Luck

Luck is an item property found on various equippable items. Luck stacks across all items that a character has equipped to make up their Luck score, which can be viewed on the Character Status Menu. This Luck score can then be augmented by various temporary Luck boosts from other sources.

A character's total Luck is used when loot is spawned on creature corpses. It gives a chance of there being a greater amount of loot, a chance of a greater number of properties on said loot, and a chance that those properties will be of greater intensity. It should be noted, however, that this is only a chance of more and better loot, and that Luck has no direct affect on what specific items will spawn and what specific properties will spawn on those items.

Effects

Normal Loot

The Roll

Normal loot that spawns on creature corpses, other than gold and a few other special items, is generated upon the death of the creature, not before. Upon the death of the creature, a roll is made against the Luck of the character who did the most damage, I.e. "the top attacker," on a scale of 0-99 in order to determine whether there is a loot increase. The process can be explained in the following steps:

1. The RNG generates a number from 0-99.
2. The top attacker's Luck is evaluated to determine their percentage (%) chance value, which is derived from the equation:
   <math>Chance = Luck^{\frac{5}{9}}\!</math>
   (This equation is explained fully in the Math section below.)
3. This percentage (%) chance value is then rounded to a whole number.
4. The rounded percentage (%) chance value is then compared against the number generated by the RNG as follows:
   • If (Luck percentage (%) chance value > RNG value)
         Increase loot
     Else
         Do not increase loot

• Example: The RNG rolls a 30. The top attacker's Luck is evaluated and results in a rounded percentage (%) chance value of 56. 56 > 30, so the loot is increased.

This roll applies to all loot that is spawned, even that which is given to other attackers in their own instanced corpses; the top attacker's Luck applies to everyone.

Number of Items

Each type of creature in the game has its loot determined by predefined loot tables that dictate both the type of loot available and the number of items that can spawn. The number of items that spawn on a particular creature's corpse is a random number in the range of one (1) to a maximum number as defined in that creature's loot table. When a creature is killed, if the roll made against the top attacker's Luck score is successful, the number of items spawned on the creature's corpse will be increased by one (1), unless this new amount would be greater than that creature's loot amount cap.

• Example: A particular creature's loot amount cap is 10 items. A character with high Luck kills the creature, the game rolls against the character's Luck score, and the roll is in favor of the character. The game rolls and decides to spawn 10 items on the corpse, which is increased by 1 from the top attacker's Luck roll, resulting in 11 items being spawned. However, this is greater than the creature's loot amount cap of 10 items, so only 10 items spawn, instead of 11.

Number of Item Properties

In the same way that creature loot tables define the number of items that drop on a particular creature's corpse, they also define the number of properties that can spawn on those items. The number of properties that spawn on an item that is dropped by a particular creature is a random number in the range of one (1) to a maximum number as defined in that creature's loot table. When an item is spawned on a creature's corpse, if the roll made against the top attacker's Luck score is successful, the number of properties spawned on the item will be increased by one (1), unless this new amount would be greater than that creature's loot amount cap.

• Example: A particular creature's cap on the number of properties per item is 3 properties. A character with high Luck kills the creature, the game rolls against the character's Luck score, and the roll is in favor of the character. The game rolls and decides to put 3 properties on the first item spawned on the corpse, which is increased by 1 from the top attacker's Luck roll, resulting in a total of 4 properties to be spawned on the item. However, this is greater than the creature's cap of 3 on the number of properties per item, so only 3 properties spawn on the item, instead of 4.

Item Property Intensities

Creature loot tables also define the range of intensity of item properties on items that drop on various creature corpses. The intensity of a property on an item dropped by a particular creature is a random number within a range which is a subset of the entire range of a particular property. When a property is spawned on an item on a creature's corpse, if the roll made against the top attacker's Luck score is successful, the property's intensity will be increased by 10% of the property's overall maximum value, unless this new amount would be greater than the top end of the possible intensity range of that creature.

• Example: The overall range for a particular property is 1 to 50. A particular creature's item property intensity range is 0.25 to 0.3, which results in possible values of that property of 13, 14, or 15. A character with high Luck kills the creature, the game rolls against the character's Luck score, and the roll is in favor of the character. The game spawns a weapon on the creature's corpse with that property with an initial value of 14, which is increased by 10% of the overall maximum value of 50 (5), resulting in a property value of 19. However, this is greater than the creature's cap of 15, so the property is capped at 15, instead of being set to the full 19.

Other

Power Scrolls that drop from Champion Spawns are not affected whatsoever by the Luck of any attacker, and are generated and distributed randomly among all players that receive looting rights.

The drop rates of Artifacts are positively affected by Luck.

The Imbuing system does not take Luck into account when calculating the chance-for-success of Imbuing a property onto an item.

Perfection

The Bushido ability Perfection also results in a Luck bonus. A character with at least 50 Bushido skill can Honor a creature and then attempt to hit that creature as many times in a row as they can. The character receives a score based on the number of consecutive hits achieved and is then rewarded a Luck bonus equal to ten percent of the square of this score. The maximum score is 100, thus the maximum Luck bonus from Perfection is 100^2 x 10% = 1000.

The Math

Luck is evaluated in the context of a logarithmic equation, which is frequently referred to colloquially as "diminishing returns." It is true that your Luck chance will increase the more Luck you have, but it is not a linear increase. The more Luck you have, the more you need to add to it to experience increases in your Luck chance.

• Example: To have a 10% Luck chance, you need approximately 63.1 Luck. One would assume that to have a 20% Luck chance, you would need 63.1 x 2 = 126.2 Luck, but this is not the case. To have a 20% Luck chance you would actually need approximately 219.7 Luck.

Luck's logarithmic equation is as follows:

<math>L=C^{\frac{9}{5}}\!</math>

• L = Luck Required
• C = Chance to Raise Loot Level.

One can substitute the percentage chance that they wish to achieve for the variable C, and thus derive the amount of Luck required to achieve it, L.

Example: You wish to obtain a 50% chance of more and better loot. The Luck required to do this is:

<math>50^\frac{9}{5}=1143.26262...\!</math>

Or, rounding up because Luck only exists in integer amounts, 1144.

If one wishes to derive the chance to raise loot level, C, that they have based on their current level of Luck, L, the equation can be solved for C as follows:

1. <math>L=C^{\frac{9}{5}}\!</math>
2. <math>\ln{L}=\frac{9}{5}*ln{C}\!</math>
3. <math>\frac{\ln{L}}\frac{9}{5}=\ln{C}\!</math>
4. <math>e^{\frac{\ln{L}}\frac{9}{5}}=e^{\ln{C}}\!</math>
5. <math>e^{\frac{\ln{L}}\frac{9}{5}}=C\!</math>
6. <math>e^{\ln{L}*\frac{1}\frac{9}{5}}=C\!</math>
7. <math>e^{\ln{L}*\frac{5}{9}}=C\!</math>
8. <math>e^{\ln{L}^\frac{5}{9}}=C\!</math>
9. <math>L^\frac{5}{9}=C\!</math>

This equation is then quite easy to solve.

Example: Your suit gives you 1500 Luck. Your chance to get more and better loot is:

<math>1500^\frac{5}{9}= 58.14269...\!</math>

Or approximately 58%.