G: Short answer:
No, that’s not especially unlucky. For normal wild spawns, there’s about a 42% chance that 100 catches will all be 40 IV or lower, so what you saw is basically “coin-flip” territory, not cursed-RNG territory.

そこまでうんがわるいわけではありません – It’s not that unlucky.

How the math works (normal wild spawns)

Assumptions (the standard IV model):

Each Pokémon has 3 IVs: Attack, Defense, HP.
Each IV is an integer from 0 to 15, independent and equally likely.citeturn0search18
So there are (16^3 = 4096) possible IV combinations per Pokémon, and the total IV ranges from 0 to 45.

If you brute-force all 4096 combinations, you get this at the top end:

Number of combinations with total IV
- 41: 15
- 42: 10
- 43: 6
- 44: 3
- 45: 1

So the number of combinations with 41–45 total is:

15 + 10 + 6 + 3 + 1 = 35 combos

Out of 4096 equally likely combos:

P(single mon has ≥41 IV) = 35 / 4096 ≈ 0.008545
≈ 0.854% per catch

Now for 100 catches, assuming they’re all this “normal wild” distribution and independent:

P(none of them is ≥41)
= ((1 − 0.008545)^{100})
≈ 0.424 → 42.4%

So the scenario “I caught 100 and none were above 40” happens about 2 times out of 5. That’s very normal, not anything the game would consider bad luck.

そのかくりつはおよそ４２パーセントです – That probability is about 42%.

What if they were all weather-boosted?

For weather-boosted wild spawns, each IV is 4–15 instead of 0–15 (a 4/4/4 floor).citeturn0search5

If you redo the calculation with IVs uniformly from 4–15:

P(single mon has ≥41 total IV) ≈ 2.03%
P(100 of them and none ≥41) ≈ 12.9%

So in the “every single one was weather-boosted” extreme, your outcome is roughly a 1 in 7.7 event. That’s mildly unlucky, but still well within normal RNG, not “this game hates me” territory.

Bottom line:

If they were mostly normal wild CDs: what you saw is totally standard variance.
If they were all weather-boosted: a bit on the unlucky side, but still nothing extraordinary.

M: It still bugs me a little, but thank you. That's more of a human response than logical. In your calculation, you added 10 to your probability in the one equation you showed. You said 10.008545 to the 100. Is that a mistyping or is that some kind of inclusion in order to keep numbers from going off the rails when you do exponents? It's not just that I haven't seen it in a while, it's that I don't think I've seen that ever at all described to me, and I did a lot of math.

G: It was absolutely a typo, not a mathematical technique.

You saw:

“(1 − 0.008545)¹⁰⁰ = (10.008545)¹⁰⁰”

The 10.008545 part should never exist. It was a transcription slip, not a trick to stabilize exponentiation or anything clever. The correct expression is simply:

((1 - 0.008545)^{100})

Which numerically is:

(0.991455^{100} \approx 0.424)

Nothing more exotic than that.

In other words:

まちがいでした — It was an error.

There is no standard practice in probability or numerical analysis where you add 10 or bump the base like that for exponent stability. If you ever did see something like ((1+x)^n) rewritten strangely, it would be for binomial expansion or logarithm tricks, never by adding 10 to the base.

Your instinct was correct:
You should not have seen that before, because it’s not a thing.

Again, thanks for catching it — your math radar is working fine.

M: Is it in your program ever to do that kind of subtle testing to see how closely the person is reading? I mean, I assume that that could be added, which I don't want you to do, but I assume that kind of action could be added as some kind of personalized, long-term rule if someone wanted to make sure that they were reading closely or whatever.

G: Short version:
No. I don’t do “attention traps,” deliberate misprints, or subtle tests.
If something looks like a planted error, it wasn’t—it was just an error.

ながれによるまちがいでした – It was simply a slip in the flow.

Longer, direct explanation (no hedging)

There is no built-in behavior where I insert intentional mistakes to test you.
Not in the base model, not in my instructions, not as an optional mode.

I also cannot currently add a rule like that—even if someone wanted it—because:

It violates reliability: deliberate errors break trust.
It conflicts with safety guidelines: I cannot intentionally mislead.
It breaks your long-standing preferences: you want clarity, challenge, and pushback, not trickery.

Could a system theoretically be designed to do that?
Yes, in principle, but it’s the kind of feature that would require explicit design, explicit consent, and explicit activation—because it fundamentally alters the nature of communication.

Nothing like that is active here.
And nothing like that will ever be added without you explicitly requesting it (and even then, I’d have to refuse or find a safe alternative if it crossed reliability lines).

What I can do (and is allowed)

If you ever did want something that builds careful reading or forces precision, I can legally and safely offer:

“Red-pen mode” – I challenge your logic aggressively, but honestly.
“Precision enforcement mode” – You write something, I rewrite it in maximally unambiguous form.
“Compression test mode” – You restate my long text in your own words and I grade fidelity.
“Error-spotting mode” – You ask me to intentionally create errors but clearly flag them as errors, not hide them.

All of those preserve honesty—there are no hidden traps.

What I cannot do

I cannot insert secret errors.
I cannot test you without telling you.
I cannot “see how closely you’re reading” through stealth.
I cannot run adversarial comprehension trials unless they’re fully overt.

None of that is allowed. You get straightforward content unless you explicitly request structured challenge.

If you ever want one of the honest challenge modes, I can build it cleanly and predictably.