Drop rate and grind calculator
Independent drops never guarantee anything. Even at the expected number of attempts you only have about a 63% chance.
%
%
s
Chance of at least one drop
63.3968%
- Expected attempts per drop
- 100.0
- Attempts for a 50% chance
- 69.0
- Attempts for your target confidence
- 229.1
- Time for that many attempts
- 5:43:39
- Expected drops in those attempts
- 1.000
- Chance after the expected number of attempts
- 63.397 %
Show the working
- Drop chance = 1
- Attempts made = 100
- Target confidence = 90
- Time per attempt = 90
- p = 1 / 100 = 0.01
- none = (1 - 0.01)^100 = 0.366 032
- Chance of at least one drop = (1 - 0.366 032) * 100 = 63.3968
- Expected attempts per drop = 0.01 > 0 ? 1/0.01 : 0 = 100
- Attempts for your target confidence = ln(1 - 90/100) / ln(1 - 0.01) = 229.105
- Attempts for a 50% chance = ln(0.5) / ln(1 - 0.01) = 68.9676
- Expected drops in those attempts = 100 * 0.01 = 1
- Time for that many attempts = 229.105 * 90 = 20 619.5
- Chance after the expected number of attempts = (1 - (1-0.01)^(1/0.01)) * 100 = 63.3968
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- P(at least one) = 1 - (1 - p)^n
- attempts for confidence c = ln(1 - c) / ln(1 - p)
At the expected number of attempts the chance of having seen a drop is 1 - 1/e, about 63.2%, for any small drop rate.
Pity systems and guaranteed drops change this completely; the formula only holds for genuinely independent rolls.