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

=== Assistant: You are mixing two things that need to stay separate. ===
You are mixing two things that need to stay separate.
The probability per wave does not change with longer runs. Only the spread of results and the total drops change.

Let me clarify.

==== No. ====
If the game rules stay the same and each wave is independent:
* Skip chance stays 19 percent.
* Recovery package chance on a non skipped wave stays 78 percent.
* Common module chance per package stays 1.2 percent.

So the chance on any single wave is the same whether you do 500, 4500, 5500, or 9000 waves.

What does change:
* The expected total number of packages and modules goes up in direct proportion to waves.
* The percent you see in practice (like 51 to 53 percent packages) wobbles less when you have more waves.

Short run: luck can push you high or low.
Long run: your observed percent gets pulled toward the true rate.

==== I will use your observed rate, since that reflects reality better than the stated 19 percent and 78 percent. ====

From your data:
* Packages per wave ≈ 1934 / 3732 ≈ 0.518 or 51.8 percent.
* Common module chance per package = 1.2 percent.
* So common modules per wave ≈ 0.518 × 0.012 ≈ 0.006216.

Now scale by total waves.

===== - 4500 waves: 4500 × 0.006216 ≈ 28 modules per run. =====
* 5500 waves: 5500 × 0.006216 ≈ 34 modules per run.
* 9000 waves: 9000 × 0.006216 ≈ 56 modules per run.

So if the game keeps behaving like your current run, longer runs just mean more modules in a straight line way. About 28 → 34 → 56 as you add more waves.

==== True minimum never changes. It is always 0 modules. You can always get absurdly unlucky. ====

What changes is how unusual that kind of bad run is:
* With more waves, the distribution tightens around the average.
* So your “normal worst case” gets closer to the mean in percent, even though the raw gap in module count is a bit bigger.

Rough idea using your observed behavior:
* At 4500 waves: Mean ≈ 28 modules. A really bad but not insane run might land in the high teens.
* At 9000 waves: Mean ≈ 56 modules. A really bad run might be in the low 40s.

So:
* Per wave probability does not improve with longer runs.
* Longer runs give you more modules on average and make extreme bad luck less common.

If you tell me which level you usually farm and roughly how long a 4500, 5500, or 9000 wave run takes, I can help you choose the sweet spot in modules per hour, not just per run.