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UserWiki:WhitePass

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Shroomster
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Special Upgrade analysis: (Note we are using the decimal representation for R-type bonus and for critical bonus; for simplicity examples and inequalities assume 30% critical rate with rank 1 critical and no other bonuses unless otherwise specified)

An S-type upgrade can give you a higher maximum critical damage than an R-type of the same level until:

  • Max Damage > (S-type Bonus/R-type bonus) * (1 + Critical Bonus)
  • Example, for a +3R Claymore to have a higher maximum critical damage than a +3S Claymore at rank 5 Critical Hit, the max damage with the sword must be greater than (21/0.26)*(1 + 1.10)=169.6.

An S-type upgrade will give you higher maximum damage across 10 hits (assuming 30% critical rate) than an R-type of the same level until:

  • Max Damage > ((S-type Bonus)(7 + 3(1 + Critical Bonus)))/(3(R-Type Bonus))
  • Example, for a +3R Claymore to have a higher maximum damage across 10 hits than a +3S Claymore at rank 5 Critical Hit, the max damage with the sword must be greater than ((21)(7 + 3(1 + 1.10)))/(3(0.26))=277.3.

Similarly, an S-type upgrade on a staff (wands are element specific which exacerbates the situation) will have higher maximum damage across 10 hits than an R-type upgrade of the same level until:

  • Magic Attack > (7 + 3(1 + Critical Bonus)) * (S-type Bonus)/(3*(R-type Bonus)) - (Base Spell Damage)/(Spell Constant)
  • Generally speaking, a user should have over 610 magic attack before upgrading a staff for a step 6 R-Type Bonus to do more damage for spells up to Lightning Rod. Lower magic attack is required for spells with higher base damage to spell constant ratios.

To modify the equations for a higher or lower critical rate, using decimal representations, replace each 3 with (10 * (critical rate)) and replace the 7 with (10 - (10 * (critical rate)))


Expectation of stones: Given the success rates of the stones, and the fact that a failure decreases the current level by one (except +5 to +6 which destroys the item), we can calculate the expected number of stones to reach each new level. For example, when trying for 2 to 3, we will either decrease to 1 or increase to 3. Hence we require the number of stones to get to +2, plus the expected number of stones to get to +2 from +1 times the number of expected failures, plus one stone for a success.

Level Rate Expected number of attempts Total Stones
0 to 1 100% 1 1
1 to 2 50% 2 1 + 1 + 1
2 to 3 50% 2 3 + 3 + 1
3 to 4 45% 20/9 7 + (11/9)(7) + 1 = 16 + 5/9
4 to 5 45% 20/9 (16+5/9) + (11/9)(16+5/9) + 1 = 34 + 1/9
5 to 6 45% 20/9 (34+1/9) + (11/9)(34+1/9) + 1 = 69 + 2/9

However, these are only good averages across a very large number of weapons (trillions of weapons). For perspective (per a recent discussion with some guy who likes python), about 50% weapons will use less than 21 stones and about 80% of weapons will use less than 45 stones.

Thus, you can consider yourself "unlucky" if you require more than 40 stones to get to +5 and you can consider yourself "lucky" if you require less than 20 stones to get to +5.