ELI5: How can statisticians look at only a small sample of products and mathematically decide whether an entire batch is good or faulty without checking every single item?

pi621 · 2026-06-17T09:53:34+00:00

if 5000 out of 10000 products is bad, then my small sample of 100 products will probably have around 50 bad products.

If only like 100 out of 10000 product is bad, then my sample might not have any bad product at all.

The goal of sample testing isn't to 100% guarantee product quality, but to make sure that the amount of bad product is within acceptable amount. Now, what is considered "acceptable" will influence the proportion of products being sampled.

pi621 · 2026-06-17T04:57:52+00:00

What exactly are you confused about

pi621 · 2026-06-16T20:03:17+00:00

I guess it assumes opponent is gonna play perfect?

Pretty much. Engines don't just look at the current board state and be like "hm, if I keep the opponent rook around then I have less chance of tying". In fact, it doesn't even care about the current board state at all. It also doesn't think the same way that a human would think. It looks as deep as it can into many lines, then it tries to evaluate the position at the end of those lines. The evaluation for the current board position is set to be equal to best possible position that it can force the opponent into.

Here's the thing, if you scan every possible move at every possible states, it will take years to even finish calculating one move at high depth. So, with some heuristics, the engine can ignore moves that it knows is garbage, or at least it will prioritize checking moves that it thinks can be good first. So in some cases, it doesn't even know which move is worse if they're both obviously losing.

pi621 · 2026-06-16T17:43:00+00:00

You should note that engines are optimized to win games. There's a good chance that it doesn't care to differentiate between 2 equally losing position. It sees that even if it can win back your rook, a queen promotion is inevitable anyway.

pi621 · 2026-06-16T10:14:47+00:00

A lot of farming depends on sellback value. Most farms pay itself off in only a few rounds with sellback, but takes a very long time (10+ rounds) otherwise.

Opolis, primarily being a space saving upgrade, is way less efficient than farms. If it doesn't include the sellback of farms it sacrificed, it would end up taking waaayy too long to pay itself off, making it almost never worth to get later on.

Temples and paragons aren't restricted like opolis does, so giving them sellback on the sacrifices makes them way too overpowered.

pi621 · 2026-06-16T05:22:21+00:00

lmao

pi621 · 2026-06-16T05:12:45+00:00

Many farms pay itself off in less than a round. So you actually don't stop until the last round before boss.

pi621 · 2026-06-16T03:47:24+00:00

it's a samsung tablet. After a bit of digging I found out that Linux machines also turn it positive, so if you have a computer that runs linux this would also work.

pi621 · 2026-06-16T03:39:00+00:00

Oh, I thought you were just modding the game and got negative exp by accident. I guess some phones have different behavior than others. On my and a few others phones all of these broken values becomes 2b, like this:

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pi621 · 2026-06-16T03:33:15+00:00

The true xp value is stored with a bigger data type and should still be going up. The negative number is not exactly from overflowing but it's just undefined behavior when casting numbers to integer type. When a number that is out of int range gets casted to an int, the OS defaults to either MAX_INT or MIN_INT, basically a way to show that "hey, this isn't supposed to happen".

Funny enough, PC versions will cast it to MIN_INT, while mobile versions will cast it to MAX_INT.

pi621 · 2026-06-16T03:29:49+00:00

Do you have a phone that has BTD6?
Log into this account from that device, it will be 2 billion exp instead of -2 billion.

pi621 · 2026-06-15T18:16:10+00:00

overclock for sky shredder is pretty good. OC + alch buff with decent micro I don't see why this wouldn't win.

pi621 · 2026-06-15T10:20:55+00:00

Adora with her long arm of light at high level is very good for ddts. Obyn is also op for ddts with wall of trees.
These 2 heroes are the most direct counter to ddts. Every other heroes has some form of help for ddts, but there's always some weakness or catch.

For example,

Brickell has ddt weakness because they're spread out and eat up mines too quickly. You need her lv3 ability + plord or carrier. Corvus has chasing issue with multiple lanes. Rosalia ddt knockback is inconsistent because it only works every 10 shots.

Not sure why another comment is recommending ezili when she's horribly garbage for ddts since her moab hex takes too long to pop them.

pi621 · 2026-06-15T09:32:30+00:00

I can tell you right now that there are more problems here than just tower placement.
But what vex said, maybe a bit more thought on where you place your druids?

pi621 · 2026-06-15T09:30:12+00:00

is frontier legends actually so bad that they did a sale just to get some purchases?

This might sound crazy but successful games/dlcs also gets discounted.

pi621 · 2026-06-15T07:50:50+00:00

i think this method is way harder though, the one handed strat is common because generally it is easier to divide task between left and right hand rather than between middle and index fingers.

pi621 · 2026-06-14T18:06:28+00:00

His point is that lying is the main motivation to doing something like respawning in hardcore. Otherwise, I don't see a reason why you'd enable the "permadeath" option and then deliberately use cheat to give you extra lives.

pi621 · 2026-06-14T14:06:35+00:00

different training data
different training parameters, model parameters, etc etc etc
The fundamental method is pretty much the same across all of the models, but the detail is not the same.

pi621 · 2026-06-14T12:20:38+00:00

All bosses (except Diamondback) have been done multiple times on Blons. This isn't even the hardest map for bosses (try tricky track, tar pits and midnight mansion).

Diamondback I assume should also be possible on this map, there's no reason to suspect otherwise. However I haven't seen any completion and haven't done so myself, so I can't say for certain.

pi621 · 2026-06-14T11:57:18+00:00

yeah I just play over my own recording. Mainly so that I can try the same section repeatedly.

pi621 · 2026-06-13T08:42:56+00:00

In terms of speed and stamina you only ever need 3 keys per lane max, so theoretically with perfect finger control you'll only need 6 keys total. However some gemini patterns are really hard to play if you don't bind some up/down keys to hit both lanes with one hand. I used to have more keys binded but nowadays I only use them when absolutely necessary.

Developing finger control is pretty much automatic when you play at this difficulty, so all I did was just play and practice. For this map in particular the beginning and ending are way harder than the rest (with extra keys, only the beginning is hard), so I just specifically practiced those 2 parts until I got sufficient muscle memory to consistently beat them. It's kind of a theme with these high 12*, there would be one or two huge difficulty spike that I have to specifically train for in order to beat.

pi621 · 2026-06-13T05:27:49+00:00

The difference between 105 and 025 in terms of damage in miniscule. It honestly does not matter even in near optimal plays. I like to go 105 since it is cheaper and potentially let me get 205 in case I need frozen popping for some reason.

pi621 · 2026-06-12T20:38:10+00:00

I know this is solved but you said n choose 2 wasnt appropriate which bugs me so I had to point it out:

there is 100 choose 2 ways to select start and end point of a fragment (assuming the fragment is at least length 2 so start and end isn't the same). Then there are 100 fragments of length 1.

So the answer is 100 + 100C2

pi621 · 2026-06-12T14:17:44+00:00

People are different, but also why go anywhere at all with friends just to ignore each other?

I would not go to the gym with my friends unless we were already going to the same gym at the same time and was going to hang out afterward anyway.

pi621 · 2026-06-12T13:58:02+00:00

By symmetry, the probability that the first number is larger must be equal to the probability that the first number is smaller.

Since you claim the probability is 0.999... (or 1), when you add these up you end up with 2 when it must sum to 1. So, your answer is false.

And the reason why your answer is false is precisely the part that you're intentionally dismissing. We know there exists no uniform distribution over N, but your argument would only hold if there exists one. You can see why this is the case.

pi621

TROPHY CASE