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

=== Assistant: This change only affects one thing. ===
This change only affects one thing.
You increased the “package → common module” chance. So every number that depends on common modules or shards improves by the same factor.

Old per package: 1.2%
New per package: 1.6%

Factor increase: 1.6 / 1.2 = 4 / 3 ≈ 1.33

So:
• Common modules per wave go up by about 33%.
• Shards per wave go up by about 33%.
• Waves and runs needed per level go down to about 75% of what they were.

Below are the updated numbers for both cases:
# Using your observed drop behavior (more realistic)
# Using the “official” 19% skip and 78% package numbers

==== 1. Using your observed data (the realistic branch) ====

From your run:
* Waves: 3732
* Packages: 1934
* So packages per wave ≈ 1934 / 3732 ≈ 0.5182

===== 1.1. Per wave probabilities =====

Old module chance per wave (1.2% per package):
* p(module per wave) = 0.5182 × 0.012 ≈ 0.00622

New module chance per wave (1.6% per package):
* p(module per wave) = 0.5182 × 0.016 ≈ 0.00829

So:
* Old: about 0.622% of waves give a common module.
* New: about 0.829% of waves give a common module.

===== 1.2. Expected common modules per run =====

4500-wave run
* Old: ≈ 27.98 modules
* New: ≈ 37.31 modules

Call it:
• Old: about 28 modules
• New: about 37 modules

5500-wave run
* Old: ≈ 34.20 modules
* New: ≈ 45.60 modules

So:
• Old: about 34 modules
• New: about 46 modules

9000-wave run
* Old: ≈ 55.97 modules
* New: ≈ 74.62 modules

So:
• Old: about 56 modules
• New: about 75 modules

===== 1.3. Shards per wave and per run =====

Each module gives 18 shards.

Old shards per wave:
* 0.00622 × 18 ≈ 0.112 shards per wave

New shards per wave:
* 0.00829 × 18 ≈ 0.149 shards per wave

So:

4500-wave run
* Old: 0.112 × 4500 ≈ 504 shards
* New: 0.149 × 4500 ≈ 672 shards

5500-wave run
* Old: ≈ 616 shards
* New: ≈ 821 shards

9000-wave run
* Old: ≈ 1007 shards
* New: ≈ 1343 shards

===== 1.4. Waves and runs needed for +1 level (3800 shards) =====

Cost per level: 3800 shards.

Old waves per level:
* 3800 / 0.112 ≈ 33,948 waves

New waves per level:
* 3800 / 0.149 ≈ 25,461 waves

So the upgrade cuts the wave requirement to about 75% of the old value.

Convert to runs:

At 4500 waves per run
* Old shards per run: ≈ 504 • Runs per level: 3800 / 504 ≈ 7.54 runs
* New shards per run: ≈ 672 • Runs per level: 3800 / 672 ≈ 5.66 runs

So 7–8 runs drop to about 5–6 runs per level.

At 5500 waves per run
* Old: 3800 / 616 ≈ 6.17 runs
* New: 3800 / 821 ≈ 4.63 runs

So about 6 runs drop to about 5 runs.

At 9000 waves per run
* Old: 3800 / 1007 ≈ 3.77 runs
* New: 3800 / 1343 ≈ 2.83 runs

So just under 4 runs drop to just under 3 runs.

Summary for the realistic branch:
* Modules per run increase by one third.
* Shards per wave and per run increase by one third.
* Runs needed per level drop by about one quarter.

==== 2. Using the “official” mechanics (19% skip, 78% package) ====

Here the game behaves exactly as described:
* Skip chance: 19%
* Not skipped: 81%
* Package on a non skipped wave: 78%
* So packages per wave: 0.81 × 0.78 = 0.6318

===== 2.1. Per wave module chance =====

Old:
* p(module per wave) = 0.6318 × 0.012 ≈ 0.00758

New:
* p(module per wave) = 0.6318 × 0.016 ≈ 0.01011

===== 2.2. Modules per run =====

4500-wave run
* Old: 4500 × 0.00758 ≈ 34.12 modules
* New: 4500 × 0.01011 ≈ 45.49 modules

5500-wave run
* Old: ≈ 41.70 modules
* New: ≈ 55.60 modules

9000-wave run
* Old: ≈ 68.23 modules
* New: ≈ 90.98 modules

===== 2.3. Shards and waves per level =====

Shards per wave:
* Old: 0.00758 × 18 ≈ 0.1365 shards
* New: 0.01011 × 18 ≈ 0.1820 shards

Waves per level:
* Old: 3800 / 0.1365 ≈ 27,845 waves
* New: 3800 / 0.1820 ≈ 20,884 waves

Again the same pattern: about one third more shards per wave, about one quarter fewer waves per level.

==== What this means in plain terms ====

Using your real observed rates:
* Old: about 7–8 runs of 4500 waves per level.
* New: about 5–6 runs of 4500 waves per level.

Or:
* Old: about 3.8 runs of 9000 waves per level.
* New: about 2.8 runs of 9000 waves per level.

If you tell me how many high end modules and how many levels you want on each, I can translate this into a total “grind budget” with the upgrade vs without it.