I have a valid reason to outlaw humour.

Because of you comment 3 things have happened.

1) I snorted, causing my hot tea to use my nostrils as an emergency exit.

2) My nose became a tea tap.

3) My screen and keyboard, bless them, are covered with tea. My shame in cleaning it up is indescribable.

Bravo.

Closely related (though not quite the identical problem): https://www.johndcook.com/blog/2010/03/30/statistical-rule-o...

Applying that directly, we would estimate that the odds of a fly in your house being marked are less than 150%, which tells us that you should be taking larger samples.

(With only two marked flies, this estimate will always be less informative than the fact that you sampled n flies -- it will tell you that the population is probably greater than 2/3 of n, while the sampling procedure tells you that the population is necessarily at least n+2. But as you mark more flies, the estimate will be more informative.)

By the rule of three, we estimate the probability that a fly in your house is marked at p < 3/100.

We can also model the probability that a fly in your house is marked as 100/n, where n is the number of flies in your house.

Then 100/n < 3/100 and n > 100*100/3 = 3,333. There are probably more than 3333 flies in your house.

The next day, same story. The flies were now appearing throughout the day. They all looked the same. Where the hell were they coming from? The windows were still closed. I kept vacuuming.

Eventually things were starting to get very irritating. I hunted for an entry point for days without finding anything and the flies just kept on appearing. I was pretty good at vacuuming flies by this point.

By day six I spotted a group of them hanging out near my Kentia palm. Aha! A fly had laid eggs in the soil of the plant. I had no idea that it was a suitable food source for larvae. Needless to say I quickly filled it with gravel and I guess that's the story of how I became a qualified Fly Detective.

Catch one in a cup or plastic bag and stick it in the freezer for about 10 minutes. When you take it out it will look dead, but it's not (unless you leave it in too long.) Being careful not to rip it's wings off, tie a small string or fishing line to one of it's legs.

In a few minutes it will thaw and start to walk around, and then start to fly. You can now walk it around the park like you were carrying a balloon.

I think repeatidly slapping them with a pretty soft plastic attraption until they stop moving is even harsher though.

Or slapping them outta the air, trying to electrocute them but having too little power on the shitty device so only their wings get burned.

Or vacuuming them up

Or flushing them down the drain.

Honestly, whatever people usually do to them it's way way crueller

It's soft to you, not to the fly. You don't slap a fly "until it stops moving". When you swat a fly, it explodes.

Don’t Google dust mites.

Because of their rarity, I find that the ones that wear tiny top hats are easily distinguishable too.

https://space.stackexchange.com/questions/9261/how-many-soli...

Oh, no.... The date on that post is 2015... "recently"... I'm old...

Your error is in stating "if we assume the captured serial numbers are randomly distributed" - you're assuming they're -uniformly- distributed. Randomly distributed != uniformly distributed.

Their method would give you 125 as a guess. It's including the known info (i.e., adding "m") to take into account the fact that they're not necessarily evenly distributed.

On that note, if you continued to get tanks at low numbers (3, 4, 6, etc), averaging gets -less- accurate, because that 99 becomes more and more of an outlier. Their method gets MORE accurate, again, because they're taking advantage of all data that is known (we know it goes at least to 99), and averaging doesn't. The new low numbers we've added mean that there are less likely to be many tanks, and the formula in the link takes that into account with m/k.

Both methods will be accurate if you have 100% of the data, but taking twice the average ignores known data, so the sparser the data the less likely it is to be correct.

Then the next 50 tanks you find are all from the range [1, 100].

Is it more reasonable to assume that there are around 1258 tanks, or that there are probably closer to 100 tanks, and that first one with the very large serial number was not a sequentially numbered tank?

But, from the article's initial proposition - "You do know that the Germans have a sequential numbering system (1, 2, …, n)" and in giving historical context "On investigation, it became clear that the serial numbers were sequential, without gaps."

So, yes, without that being a prior, of course it's more likely that that outlier is a strange one off, and you'd do better to exclude it from your data set (and/or continue to investigate, because it's NOT at all clear that the serial numbers are sequential yet).

But, that context and ordering matters. Assume just the opposite series of events - you started by finding 50 tanks with serial numbers [1, 100]. And then three or four months go by you didn't get any tank serials sent to you. And then you get 1234. 1258 tanks seems really reasonable at that point (and, in fact, would fit the reality; the Germans were producing ~256 tanks per month per the article).

In comparison, I have to wonder why the "intelligence estimates" were so bad/severe over estimates.

You can send fake reports if you think the other side is listening. You can move or mock material if you think the other side is watching. You can feed false information if you are captured.

For example, when estimating tiger populations, instead of painting a white dot, rangers set up camera traps to take photos. Then they can use stripe patterns as a signature for subsequent re-appearances. Quite an interesting intersection for image AI with statistical counting methods.

It's kind of giving you an invariant number: * 100 flies -> 5 flies (5%), 100 / 0,05 = 2000 * 80 flies -> 4 flies (5%), 80 / 0,04 (not 0,05) = 2000

But if you used the percent instead (which seems to be what you hinted at) then the results vary: * 100 flies -> 5 flies (5%), 100 / 0,05 = 2000 * 80 flies -> 4 flies (5%), 80 / 0,05 = 1600

What's the principle, does it have a name I could read more about on Mathworld / Wiki?