Bad luck mitigation

Bad luck mitigation refers to any mechanic that adjusts the drop rate of certain rare items or other events to prevent particularly long dry streaks. This can be accomplished by increasing the chance of a drop after reaching some threshold, or by guaranteeing the drop on a specific kill count, among other methods.

Bad luck mitigation is motivated by the fact that most random drops are rolled independently, so individual kills do not guarantee progress towards the drop (referred to in statistics as being memoryless). Due to the nature of randomness, a small percentage of players would be expected to go dry on getting a drop, potentially several times over the drop rate. For example, the probability of a standard 1/100 drop rate has a 63% chance of getting the drop after 100 kills, and 1 in 1000 players would need more than 680 kills for the drop. To calculate this, use the following formula:

Probability $=(1-(1-Drop\,Rate\,)^{Attempts}\times 100=(1-(1-{1 \over 100})^{100})\times 100=(1-0.336)\times 100=63.4\%$

Number of kills for the 99.9th Percentile:

$(0.99)^{k}={1 \over 1000}$ → $k\times \ln(0.99)=\ln(0.001)$ → $k\approx 687$

Examples

Combat

• Vorkath's head typically has a drop rate of 1/50 from Vorkath, but is a guaranteed drop on the 50th kill.
• Kq head is typically a 1/128 drop from the Kalphite Queen, but a Kq head (tattered) is guaranteed on the 256th kill, which is sufficient for completing the Elite Desert Diary.
• Brimstone ring is made by combining 3 drops from hydras, rather than a single drop. The eye, fang, and heart are dropped in order, and are dropped sequentially without duplicates until all 3 have been obtained. This has a lower variance than a single, rarer drop, and allows the player to make progress over the series of kills. This also applies to the noxious halberd from Araxxor and the abyssal bludgeon from the Abyssal Sire.
• Thread of elidinis initially has a 1/10 drop rate from Tombs of Amascut, but scales with the number of raid completions up to 3/10 after completing 15 raids. The rate reduces to 1/50 after receiving the first drop.
• Venator bow is made by combining 5 venator shards, which are individually a 1/100 drop rather than a single, rarer drop.
• The Desert Treasure 2 bosses' vestiges progress in 3 stages of "drops", invisibly to the player. Once it has been rolled 3 times, their respective vestige will drop.
• The rewards chest from the Moons of Peril does not give duplicate pieces from a set until that entire set has been dropped.
• To prevent being overly reliant on successful hits when draining Tekton's high Defence level, the special attacks of the dragon warhammer and elder maul will drain 5% of his Defence level if the player misses, whilst the Bandos godsword will drain 10 Defence levels.

Skilling

• Skilling pets become 15 times more likely after reaching 200 million experience in the corresponding skill. Before that point, they become moderately more likely at higher levels, following the formula ${\text{DropRate}}={\frac {1}{{\text{BaseChance}}-({\text{SkillLevel}}*25)}}$ where the base chance depends on the pet and activity.
• Hunters' Rumours require getting a special rare drop from each Hunter creature, which becomes a guaranteed drop after going twice the drop rate (e.g. a 1/20 drop is guaranteed on the 40th kill). Wearing the guild hunter outfit decreases the "pity threshold" count by 5%.
  • The enhanced quetzal whistle blueprint is a 1/50 drop from a hunters' loot sack, but an untradeable torn variant is guaranteed on the 100th rumour. This can be used to make the whistle for personal use, but cannot be sold. A torn perfected blueprint is also guaranteed after 250 rumours.

Other

• Some players may humorously refer to the Grand Exchange as bad luck mitigation.

See also

• Drop rate
• Calculator:Dry calc
• Kill count