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firagadam

Cross-V2

firagadam
Nov 25th, 2012
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  1. [3:16:55 PM] gustavo tani: and here we go
  2. [3:17:25 PM] gustavo tani: Alice meet, hiro, hiro meet alice, the one who made the blog and does fuckloads amount of research on that
  3. [3:17:28 PM] Alice Brunhild: So there seems to be some doubt about the probability to crossride
  4. [3:18:33 PM] Alice Brunhild: The probability that you crossride in a given game is the probability that you normal ride the previous Grade 3 on Turn 3. The probability that you normal ride any given 4-copy Grade 3 in any given deck without assistance is 68%. You can find this number yourself by using a hypergeometric calculator. You just need the correct inputs
  5. [3:19:48 PM] Alice Brunhild: First you have to find all the chances that you don't get that Grade 3 by your Turn 3 ride phase. That would be the chance you don't draw it in opening, chance you don't draw it in mulligan, and the chance you miss it in 2 draw phases and a drive check.
  6. [3:20:14 PM] Hiro: what about the chances that it goes to damage?
  7. [3:20:23 PM] Alice Brunhild: Once you find all the chances (I have them), you multiply the chances to fail and subtract the result from 1. That's the chance to successfully ride the previous form Grade 3 and therefore crossride
  8. [3:20:49 PM] Alice Brunhild: There are, on average, 2 chances to hit the damage zone with one copy. Those chances are just over 90% failures each.
  9. [3:20:58 PM] Alice Brunhild: That is all factored in
  10. [3:21:02 PM] Alice Brunhild: So here's how you do it
  11. [3:21:26 PM] Alice Brunhild: http://stattrek.com/online-calculator/hypergeometric.aspx
  12. [3:21:43 PM] Alice Brunhild: Population size is 49. That's your deck size after taking out your starting vanguard.
  13. [3:22:09 PM] Alice Brunhild: Number of successes in population is 4. Maximum number of copies of the proper Grade 3
  14. [3:22:23 PM] Alice Brunhild: Sample size is 5. Our first result is just drawing the opening hand
  15. [3:22:37 PM] Alice Brunhild: We only care about getting at least 1 copy. So successes is 1
  16. [3:23:09 PM] Alice Brunhild: Now you have to look for the FAILURE chance. The reason is you have to multiply all the total failure chances at the end
  17. [3:23:28 PM] Alice Brunhild: So that's the Probability of getting less than 1 copy in 5 cards. The second box from the top shows that
  18. [3:23:33 PM] Alice Brunhild: P(X < 1)
  19. [3:23:40 PM] Alice Brunhild: 0.64 or 64%
  20. [3:23:53 PM] Alice Brunhild: See in the article where it says 64%? http://vmundi.blogspot.com/2012/07/everything-about-ride-chains.html
  21. [3:24:14 PM] Alice Brunhild: It's in the section that discusses vanilla Grade 3 ride chain probabilities.
  22. [3:25:18 PM] Alice Brunhild: Now you have to check for mulligan. You can't sacrifice your rides just to get the correct specific Grade 3. Therefore, if you mulligan 2, that means you got grades 1, 2, and 3 already. And any mulligan less than 2 means your hand has all the rides and is a good hand otherwise so those instances don't count. The most average number of mulligans is 3. So we calculate mulligan 3 for this.
  23. [3:26:17 PM] Alice Brunhild: Now you have to do a new calculation. Plug in all the numbers. Sample size 3, success check 1, number of successes 4, population is 49-2 = 47 (you kept 2 cards out)
  24. [3:26:34 PM] Alice Brunhild: Again you look for the chance of failure
  25. [3:26:55 PM] Alice Brunhild: That's going to be around 69%
  26. [3:27:10 PM] Alice Brunhild: Now you have to assume you can wait up until the last second before your Turn 3 ride phase.
  27. [3:27:38 PM] Alice Brunhild: each chance to draw, damage, or drive check is just over a 90% failure rate. Since fractions of a percent mean basically nothing, just count each of those as 90%
  28. [3:28:27 PM] Alice Brunhild: Multiply all the calculations together.
  29. [3:28:46 PM] Alice Brunhild: The chance that you don't misride and you get the proper Grade 3 in time is 68%.
  30. [3:29:45 PM] Alice Brunhild: You can find this with the 3 instances of 0.9 that you multiply (0.9**3 or cubed) * 0.64 (opening * 0.69 (mulligan) = 0.68
  31. [3:30:37 PM] Hiro: i came at approximately 65 actualy
  32. [3:30:43 PM] Alice Brunhild: I left off the explanation where I subtract it from 1
  33. [3:30:43 PM] Hiro: but is still prety acurate
  34. [3:30:50 PM] Alice Brunhild: 1 - (0.64 * 0.69 * 0.73)
  35. [3:31:09 PM] Hiro: i have to say
  36. [3:31:11 PM] Hiro: im impressed
  37. [3:31:13 PM] Hiro: numbers dont lie
  38. [3:31:19 PM] Alice Brunhild: 0.677632 exactly
  39. [3:31:27 PM] Alice Brunhild: Rounded up
  40. [3:31:30 PM] Alice Brunhild: Welp thanks
  41. [3:31:42 PM] Alice Brunhild: All of that is in the article though
  42. [3:31:44 PM] Hiro: i came to 0,6454144
  43. [3:31:53 PM] Alice Brunhild: What were your multiplications
  44. [3:32:06 PM] Alice Brunhild: because 1 - (0.64 * 0.69 * 0.73) = my answer
  45. [3:32:48 PM] Alice Brunhild: If you wonder where 0.73 comes from, it's the simplification of 0.9 cubed. Which is 0.729 rounded up to 0.73
  46. [3:32:53 PM] Hiro: (.64 * .76 * .90³) - 1
  47. [3:33:10 PM] Hiro: the second were u say .69
  48. [3:33:25 PM] Hiro: i sampled in the calculator but got .76
  49. [3:33:51 PM] Hiro: with a 47 population size, 4 sucess, 3 sample and sucess in sample
  50. [3:33:58 PM] Hiro: 1* sucess in sample
  51. [3:34:06 PM] Hiro: did i got it wrong?
  52. [3:35:14 PM] Alice Brunhild: Oh you know what, I told you the mulligan 4. The reason being is that mulligan 3 was the minimum and 4 was the most probable for that type of calculation
  53. [3:35:23 PM] Alice Brunhild: Mulligan 4 is 0.59
  54. [3:35:27 PM] Alice Brunhild: *0.69
  55. [3:35:41 PM] Alice Brunhild: Any case, you're looking at a 2/3 or higher chance of getting it.
  56. [3:36:07 PM] Hiro: makes sence, correct it just now
  57. [3:36:24 PM] Hiro: yeah numbers dont lie and cross-ride is op =/
  58. [3:36:41 PM] Alice Brunhild: That's pretty OP for a costless defense
  59. [3:37:16 PM] Alice Brunhild: Unfortunately, that little 13k defense now means that there's no way to balance them. The other skill could say "You get to make funny faces for the rest of the fight" and it would still be OP
  60. [3:37:48 PM] Alice Brunhild: And the Platinum Ezel is worse. I forget the exact number, but the superior ride for Ezel increases the probability to closer to 86%
  61. [3:38:12 PM] Alice Brunhild: Just FYI. with a normal deck, the best possible grade ratio to never miss a ride will only give you 83% total chance.
  62. [3:38:27 PM] Alice Brunhild: Yet Blond Ezel has 86% to both not miss any rides AND crossride
  63. [3:38:57 PM] Hiro: the perfect way to break a balance in Clans power
  64. [3:39:08 PM] Hiro: and i play as Spike Brothers
  65. [3:39:17 PM] Hiro: so that realy makes me sad =/
  66. [3:39:30 PM | Edited 3:39:48 PM] gustavo tani: Alice plays Spikes too man
  67. [3:39:56 PM] Alice Brunhild: Unfortunately Spikes get the shaft too. only Juggernaut can reach 3 stages versus crossride defense
  68. [3:40:17 PM] Alice Brunhild: All the other units like Brakki and Reckless just become -1 to hit 2 stages
  69. [3:40:36 PM] Hiro: Reckless can't even hit without boost
  70. [3:41:49 PM] Alice Brunhild: Oh there's that too. None of them can hit 2 stages without a boost now. Juggs used to could versus an 11k
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