic and Legendary cards), the chance of finding at least one card of any given rarity cannot be simply mathematically computed from the numbers above. However, for all pack openings since the TGT expansion the card rarities in any individual pack have been recorded. With these data, it is possible to determine the chances for these events:

Golden cards
The data from Marinconz does not include details of regular vs. golden opened in the packs. However, all other studies did include this data. After excluding the 5,000 cards from Marinconz' study, this results in the following probabilities of finding regular or golden cards of any rarity when opening packs. (For readability, the totals and the percentages are split over two separate tables):

Disregarding the data from GvG (which is statistically irrelevant because of the small sample size), it appears that the chance of receiving a golden common card has been slightly increased as of the Old Gods expansion, while simultaneously lowering the chance of a regular common card. In other words, the chance of a common is unchanged, but any common card generated has an increased chance to be golden.

A different way to look at the data is to compute, for any given rarity, the ratio of regular versus golden cards. This is shown in the next table:

This data again shows the increased chance of a Common card being golden since the Old Gods expansion. The seemingly erratic changes in the chance of a Legendary card being golden are probably a result of the relatively low amount of legendaries in the data, making the data statistically less trustworthy. However, it cannot be ruled out that the rules for generating a Legendary as golden or regular have been changed by Blizzard.

Class distribution
Only a single data set (the HearthSim data) tracked the class of the cards opened in addition to their rarity. Fortunately, this data set by itself is large enough for statistical relevant. However, this obviously means that there is no way to verify whether there have been changes in distribution across the classes over time, and whether the same pattern applies for expansions other than TGT.

The table below shows, per rarity and by class, the average number of times each card was opened. (Example: A total of 3,227 Common Mage cards were opened; since the TGT expansion includes 3 Common Mage cards the average number per card is 1,075.67).

The variations in the numbers are all within the boundaries of expected statistical variance. This suggests that the pack opening algorithm does not favor any specific class, nor neutral cards over class-speecific cards. However, that does not mean that there is an equal chance of finding any class or neutral; it means that any card of a given rarity is equally likely to be found. Since TGT (like all other expansions) has more neutral cards than it has class-specific cards, the chance of getting a neutral card is still higher.

June 5, 2014: Steve Marinconz
On June 5th 2014 Steve Marinconz published the following results in an article on Kotaku.com. The data was collected by aggregating the results of numerous card pack opening videos found online, with a total of 1,000 packs. The study used only videos filmed in the last two months.

''* NOTE: The data in this row is as published in the article, but appears to be incorrect. According to these numbers, the chance of finding at least one Rare or better card in a pack is (73.11 + 19.73 + 6.33) = 99.17%, which is inconsistent with the guarantee of at least one Rare or better card. Apparently Marinconz computed these figures from the "Percentage of total" chances, based on the assumption of a flat distribution; however the "at least 1 Rare or better" guarantee invalidates this assumption and hence these numbers.''

Based upon this data, Marinconz provided some interesting 'fun facts'. While these are based on the results of this single, relatively small study, the closeness of the study's results to those of other and larger studies suggests that the below information should still be relatively accurate, at least for the lower rarities.


 * The chances of getting a pack with any 5 legendary cards is one in a million
 * The chances of getting a pack with any 5 golden legendary cards is 1 in 3.2 billion
 * There's a 0.04% (that is, 1 in 2,500) probability of getting 2 legendaries in a single pack
 * The probability of getting a pack with only one common card is about ~0.80%
 * There's a 16.26% (slightly less than 1 in 6) probability of getting a pack with any golden card
 * Only 2.19% of common cards were golden, while 7.69% of legendaries were
 * The average $50 purchase of 40 packs will be worth about 3,600 Arcane Dust
 * The most common distribution was a '4100' - 4 commons and 1 rare - accounting for 61% of packs opened
 * The second most common distribution was a '3200' - 3 commons and 2 rares - accounting for 12.2% of packs opened

Unfortunately, Marinconz only posted aggregated data. Without data about individual packs, it is not possible to use this data for the "Probability of at least 1 per pack" table in the Meta-study. Also, since Steve didn't publish the exact number of golden cards, this study has also been excluded from any of the tables representing the chance of golden cards.

August 2014: E. R. Kjellgren
In August 2014 E. R. Kjellgren published an investigation into the rarities of cards found in card packs. This was achieved by collecting user data from forums regarding the contents of 11,359 different card packs. The author notes that the investigation suffered from two main problems: the information collected was anonymous and its accuracy cannot be guaranteed; and the sample size, while adequate for the lower rarities, is still smaller than might be desired for the higher rarities. Kjellgren also divided rarities into golden and regular versions.

Based on the data below, the average card's dust value is 21.51 dust. The average pack's dust value is 107.54.

The data showed golden cards to be on average around 30 times less common than regular cards. However, the proportion of golden and regular versions varied substantially by rarity. The author also notes that the sample sizes for the higher golden rarities are too small to be considered conclusive.

Unfortunately, Kjellgren only posted aggregated data. Without data about individual packs, it is not possible to use this data for the "Probability of at least 1 per pack" table in the Meta-study.

February 12, 2015: Amaz opens 400 GVG Packs
Sources: YouTube - Reddit


 * The average card's dust value is 21.22 dust. The average pack's dust value is 106.10.

Percentage of cards of each rarity that are golden:

Unfortunately, the sources for this pack opening only include aggregated data. Without data about individual packs, it is not possible to use this data for the "Probability of at least 1 per pack" table in the Meta-study.

August 29, 2015: HearthSim compiles 15,109 TGT Packs
Sources: Reddit (initial post) - Reddit (update) - HearthSim - Raw CSV data


 * The average card's dust value is 19.65 dust. The average pack's dust value is 98.25.

Percentage of cards of each rarity that are golden:

April 28, 2016: Kripparian opens 713 Old Gods Packs
Sources: Youtube - Raw data


 * The average card's dust value is 21.11 dust. The average pack's dust value is 105.54.

Percentage of cards of each rarity that are golden:

April 28, 2016: Amaz opens 413 Old Gods Packs
Sources: Youtube - Raw data


 * The average card's dust value is 20.33 dust. The average pack's dust value is 101.63.

Percentage of cards of each rarity that are golden:

December 1, 2016: Kripparian opens 896 Gadgetzan Packs (Before Tri-Class Bug Hotfix)
Sources: YouTube - Raw data


 * The average card's dust value is 20.73 dust. The average pack's dust value is 103.63.
 * The "tri-class bug" was a time when, during the opening day for Mean Streets of Gadgetzan, tri-class cards had a higher chance of being opened from packs than other cards.
 * The raw data here was collected from the original Twitch VOD, not the YouTube video referenced above. It is unknown whether the YouTube video catches all of the pack openings, since there were a lot of segues in-between pack openings, so the creator of the YouTube video might not have caught them all.
 * Of the 896 packs, 6 were from the 3 promo quests.

Percentage of cards of each rarity that are golden:

December 1-2, 2016: Kripparian opens 450 Gadgetzan Packs (After Tri-Class Bug Hotfix)
Sources: YouTube (end of video, first 300 packs) - Raw data


 * The average card's dust value is 21.00 dust. The average pack's dust value is 104.99.
 * YouTube video should include the first 300 of the pack openings. The last 150 pack openings were opened the day after the YouTube video was created.
 * Data was recorded by watching the original two Twitch VODs, not the YouTube video.

Percentage of cards of each rarity that are golden:

April 6, 2017: Kripparian opens 1101 Journey to Un'Goro Packs
Sources: Twitch VOD (will eventually be deleted) - Raw data


 * The average card's dust value is 21.57 dust. The average pack's dust value is 107.86.
 * The data shows that golden Rares, all Epics, and all Legendary cards appear more frequently in Journey to Un'Goro when compared to the data in HearthSim's August 2015 study for The Grand Tournament.
 * The data shown here is somewhat similar to the data gathered during Whispers of the Old Gods, with the exception of golden Rares appearing more in Journey to Un'Goro than in Whispers of the Old Gods.
 * Data was recorded by watching the original Twitch VOD.
 * Refer to Kripp's YouTube channel for video footage of the card pack openings when the Twitch video eventually gets deleted.

Percentage of cards of each rarity that are golden:

April 8, 2017: N. Millar opens 1256 Journey to Un'Goro Packs
Sources: YouTube - Raw data


 * The average card's dust value is 20.88 dust. The average pack's dust value is 104.38.
 * Data was recorded by watching the YouTube video.

Percentage of cards of each rarity that are golden:

Prior to Patch 17.0.0.44222 (2020-03-26)
Prior to Patch 17.0.0.44222 implemented on March 26th 2020, the duplicate protection rule only applied to legendaries when opening card packs. The following are some statistics from that period:
 * Pack opening
 * Opening 100 packs from an expansion set was roughly equivalent to obtaining 75% of the cards in that set.
 * 100 packs is approximately (98/98) Commons, (64/72) Rares, (20/54) Epics, and (4.5/20) Legendaries (taking Mean Streets of Gadgetzan as the example set).
 * Expected leftover dust for a set
 * The expected leftover dust from buying a specific number of packs for a set will be defined here as the amount of dust a player receives when he/she has opened "n" packs for a set, and has disenchanted all extra copies.
 * The amount of expected leftover dust a player receives from opening 70 packs is about 1600 dust, or about 23 leftover dust per pack.
 * The amount of expected leftover dust a player receives from opening 100 packs is about 3000 dust, or about 30 leftover dust per pack.
 * Moreover, if the player decides to disenchant more cards (cards which are not extras) which the player presumes to have no use for, then he/she will be expected to obtain more dust than the values calculated above.
 * A player can approximately calculate his/her leftover dust for a set by doing the math themselves, given the number of packs they purchased and given the amount of dust before and after the purchase. Include the disenchantment of extra golden cards before observing the dust difference on the "Mass Disenchant" button.