Probability mass function
How likely each number of drops is across n attempts.
Inspect a specific outcome
Pick k, the number of drops you care about.
Cumulative distribution function
Chance of getting at most k drops. Each step up is one bar from the chart above.
Show the maths — probability of exactly k drops
Show the maths — cumulative probability
Show the maths — expected value and variance
Simulate playthroughs
Roll the dice for real, then compare the result against the theory.
Empirical vs theoretical
simulated frequency theoretical binomial PMF
Convergence
The empirical statistics should close in on the theoretical ones as the number of playthroughs grows.
Show the maths — what the simulation is doing
How long are players waiting?
The share of players who still have nothing after this many attempts.
Where would you put the pity counter?
A hard pity at attempt k guarantees the drop; these are the k values that cover a given share of players.
Drought analysis
The complaint-generating question: how likely is a losing streak this long somewhere in a session?
Show the maths — expected attempts until the first drop
Show the maths — probability of a dry run
Show the maths — choosing the pity threshold
Show the maths — losing streaks across a whole session
Side-by-side comparison
Pin two configurations and see how the tuning change actually lands.