Expected
runs
- 90% probability
- to succeed at least once
- runs back to back
- equal drop chance per run
Nearly guaranteed
runs
- 99% probability
- to succeed at least once
- runs back to back
- equal drop chance per run
Facts
% per run
- probability to get item per run
- 10 runs, % probability
- 20 runs, % probability
- 30 runs, % probability
- to succeed at least once
Do not misunderstand drop chance
One of the most common misconceptions about drop chance is taking the percentage for granted:
- A 10% drop chance does not mean every 10th repetition.
- A 10% drop chance does not mean 10 of 100 tries is a success.
- A 10% drop chance only means that over a large enough sample size or number of tries - tens of thousands - roughly 10% of those tries will lead to success.
And because randomness is involved it is possible that with a 10% drop chance you fail 900 times before you succeed the next 100 times. That is the beauty of randomness.
Math used
The calculation of how many tries should give at least one positive result is done by using the chance to fail:
10% drop chance means a 90% probability (0.9) to fail.
This means for 10 consecutive runs the probality to fail equals 0.9^10 = 0.3486784401
Rounded to two decimal places we now have a probality to fail at 0.35 or 35%.
And this again means 65% chance of succeeding (at least once) in 10 runs when having a drop chance of 10%.
Explaining drop chance
The youtube video on left explains how Random Number Generation (RNG) in video games works. It goes into more depth of the maths involved and has some sample program code written in Java.
Indepth article
If you prefer a written version of the youtube video there is a lengthy transcript RNG or drop chance in video games with focus on Warframe available in my blog.