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The Mathematics of Love Mixology by iloath

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Feb 14th, 2019
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  1. The Mathematics of Love Mixology by iloath
  2.  
  3. This assumes you follow mus test-> mys test-> mox test for HCCS
  4.  
  5. The last love potion decision point is the mox stats service quest, we must determine whether to (A) use the love potion on hand or (B) not. We use it if the mox component of the potion is positive which happens in 21 of the 42 scenarios as Moxie (de)buff = +105 - (N mod 42)*5. We can calculate the expected stat gain during the mox test if we reroll the potion before the mox test and discard negative results, which is 27.5.
  6.  
  7. https://pastebin.com/Tiph1kmC
  8.  
  9. Now consider the previous test(mys), just before we take the mys test we must decide whether to (A) use potion on test and reroll for mox or (B) save potion, saving potion can lead to either (B1) using for mox test or (B2) discarding the potion. The expected return in the future for (A) is the current love potion's mys and the average gain next quest where we have a rerolled potion, this is the 27.5 calculated above as we discard the potion is the mox is negative. The expected return in the future for (B1) is the current potion's mox it can be negative since we cannot reroll if we don't use for this test. The expected return in the future for (B2) is obviously 0. The optimal decision here is obviously to pick the choice with the highest return given our current potion. Calculate the expected return for all 3 choice and pick the highest. [max(mys+27.5,mox,0.0)]
  10.  
  11. A use on mys E(mox) = 27.5 E(mys+mox)=mys+27.5
  12. B1 use on mox(skip mys&use on mox) E(mox) = mox E(mys+mox)=mox
  13. B2 discard/fold(skip mys&mox) E(mox) = 0 E(mys+mox)=0
  14.  
  15. Now consider if we reroll the potion before the mys test, there are 35*42 scenarios as Mysticality (de)buff = +102 - (N mod 35)*6 and we also take mox into consideration as we save the potion is mys is too negative or mox is too high. We can calculate the best choice for each of the 35*42 scenarios and the expected return. We can obtain the expected stat gain during the mys AND mox test if we reroll the potion before the mys test and pick OPTIMAL results, which is 56.43333333 ~= 56.5.
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  17. Now consider the previous test(mus), just before we take the mus test we must decide whether to (A) use potion on test and reroll for mys and mox or (B) save potion, saving potion can lead to either (B1) using for mys test or (B2) using for mox test or (B3) discarding the potion. The expected return in the future for (A) is the current love potion's mus and the average gain in future quest where we have a rerolled potion, this is the 56.5 calculated above as we pick optimal choices. The expected return in the future for (B1) is the current potion's mys and 27.5 from mox test since potion is rerolled by using in mys test. The expected return in the future for (B2) is obviously the current potion's mox. If the potion stats are very negative such that we can't expect to regain in the future even if you endure the lose in a stat test and reroll we can always fold and expect (B3) 0 value. The optimal decision here is obviously to pick the choice with the highest return given our current potion. Calculate the expected return for all 4 choice and pick the highest. [max(mus+56.5,mys+27.5,mox,0.0)]
  18.  
  19. A use on mus E(mus+mys+mox)=mus+56.5
  20. B1 use on mys E(mus+mys+mox)=mys+27.5
  21. B2 use on mox E(mus+mys+mox)=mox
  22. B3 fold E(mus+mys+mox)=0
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  24. Now consider if we reroll the potion before the mus test, there are 30*35*42=840 scenarios as Muscle (de)buff = +105 - (N mod 30)*7 and we also take the mys and mox into consideration as we save the potion if mus is too negative and mys or mox is very high. We can calculate the best choice for each of the 840 scenarios and the expected return. We can obtain the expected stat gain during the ALL test if we reroll the potion before the mus test and pick OPTIMAL results, which is 86.53571429 ~= 86.5.
  25.  
  26. optimal = mus %
  27. 0.423809524
  28. optimal = mys %
  29. 0.285714286
  30. optimal = mox %
  31. 0.176190476
  32. optimal = fold %
  33. 0.114285714
  34. avg E(mus+mys+mox)
  35. 86.53571429
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  37. Now blood donation is generally to quick (<20 adv) to reroll, but the all previous service quests take long enough (If you don't have many great IotM/perms) for you to reroll your love potion is they don't have bad stats, and you don't even lose adv for any negative stats in those tests. Before steam tunnel and all those service quests you have a decision which depend only on your current love potion's stats. We must decide whether to (A) use potion on test and reroll all stats or (B) save potion, saving potion can lead to either (B1) using for mus test or (B2) using for mys test or (B3) using for mox test or (B4) discarding the potion. The expected return in the future for (A) is 86.5 since we don't use any of our potion's current stats but perform future choices optimally. The expected return in the future for (B) is same as that in the mus test. Since (A) always gives a positive result we never have a reason to fold here. The optimal decision here is obviously to pick the choice with the highest return given our current potion. Calculate the expected return for all 5 choice and pick the highest. [max(86.5,mus+56.5,mys+27.5,mox,0.0)]
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  39. Now consider if we reroll the potion before the mus test, calculate the best choice for each of the 840 scenarios and the expected return. We can obtain the expected stat gain during the ALL test if we reroll the potion before the steam tunnel and pick OPTIMAL results, which is 105.2142857 ~= 105.2.
  40.  
  41. optimal = reroll%
  42. 0.438095238
  43. optimal = mus %
  44. 0.333333333
  45. optimal = mys %
  46. 0.171428571
  47. optimal = mox %
  48. 0.057142857
  49. optimal = fold %
  50. 0
  51. sum %
  52. 1
  53. avg E(mus+mys+mox)
  54. 105.2142857
  55.  
  56. Now we can do the same for the previous decision. Using 105.2 instead of 86.5. Then use the result for the previous decision again. We finally obtain the optimal solution:
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  58. Calculate your potions's expected value, use up your potion and remake after quest if your potion's expected value is lesser than the threshold.
  59. Expected Value(EV) = max(mus+56.5,mys+27.5,mox), it represents the amount of useful stats you can still expect from your love potion(s), every 30EV equals 1 adv saved on average.
  60.  
  61. threshold
  62. 7 rerolls 132.8
  63. 6 rerolls 129.8
  64. 5 rerolls 126.1
  65. 4 rerolls 121.4
  66. 3 rerolls 114.9
  67. 2 rerolls 105.2
  68. 1 rerolls 86.5
  69. b4 mus test use if mus+56.5=max(mus+56.5,mys+27.5,mox,0.0)
  70. b4 mys test use if mys+27.5=max(mys+27.5,mox,0.0)
  71. b4 mox test use if mox=max(mox,0.0)
  72.  
  73. Check the number of rerolls you have remaining here (Low IotM/Perms)
  74. START
  75. 5
  76. COIL WIRE
  77. 4
  78. MAKE MARGARITAS
  79. 3 <-if between MAKE MARGARITAS and MAKE SAUSAGE, you have 3 rerolls
  80. MAKE SAUSAGE
  81. 2
  82. REDUCE GAZELLE POPULATION (Be careful here is you have bow-legged swagger)
  83. 1
  84. STEAM TUNNELS (cannot reroll if >40 hot res)
  85. 0
  86. DONATE BLOOD
  87. 0 b4 mus test
  88. FEED CHILDREN
  89. 0 b4 mys test
  90. BUILD PLAYGROUND MAZES
  91. 0 b4 mox test
  92. FEED CONSPIRATORS
  93.  
  94.  
  95. This may be adapted for solving optimal love potion rerolling for non-CS Ascension's tower stat test.
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  97.  
  98.  
  99. If you run my 2day HCCS script (UPDATED! ONLY NEED VIP KEY & GENIE)
  100. This will all be done for you along with everything else.
  101.  
  102. 2IOTM 2DAY HCCS SCRIPT
  103. https://gitgud.io/iloath/HCCSauto/tree/master
  104.  
  105. 3IOTM 2DAY HCCS GUIDE
  106. https://www.reddit.com/r/kol/wiki/guides/iloath_hccs
  107.  
  108. 2IOTM 2DAY HCCS GUIDE
  109. https://www.reddit.com/r/kol/wiki/guides/iloath_hccs2
  110.  
  111. EXCEL CALCULATION FILE
  112. https://files.catbox.moe/47s67z.xlsx
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