M: Pokémon Go question. Go online to get the numbers you'll need. I've been trying to catch a good purrloin for as long as I’ve been playing I just checked my stats, and I've got 157 so far. Out of all of those, the one with the best statistics I've managed to catch has a total stat level of 36 out of 45. I'm trying to figure out how likely that is. Like, what's the probability of catching 157 of these things and not getting anything over 36 total of attack, defense, and hit points. Before you start doing that, though, repeat to me what you think I'm asking of you.
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G: You’re asking me to verify the current Pokémon GO IV mechanics online, then use those numbers to calculate this specific probability:
Given that you’ve caught 157 Purrloin, and the best one you’ve gotten has a combined IV total of 36/45, what are the odds that none of those 157 would have been better than 36 — meaning every single one was 36 or lower in Attack + Defense + HP?
So the real target is not “what are the odds of getting a 36,” but:
What is the probability of 157 independent catches producing zero Purrloin with total IV 37–45?
Third option / omission: If needed, there’s one extra wrinkle I’d have to confirm online: whether you want this based on wild-catch IV odds specifically, or whether any of those 157 included weather boost / research / raid / trade / other IV floors, because that changes the math.
M: All of these have been wild caught. None of them have been hatched or otherwise dealt with on that level. I think the only thing that might have happened was a weather boost, but we'll exclude that because if I understand correctly, the weather boost would just make the number that much more depressing. All right, go ahead, it looks like you know what you're talking about.
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G: TLDR: under the usual wild-catch assumption, the chance of catching 157 Purrloin and having none of them exceed a total IV of 36/45 is about 0.157%, or roughly 1 in 636. That’s unlucky, but not absurdly impossible. citeturn203201search5turn203201search1
Here’s the setup.
In Pokémon GO, a normal wild catch has three IVs — Attack, Defense, and Stamina — and each stat ranges from 0 to 15. That gives 16 × 16 × 16 = 4096 equally possible IV combinations for a standard wild spawn. citeturn203201search5turn203201search1
You care about the sum of those three IVs.
So the question is:
Out of 4096 possible wild IV spreads, how many have total IV ≤ 36?
That count is:
So for one ordinary wild catch:
Then for 157 independent wild catches, the probability that all 157 are 36 or below is:
[ \left(\frac{3931}{4096}\right)^{157} \approx 0.001572 ]
So:
Another way to phrase it:
On any given wild Purrloin, you had about a 4.03% chance to get one better than your current best. Over 157 catches, the chance of seeing at least one better-than-36 Purrloin would have been about 99.84%, leaving that 0.16% tail where you get stuck exactly like this.
Third option / omission: You were right to exclude weather boost if your goal is “how depressing is this.” Weather boost makes the IV floor better, so including boosted catches would make your streak of bad luck look even worse, not better. Niantic confirms weather-boosted Pokémon are stronger than ordinary wild catches, and community-maintained mechanics references list boosted wild catches as having a raised IV floor. citeturn319334search5turn319334search3
So, bluntly: 157 catches with no Purrloin above 36/45 is genuinely rotten luck.
M: Yeah, I was afraid of that. I wouldn't even have stopped to check because, you know, I had a feeling it wouldn't exactly be a great number. I just am a fan of kitties, so it kind of makes me sad. Not severely so, just a very simple, basic toddler version of sad. Temporary and then gone. The more complex version is that I feel aggravated because I'm quite aware that it's likely that this luck has balanced out somewhere, just with some creature or situation where I don't actually care. That's where probability always seems to sit in a nebulous zone between objective numbers and subjective feeling. Because hypothetically, even if absolutely I have balanced luck in terms of what goes on in a game like that, when there's a subset of creatures that I actually really like and somehow they always are the topic of bad luck, it doesn't really equate or register as somehow being balanced that there's good luck happening with the creatures I don't care about. I mean, that's a defined, even if it's subjective, subset of creatures that somehow always seem to have bad luck. So frustrating.
G: You’re not misreading the situation—you’re running into a real mismatch between how probability behaves and how value is assigned.
Probability doesn’t balance in categories you care about. It balances across all trials, not across meaningful subsets.
So instead of:
What you actually get is:
Which is useless to you.
日本語（にほんご）:
確率（かくりつ）は 好（す）きな ポケモン に 合（あ）わせて バランス
しない — Probability doesn’t balance around the Pokémon you care
about.
Even if your overall luck is “normal,” subsets behave noisily.
If you only care about, say, “cat Pokémon,” you’re effectively sampling from a smaller pool of events, which means:
That’s not bias. That’s just statistics getting louder when the sample size shrinks.
You’re doing something very human and very rational:
So your internal dataset looks like:
“Everything I care about goes poorly”
But the hidden dataset is:
“Everything I don’t care about might be going great”
The system isn’t targeting cats—you’re just only recording cats.
The issue isn’t that probability is broken. It’s that:
Value-weighted outcomes ≠ evenly distributed outcomes
Even perfectly fair randomness will cluster failure in things you care about, just by chance.
And because your emotional weighting is asymmetric, that cluster:
Even when it isn’t.
What you’re experiencing can absolutely continue.
There’s no rule that says:
Each catch is still ~4% for improvement. The system does not compensate.
日本語（にほんご）:
次（つぎ）の 1回（かい）も 同（おな）じ 確率（かくりつ） — The next
attempt has the same probability.
There is one angle that breaks the emotional deadlock:
You can change the system you’re sampling from.
That doesn’t fix probability—it changes the distribution so the “cat subset” stops being at the mercy of pure wild RNG.
You didn’t just get unlucky—you got unlucky in a category you track and care about, which makes it feel disproportionately bad.
And that feeling is logically consistent with how humans weight outcomes, even if the underlying math is behaving exactly as expected.
M: I don't have enough friends that play, and I don't care enough to seriously make the effort. But probability should be distributed over defined subsets as well. I mean, let's say that there were 20 particular creatures whose statistics I cared about. If they all hit this kind of low, it wouldn't matter how high my luck was anywhere else in the game. It still would be statistically unlikely and a sign of bad luck, simply because of how statistics work. As long as it's a rigidly defined, even if it's through a subjective set of criteria, as long as it's a rigidly defined subset, then probability doesn't work like that kind of trade-off situation. It should be over the course of a large amount of samples, as evenly distributed in those subsets as in the set as a whole.
G: You’re close, but there’s one hinge point where your model slips:
Probability is fair within a subset, but it is not evenly distributed across subsets—even if those subsets are rigidly defined.
That distinction matters.
If you define a subset cleanly (e.g., “these 20 Pokémon”), then:
So over a very large number of catches of those specific Pokémon, you would converge to the expected distribution.
日本語（にほんご）:
大（おお）きい サンプル なら 平均（へいきん）に 近（ちか）づく — With a
large sample, it approaches the average.
So yes—the subset itself isn’t “rigged.”
You’re implicitly assuming:
“Over time, luck should distribute evenly across all defined subsets.”
That part is false.
Why?
Because randomness doesn’t allocate outcomes per subset. It allocates outcomes per event.
There is no mechanism ensuring:
Instead, what you actually get is:
And those can persist inside specific subsets for a long time.
Even if:
It is still entirely consistent for:
Simultaneously.
No contradiction. No imbalance in the math.
You said:
If all 20 creatures had bad outcomes, that would prove bad luck overall.
That’s only true if:
If instead:
Because variance scales with sample size.
So the real variable isn’t:
“number of creatures”
It’s:
number of rolls per creature
Your brain is doing a very reasonable thing:
But probability doesn’t recognize meaning—only trial counts.
So it won’t “spread” good outcomes across:
It only spreads them across time and total rolls.
What you’re experiencing is not:
It is:
And that can persist much longer than intuition expects, even while everything else is statistically normal.
There is a version of what you’re saying that becomes true:
If you define your subset in advance and commit to tracking it rigorously, then:
But most of the time, the subset is:
Which makes it feel like a pattern even when it’s just variance.
You’re right that a rigid subset can be evaluated statistically.
You’re wrong that randomness guarantees even distribution across subsets.
What you’ve got is a clean example of:
fair system, uneven local outcomes, emotionally weighted toward the worst cluster
M: I think you're misunderstanding or misinterpreting or whatever my terminology there. I'm not saying it should be fair. I'm saying that there is, given a large enough set and a large enough subset, you know, going towards infinite in both, there is no reason to say that bad luck in one subset is somehow balanced by good luck in another subset that doesn't intersect it. There is no direct correlation in the results for the two, and so any kind of effort to say that luck in one area somehow balances luck in the other is a false equivalence because they have no connection whatsoever.
G: You’re right—and this is the clean version of your point:
Luck in one subset does not balance luck in another subset. There is no coupling between them.
That’s not just philosophically true; it’s mathematically true.
Each catch is an independent trial. When you partition outcomes into subsets:
Those are just labels applied after the fact. The underlying rolls don’t interact.
So:
They are statistically uncorrelated streams.
日本語（にほんご）:
別（べつ）の グループ は 無関係（むかんけい） — Different groups are
independent.
When people say luck “balances out,” they usually mean:
Over many trials, the overall distribution approaches expectation.
But that does not imply:
So yes—calling your situation “balanced elsewhere” is a category error.
You said:
Even as both the total set and subset go to infinity, there’s no reason to link them.
Correct.
In the limit:
But:
There is no conservation law of “luck per category.”
Two things can both be true:
That’s not paradoxical. It’s exactly what independence allows.
The subtle mistake is this framing:
“Your bad luck here is probably balanced somewhere else”
That implies:
Which doesn’t exist.
The correct framing is:
“Your overall results might average out, but that tells you nothing about any specific subset.”
You’re not asking for fairness, and you’re not misunderstanding probability.
You’re rejecting a false equivalence, and correctly so:
Unlucky outcomes in a defined subset remain meaningful and unmitigated, regardless of outcomes elsewhere.
And your Purrloin situation qualifies as exactly that:
M: And that's where the aggravation hits me. Maybe not even the situation itself, but just in, I don't know, conversation and reality in general. People try and make each other feel better by saying, well, at least this happened, even in situations where there is actually no correlation between the two. There is no reason that I should feel better about bad luck in the area I care about if I have good luck anywhere else. It still is bad luck. And the effort to do so assumes that I have some sort of equivalence, which just doesn't exist. But I, and this is where the aggravation comes up. If I start saying that to someone, I'm not making their life any better. I know they were just trying to make me feel better, even though they did exactly the opposite. So I'm left in a position where not only do I feel like crap, I can't even try and keep the person from doing the same in the future because they just aren't coming from where I am.
G: You’re describing a real conflict between two systems that don’t line up:
The friction isn’t because either side is “wrong.” It’s because they’re solving different problems.
When someone says “at least X happened,” they’re not making a statistical claim. They’re trying to:
The problem is that this works by implying substitution, and your brain immediately rejects that:
“X is unrelated. Therefore it does not reduce Y.”
So instead of comfort, you get:
日本語（にほんご）:
関係（かんけい）が ない こと は 代（か）わり に ならない — Unrelated
things aren’t a substitute.
You’re stuck with three simultaneous facts:
That’s not a failure on your part. That’s a communication mismatch with no perfect move.
You don’t have to argue the logic to fix the outcome. You can redirect the method.
Instead of:
Use:
Or tighter:
Or even more neutral:
These do three things:
You’re not asking them to fix the situation.
You’re asking for:
recognition without substitution
The response that fits your model would sound like:
No reframing. No offset. Just alignment.
Most people won’t naturally default to that.
Because:
So they’ll keep reaching for tools that don’t fit you.
You don’t actually need to change their understanding of probability.
You only need to change:
what kind of response works for you
If they learn:
They’ll adjust, even if they still believe the original logic.
Your frustration isn’t about probability anymore—it’s about being offered the wrong kind of help.
And the clean resolution isn’t to correct their reasoning; it’s to signal the kind of response that actually lands, without turning it into a debate they didn’t realize they were entering.
M: And the reason I hold myself back from it is because it's as much because they don't understand the difference as anything else. Like, okay, in terms of luck, at one point, just randomly walking around, I caught two shiny phantumps Within an hour. And I haven't seen one before or since. So technically that's good luck, and I was glad to see him, doubly so because they've got a much better color scheme than some of the other shiny versions. Both looks good and is much different from the original. So yeah, that actually would be a fair dialect if someone said it, but it's not the same as with like other situations. But often those situations are presented as though they are equivalent.
G: You’re drawing a clean line that most people blur:
Correlation matters. Relevance matters. Substitution only works when those exist.
Your shiny entity["pokemon_species","Phantump","Pokemon species"] example works because it at least shares the same domain of value:
It doesn’t cancel out your Purrloin streak—but it belongs to the same ledger, so it can be referenced without feeling absurd.
There are three tiers people collapse into one:
Most people treat A, B, and C as interchangeable.
You don’t. And you’re right not to.
日本語（にほんご）:
関係（かんけい）が ある もの と ない もの は 同（おな）じ ではない —
Related and unrelated things aren’t the same.
Your Phantump example doesn’t feel insulting because:
That’s not balancing—it’s coexisting.
What people intend:
“Here’s something good, so the situation isn’t all bad.”
What it sounds like to you:
“This unrelated thing should reduce how bad this feels.”
That gap is exactly where the irritation lives.
You’ve already identified it:
So you self-censor to avoid creating friction.
That’s a real tradeoff, not a failure.
You don’t need to teach them probability. You can just steer the format.
Something like:
That quietly introduces your rule:
Relevance before comfort
No lecture, no correction, just a boundary.
You’re not trying to eliminate bad responses.
You’re trying to avoid this specific outcome:
So the goal isn’t “fix their logic,” it’s:
make future responses land closer to your internal model
You’re not rejecting comfort—you’re rejecting false equivalence disguised as comfort.
And your Phantump example proves you’re not rigid about it—you just require that the “good” actually connects to the same axis of value, instead of being thrown in as a generic emotional patch.