Editing Openai/692e9127-f13c-800a-8bd6-4bf3c4a385c8 (section)

==== Step 1: chance of a package on any given wave ====
* Probability wave is not skipped: 1 − 0.19 = 0.81
* Given not skipped, probability of package: 0.78

Per wave:

P(package per wave)=0.81×0.78=0.6318 or 63.18%P(\text{package per wave}) = 0.81 \times 0.78 = 0.6318 \text{ or } 63.18\%P(package per wave)=0.81×0.78=0.6318 or 63.18%
Step 2: chance of a common module on any given wave

Every package has a 1.2% chance of a common module:

P(module per wave)=0.6318×0.012=0.0075816≈0.758%P(\text{module per wave}) = 0.6318 \times 0.012 = 0.0075816 \approx 0.758\%P(module per wave)=0.6318×0.012=0.0075816≈0.758%
Step 3: expected commons per 4500-wave run

E[modules per run]=4500×0.0075816≈34.1E[\text{modules per run}] = 4500 \times 0.0075816 \approx 34.1E[modules per run]=4500×0.0075816≈34.1
So under the official 19% / 78% numbers:

Expected common modules per 4500-wave run ≈ 34.

Step 4: what is a “minimum” in a normal run

True minimum is 0. You could get insanely unlucky and see no modules.

If you want “how low before it is very unlikely,” use a binomial approximation:
* Mean ≈ 34.1
* Standard deviation ≈ 5.8

Then, roughly:
* About 95% of runs will be above: 34.1 − 1.645 × 5.8 ≈ 25 modules
* About 99% of runs will be above: 34.1 − 2.33 × 5.8 ≈ 21 modules

So, with the stated mechanics, a realistic “minimum”:
* Normal bad run (about 1 in 20): around 25 modules
* Very bad run (about 1 in 100): around 21 modules