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1 | Spreadsheet Information | Discover Probability Calculator | ||||||||||||||||||||||||

2 | ||||||||||||||||||||||||||

3 | Author | /u/MetronomeB | Version | 4.0 | Discussion | Reddit Thread | Please input your scenario in the yellow cells below (Note: drop-down menus). | |||||||||||||||||||

4 | ||||||||||||||||||||||||||

5 | Table of Contents | Format | Standard | |||||||||||||||||||||||

6 | Sheet 1: Probability Calculator | Discover Card | Stonehill Defender | |||||||||||||||||||||||

7 | Sheet 2: Card Count Database | Class | Paladin | |||||||||||||||||||||||

8 | Sheet 3: Mathematical Documentation | Neutral Outs | 2 | |||||||||||||||||||||||

9 | Class Outs | 3 | ||||||||||||||||||||||||

10 | Color Coding | Class Weight | 4 | |||||||||||||||||||||||

11 | User Defined Variable | Static Variable | Result | Neutral Cards | 40 | |||||||||||||||||||||

12 | Class Cards | 5 | ||||||||||||||||||||||||

13 | How To Use | |||||||||||||||||||||||||

14 | 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% | |||||||||||||||||||||||

15 | Use the drop-down menus in the yellow cells to select Format and Discover Card. | |||||||||||||||||||||||||

16 | Class will be automatically suggested upon selection of Discover Card; change if necessary. | |||||||||||||||||||||||||

17 | Input number of Neutral/Class Outs. Results are updated automatically within seconds. | Average amount of class cards discovered | 0.96 | |||||||||||||||||||||||

18 | ||||||||||||||||||||||||||

19 | FAQ | |||||||||||||||||||||||||

20 | Q: What about the rest of the Discover cards? | Probability of getting a specific neutral card | 5.09% | |||||||||||||||||||||||

21 | A: Several Discover cards are unaffected by the weighting of class cards due to the non-existence of | |||||||||||||||||||||||||

22 | neutral spells/hero powers (e.g. Primordial Glyph) and thus omitted from this calculator. Calculations | |||||||||||||||||||||||||

23 | related to these cards follow the same rules/distribution as cards like Arcane Intellect etc. | Probability of getting a specific class card | 19.27% | |||||||||||||||||||||||

24 | ||||||||||||||||||||||||||

25 | Q: How are these results calculated? Where are the formulas? | |||||||||||||||||||||||||

26 | A: Most of the calculations happen in the apps script bound to this spreadsheet. This is the Google | Probability of getting at least 1 class card | 71.13% | |||||||||||||||||||||||

27 | equivalent of macros in Excel. To view the script, go to [Tools] -> [Script Editor...]. Mathematical | |||||||||||||||||||||||||

28 | documentation can be found in sheet #3; 'Math' (active sheet may be changed in the bottom taskbar). | |||||||||||||||||||||||||

29 | Probability of getting all class cards | 2.20% | ||||||||||||||||||||||||

30 | Q: It's not working? | |||||||||||||||||||||||||

31 | A: Try deleting your copy and creating a new one. Only the yellow cells are meant to be edited. | |||||||||||||||||||||||||

32 | ||||||||||||||||||||||||||

33 | Q: What are "outs"? | |||||||||||||||||||||||||

34 | A: Outs is poker terminology. A set of cards can be viewed as consisting of two subsets - the set of | |||||||||||||||||||||||||

35 | cards that grant you "success" if drawn, and the set of cards that don't. The former are your outs. | |||||||||||||||||||||||||

36 | ||||||||||||||||||||||||||

37 | Changelog | |||||||||||||||||||||||||

38 | v1.0 | 11.23.2015 | Spreadsheet release. | |||||||||||||||||||||||

39 | v1.1 | 11.24.2015 | Hotfix addressing an issue with Google's spreadsheet platform. | |||||||||||||||||||||||

40 | v2.0 | 09.04.2016 | Updated to reflect Old Gods and Karazhan releases. | |||||||||||||||||||||||

41 | v3.0 | 04.05.2017 | Updated to reflect Gadgetzan and Un'Goro releases. | |||||||||||||||||||||||

42 | v3.1 | 04.06.2017 | Overhauled all text to be up-to-date. | |||||||||||||||||||||||

43 | v3.2 | 08.10.2017 | Updated to reflect patch 8.4 Elemental tag changes. | |||||||||||||||||||||||

44 | v4.0 | 08.10.2017 | Updated to reflect The Frozen Throne release. | |||||||||||||||||||||||

45 | ||||||||||||||||||||||||||

46 | Example Use Case 1 | |||||||||||||||||||||||||

47 | Q: Jim's opponent just got a clutch Tirion off of Stonehill Defender. How lucky was the opponent? | |||||||||||||||||||||||||

48 | A: Select appropriate Format, Card and Class. See "Probability of getting a specific class card" | |||||||||||||||||||||||||

49 | -- Note: Setting Neutral Outs to 0 and Class Outs to 1 results in P(outs>0) yielding the same result. | |||||||||||||||||||||||||

50 | ||||||||||||||||||||||||||

51 | Example Use Case 2 | |||||||||||||||||||||||||

52 | Q: Alice is 1 damage off lethal as Murloc Paladin. How likely is Primalfin Lookout to discover lethal? | |||||||||||||||||||||||||

53 | -- 5 (standard) Murlocs grant 1+ damage; all are neutral: Oracle, Sniper, Warrior, Hunter, Warleader. | |||||||||||||||||||||||||

54 | -- Assuming Alice has a Bluegill Warrior in hand, being her only Murloc, Grimscale Chum is also an out. | |||||||||||||||||||||||||

55 | A: Select Format, Card and Class. Set Neutral Outs to 5 and Class Outs to 1. See P(outs>0) | |||||||||||||||||||||||||

56 | ||||||||||||||||||||||||||

57 | Example Use Case 3 (Warning! Advanced shit ahead!) | |||||||||||||||||||||||||

58 | Q: When Lookout fails to discover lethal, how likely is Alice to tie with Hydrologist into Eye f.a. Eye? | |||||||||||||||||||||||||

59 | A: From Use Case 2 we know that Alice discovers lethal 70.33% of the time, meaning she fails 29.67% | |||||||||||||||||||||||||

60 | of the time. Now we want to calculate the proportion of ties and losses within those 29.67%. This is a | |||||||||||||||||||||||||

61 | 2-step process. First - How likely is Alice to discover Hydrologist when lethal fails? Secondly - How | |||||||||||||||||||||||||

62 | likely is Hydrologist to discover Eye f.a. Eye? The Latter is easy to calculate: There are 5 Standard | |||||||||||||||||||||||||

63 | Paladin secrets, meaning Hydrologist discovers EfaE 3/5 = 60% of the time. The former require us to | |||||||||||||||||||||||||

64 | calculate the odds of discovering a specific class card in the hypothetical scenario where the 6 original | |||||||||||||||||||||||||

65 | outs no longer exists in the draw pool. In order to achieve this we have to adjust the card counts | |||||||||||||||||||||||||

66 | automatically provided by the card DB as static variables (blue cells). We reduce the neutral card count | |||||||||||||||||||||||||

67 | 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. | |||||||||||||||||||||||||

68 | We learn that Hydrologist is discovered 52.30% of the 29.67% of times Alice failed to discover lethal, | |||||||||||||||||||||||||

69 | which in turn results in a tie 60% of the time. 0.6 * 0.523 = 31.38% - the proportion of ties within the | |||||||||||||||||||||||||

70 | 29.67% of time that lethal failed to be found, meaning the game is lost 68.62% of the time lethal failed | |||||||||||||||||||||||||

71 | to be found. Finally we have the complete knowledge of the expected value of Alice' proposed play: | |||||||||||||||||||||||||

72 | Playing Primalfin Lookout results in a win 70.33% of the time, a tie 0.2967 * 0.3138 = 9.38% of the time, | |||||||||||||||||||||||||

73 | and a loss 0.2967 * 0.6862 = 20.36% of the time. | |||||||||||||||||||||||||

74 | ||||||||||||||||||||||||||

75 | Example Use Case 4 (Warning! Memes ahead!) | |||||||||||||||||||||||||

76 | Q: xRoachboyx is grinding rank 26 with his dank burgle Rogue deck when he happens to queue into an | |||||||||||||||||||||||||

77 | Explore Un'Goro Warrior. "LOL, playing a worse Renounce Darkness in 2017, what a scrub. This'll be | |||||||||||||||||||||||||

78 | over quick." He proceeds to start his crusade of theft and robbery, never forgetting a single obligatory | |||||||||||||||||||||||||

79 | "Thank you."-emote as he gathers cards from his opponent's class. Putting in the hours to get the | |||||||||||||||||||||||||

80 | Maiev Shadowsong Rogue hero was worth it, afterall. Suddenly, the most magical of things occurs: | |||||||||||||||||||||||||

81 | Having stolen a Choose Your Path card (the discover tokens produced by Explore Un'Goro), he finds | |||||||||||||||||||||||||

82 | himself looking at a perfect trifecta of exactly the 3 Rager's left in Standard offered as the discover | |||||||||||||||||||||||||

83 | options. Wasting no time, he uploads a screenshot of the event to Imgur and proceeds to post on | |||||||||||||||||||||||||

84 | Reddit's /r/Hearthstone. It doesn't even take 5 minutes for the post to reach the front page of the | |||||||||||||||||||||||||

85 | subreddit. A distinct distaste for personal hygiene isn't the only thing the wretched, lost, souls of | |||||||||||||||||||||||||

86 | /hearthstone/new/ share with Gollum - they also share his flare for preciously rare RNG. 6 minutes in, | |||||||||||||||||||||||||

87 | the first comment appears. User Ayachan69 proclaims "wooow, that's amazing!!1 what are the odds??!" | |||||||||||||||||||||||||

88 | User KarmaWhore123, always lurking /new/ ready to pounce at a chance for some of that juicy, juicy, | |||||||||||||||||||||||||

89 | karma, eyes an opportunity. He Google's "discover probability" and finds this very calculator, but finds | |||||||||||||||||||||||||

90 | himself in a peculiar position - how can he use it to calculate this very scenario?! Unable to come up | |||||||||||||||||||||||||

91 | with a solution, he simply inputs some random numbers and posts a reply to Ayachan69, selling one of | |||||||||||||||||||||||||

92 | the results off as the actual probability and making sure to cite the calculator as his source. If there's | |||||||||||||||||||||||||

93 | one thing his years of karma whoring has taught him, it's that Reddit users get particularily wet | |||||||||||||||||||||||||

94 | whenever a comment cites a source. Not like anyone cares to verify anyways. Their comments quickly | |||||||||||||||||||||||||

95 | garners hundreds of upvotes from unsuspecting Redditors, and it doesn't take long for the upvote count | |||||||||||||||||||||||||

96 | becomes a self-fulfilling prophecy in and of it's own; users assuming the vote count indicates others | |||||||||||||||||||||||||

97 | have already verified Karmawhore123's assertions; proceeding to further fuel the upvotes. An hour | |||||||||||||||||||||||||

98 | passes, when suddenly another peculiar event occurs - someone actually thinks to check the solution. | |||||||||||||||||||||||||

99 | It is user TotallyNotASmartass. He knows there's no way the correct probability is as high as 4.20% as | |||||||||||||||||||||||||

100 | proclaimed by Karmawhore123 and proceeds to calculate the probability on his own. Smartass doesn't |

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