Discover Calculator w/Math Proof v4.0
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Discover Probability Calculator
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Sheet 1: Probability Calculator
Discover Card
Stonehill Defender
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Sheet 3: Mathematical DocumentationNeutral Outs2
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Class Outs3
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Color CodingClass Weight4
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User Defined VariableStatic VariableResult
Neutral Cards
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Class Cards5
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How To Use
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Make a copy of the spreadsheet in order to gain access ([File] -> [Make a copy...]). Requires log-in.P(outs>0) (Probability of hitting any of your outs)56.03%
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Use the drop-down menus in the yellow cells to select Format and Discover Card.
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Class will be automatically suggested upon selection of Discover Card; change if necessary.
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Input number of Neutral/Class Outs. Results are updated automatically within seconds.Average amount of class cards discovered0.96
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FAQ
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Q: What about the rest of the Discover cards?Probability of getting a specific neutral card5.09%
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A: Several Discover cards are unaffected by the weighting of class cards due to the non-existence of
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neutral spells/hero powers (e.g. Primordial Glyph) and thus omitted from this calculator. Calculations
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related to these cards follow the same rules/distribution as cards like Arcane Intellect etc.Probability of getting a specific class card19.27%
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Q: How are these results calculated? Where are the formulas?
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A: Most of the calculations happen in the apps script bound to this spreadsheet. This is the GoogleProbability of getting at least 1 class card71.13%
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equivalent of macros in Excel. To view the script, go to [Tools] -> [Script Editor...]. Mathematical
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documentation can be found in sheet #3; 'Math' (active sheet may be changed in the bottom taskbar).
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Probability of getting all class cards2.20%
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Q: It's not working?
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A: Try deleting your copy and creating a new one. Only the yellow cells are meant to be edited.
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Q: What are "outs"?
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A: Outs is poker terminology. A set of cards can be viewed as consisting of two subsets - the set of
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cards that grant you "success" if drawn, and the set of cards that don't. The former are your outs.
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Changelog
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v2.009.04.2016Updated to reflect Old Gods and Karazhan releases.
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v3.004.05.2017Updated to reflect Gadgetzan and Un'Goro releases.
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v3.104.06.2017Overhauled all text to be up-to-date.
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v3.208.10.2017Updated to reflect patch 8.4 Elemental tag changes.
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v4.008.10.2017Updated to reflect The Frozen Throne release.
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Example Use Case 1
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Q: Jim's opponent just got a clutch Tirion off of Stonehill Defender. How lucky was the opponent?
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A: Select appropriate Format, Card and Class. See "Probability of getting a specific class card"
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-- Note: Setting Neutral Outs to 0 and Class Outs to 1 results in P(outs>0) yielding the same result.
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Example Use Case 2
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Q: Alice is 1 damage off lethal as Murloc Paladin. How likely is Primalfin Lookout to discover lethal?
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-- 5 (standard) Murlocs grant 1+ damage; all are neutral: Oracle, Sniper, Warrior, Hunter, Warleader.
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-- Assuming Alice has a Bluegill Warrior in hand, being her only Murloc, Grimscale Chum is also an out.
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A: Select Format, Card and Class. Set Neutral Outs to 5 and Class Outs to 1. See P(outs>0)
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Q: When Lookout fails to discover lethal, how likely is Alice to tie with Hydrologist into Eye f.a. Eye?
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A: From Use Case 2 we know that Alice discovers lethal 70.33% of the time, meaning she fails 29.67%
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of the time. Now we want to calculate the proportion of ties and losses within those 29.67%. This is a
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2-step process. First - How likely is Alice to discover Hydrologist when lethal fails? Secondly - How
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likely is Hydrologist to discover Eye f.a. Eye? The Latter is easy to calculate: There are 5 Standard
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Paladin secrets, meaning Hydrologist discovers EfaE 3/5 = 60% of the time. The former require us to
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calculate the odds of discovering a specific class card in the hypothetical scenario where the 6 original
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outs no longer exists in the draw pool. In order to achieve this we have to adjust the card counts
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automatically provided by the card DB as static variables (blue cells). We reduce the neutral card count
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from 14 to 9, and the class card count from 4 to 3. Finally we set Neutral Outs to 0 and Class Outs to 1.
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We learn that Hydrologist is discovered 52.30% of the 29.67% of times Alice failed to discover lethal,
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which in turn results in a tie 60% of the time. 0.6 * 0.523 = 31.38% - the proportion of ties within the
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29.67% of time that lethal failed to be found, meaning the game is lost 68.62% of the time lethal failed
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to be found. Finally we have the complete knowledge of the expected value of Alice' proposed play:
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Playing Primalfin Lookout results in a win 70.33% of the time, a tie 0.2967 * 0.3138 = 9.38% of the time,
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and a loss 0.2967 * 0.6862 = 20.36% of the time.
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Example Use Case 4 (Warning! Memes ahead!)
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Q: xRoachboyx is grinding rank 26 with his dank burgle Rogue deck when he happens to queue into an
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Explore Un'Goro Warrior. "LOL, playing a worse Renounce Darkness in 2017, what a scrub. This'll be
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over quick." He proceeds to start his crusade of theft and robbery, never forgetting a single obligatory
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"Thank you."-emote as he gathers cards from his opponent's class. Putting in the hours to get the
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Maiev Shadowsong Rogue hero was worth it, afterall. Suddenly, the most magical of things occurs:
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Having stolen a Choose Your Path card (the discover tokens produced by Explore Un'Goro), he finds
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himself looking at a perfect trifecta of exactly the 3 Rager's left in Standard offered as the discover
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options. Wasting no time, he uploads a screenshot of the event to Imgur and proceeds to post on
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Reddit's /r/Hearthstone. It doesn't even take 5 minutes for the post to reach the front page of the
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subreddit. A distinct distaste for personal hygiene isn't the only thing the wretched, lost, souls of
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/hearthstone/new/ share with Gollum - they also share his flare for preciously rare RNG. 6 minutes in,
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the first comment appears. User Ayachan69 proclaims "wooow, that's amazing!!1 what are the odds??!"
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User KarmaWhore123, always lurking /new/ ready to pounce at a chance for some of that juicy, juicy,
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karma, eyes an opportunity. He Google's "discover probability" and finds this very calculator, but finds
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himself in a peculiar position - how can he use it to calculate this very scenario?! Unable to come up
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with a solution, he simply inputs some random numbers and posts a reply to Ayachan69, selling one of
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the results off as the actual probability and making sure to cite the calculator as his source. If there's
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one thing his years of karma whoring has taught him, it's that Reddit users get particularily wet
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whenever a comment cites a source. Not like anyone cares to verify anyways. Their comments quickly
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garners hundreds of upvotes from unsuspecting Redditors, and it doesn't take long for the upvote count
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becomes a self-fulfilling prophecy in and of it's own; users assuming the vote count indicates others
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have already verified Karmawhore123's assertions; proceeding to further fuel the upvotes. An hour
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passes, when suddenly another peculiar event occurs - someone actually thinks to check the solution.
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It is user TotallyNotASmartass. He knows there's no way the correct probability is as high as 4.20% as
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proclaimed by Karmawhore123 and proceeds to calculate the probability on his own. Smartass doesn't