# More Warframe-Mathematics (Kubrow Dens And Eggs Edition)

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From this thread, DAFIRE has found out that the chances of a Kubrow den dropping a Kubrow egg when destroying the den is between 0.3378% to 0.3861%. Now, in this thread, we will take the average of these chances, and it will give us 0.36195%.

I then asked myself, "How many dens must I destroy in order to obtain one Kubrow egg at least 99.9% of the time [due to long incubation + maturation periods, meaning I would want to stockpile some eggs], assuming the probability of obtaining a Kubrow egg from destroying a den is 0.36195%?". Thus, here are the calculations:

P(E) = 0.0036195, P(E') = 0.996381

X = No. of dens player has to destroy to get one Kubrow egg.

X ~ B(n, 0.0036195)

P(X = r) = nCr(n, r) * 0.0036195^r * 0.996381^(n-r)

P(X = 0) < 0.001

Assume P(X = 0) = 0.001

0.001 = 1 * 0.996381^n

n = 1905.29 (1906 dens, as dens are to the nearest integer).

Now, since in that thread, DAFIRE has mentioned that the number of Kubrow dens spawning in a Earth mission is around 7 to 8, meaning it would take between:

1906 / 7 = 272.286 (273 missions)

1906 / 8 = 238.25 (239 missions)

If it takes around 15 minutes to search around the whole map for the dens, then the total time needed to obtain one Kubrow egg from destroying a den at least 99.9% of the time is between:

273 * 15 minutes = 4095 minutes = 68.25 hours

239 * 15 minutes = 3585 minutes = 59.75 hours

Quite a bit of a grind, is it not?

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Well, yeah, I mean if all the numbers aren't tampered with at all, and I have no reason to believe they are...yep, quite a grind.  Not very fun.  Like farming for many things, come to think of it.  :P

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But isn't the way the chance works is that: you not getting a kubrow egg has no impact what so ever on the kubrow egg drop chance?

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But isn't the way the chance works is that: you not getting a kubrow egg has no impact what so ever on the kubrow egg drop chance?

Binomial distribution calculations. Search it up.

What this thread is trying to calculate is assuming the probability of a Kubrow egg dropping from a destroyed den is 0.36195%, how much dens I must destroy to get one Kubrow egg from the destroyed dens at least 99.9% of the time.

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This is some strange math considering that the OP of the thread you are referring to wrote that he himself needed a single / 37 runs. Somehow you manage to turn that into 239+, now thats some abuse of science at its best. Using a single user experience as a base to calculate chances is as good as looking into your magic glass bowl.

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i got mine in 2 runs

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This is some strange math considering that the OP of the thread you are referring to wrote that he himself needed 37 runs. Using a single user experience as a base to calculate chances is as good as looking into your magic glass bowl.

Well, I really do not want to go through dealing with statistics and stuff for now, so I just took one user's findings to calculate it.

After all, it is for fun.

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Somehow you manage to turn that into 239+ now thats some abuse of science at its best.

That is value is how much dens I must destroy in order to obtain one Kubrow egg at least 99.9% of the time, based on DAFIRE's findings about the probability of a Kubrow eggs dropping from destroyed dens.

Search up binomial distribution calculations. That should give you a more clearer image on what I am doing.

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You cant distribute a single value. Binomial Distribution is a branch of statistics - you cant build statistics based on a single try of a single person. ^^

It took me around one hour so I was on the lucky side as it seems.

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I got my first egg in my first run...

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You cant distribute a single value. Binomial Distribution is a branch of statistics - you cant build statistics based on a single run of a single person. ^^

It took me around one hour so I was on the lucky side as it seems.

It was for fun (and I just thought this up in around ten minutes). I am not going to collect a huge amount of data then analyse it, because it is the most tedious out of all mathematics subjects.

And I could distribute DAFIRE's findings by just splitting up percentage of finding a Kubrow egg from a destroyed den and the percentage of not finding a Kubrow egg from a destroyed den.

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It was for fun (and I just thought this up in around ten minutes). I am not going to collect a huge amount of data then analyse it, because it is the most tedious out of all mathematics subjects.

And I could distribute DAFIRE's findings by just splitting up percentage of finding a Kubrow egg from a destroyed den and the percentage of not finding a Kubrow egg from a destroyed den.

I agree that trying to apply statistics to a single case is funny. As long as people arent scared by a creepy 60 hours grinding value "seemingly calculated with advanced maths".

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I agree that trying to apply statistics to a single case is funny. As long as people arent scared by a creepy 60 hours grinding value "seemingly calculated with advanced maths".

First off, binomial distribution is quite advanced, and does require the user to know what he/she is doing (but very useful).

And if I were to collect everyone's findings then get the average, it should (emphasis on should) be around the same value, or ±X%.

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The guy you based your "calculations" on required a single run to get an egg on earth and 37 runs to get it on Everest. You assume a single run takes approximatly 15 minutes. So the guy you are referring to required 15 minutes at his first attempt and 11.1 hours on his second attempt. His personal average to get 2 eggs was less than 6 hours. How you turn this into an anticipated average time of 60+ hours to get an egg is a secret of your personal interpretation of maths and if you dont realize that I just hope you dont calculate essential / vital things in real life.

I agree - what you did is funny.

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The guy you based your "calculations" on required a single run to get an egg on earth and 37 runs to get it on Everest. You assume a single run takes approximatly 15 minutes. So the guy you are referring to required 15 minutes at his first attempt and 11.1 hours. His personal average to get 2 eggs was less than 6 hours. How you turn this into an anticipated average time of 60+ hours to get an egg is a secret of your personal interpretation of maths and if you dont realize that I just hope you dont calculate essential / vital things in real life.

The time taken for each mission is calculated by myself after three trials.

And for binomial distribution, that is the correct way to solve this problem.

How about I give you this problem to solve, just so we are on the same wavelength (as the question is almost exactly the same as what I am doing, up until the number of dens needed to destroy to get at least a 99.9% of getting one Kubrow egg):

The probability of hitting a target with one bomb is 0.5. It is required to have at least a 90% chance of destroying the target. If three direct hits are required to destroy the target completely, how many bombs must be dropped?

Using the same question format and placing it into this thread, it would be:

The probability of getting a Kubrow egg from a destroyed den is 0.0036195. It is required to have at least a 99.9% chance of getting a Kubrow egg from a destroyed den. If one Kubrow egg is needed to succeed, how many dens must be destroyed?

Do it, and I think you may get a slightly clearer picture.

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273 * 15 minutes = 4095 minutes = 68.25 hours

239 * 15 minutes = 3585 minutes = 59.75 hours

I think one of the missing pieces of information that is generating some dispute of the mathmatics is that this is not how long it is going to take you to get an egg... more like the maximum possible time it could take to gaurantee (within a margin of 0.01% failure) you will find an egg. If it takes you more than 30 hours of farming, consider yourself unlucky and in the bottom 50%. As stated in the original post, that is the time to get 99.9% probability of finding one... not the time it is likely to take you. If you even take that time in half, you could say that would be the time "likely" to give you one, as it would provide grater than a 50% chance of finding one. 1 in 4 should find one in 15 hours, and you should find in this size of a community enough people who find their eggs in the top 10% (within 6 hours or perhaps 24 tries) to generate enough forum rhetoric to make you think these numbers are innacurate, but as an analysis of statistical probability, seems legit to me.

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273 * 15 minutes = 4095 minutes = 68.25 hours
239 * 15 minutes = 3585 minutes = 59.75 hours

I think one of the missing pieces of information that is generating some dispute of the mathmatics is that this is not how long it is going to take you to get an egg... more like the maximum possible time it could take to gaurantee (within a margin of 0.01% failure) you will find an egg. If it takes you more than 30 hours of farming, consider yourself unlucky and in the bottom 50%. As stated in the original post, that is the time to get 99.9% probability of finding one... not the time it is likely to take you. If you even take that time in half, you could say that would be the time "likely" to give you one, as it would provide grater than a 50% chance of finding one. 1 in 4 should find one in 15 hours, and you should find in this size of a community enough people who find their eggs in the top 10% (within 6 hours or perhaps 24 tries) to generate enough forum rhetoric to make you think these numbers are innacurate, but as an analysis of statistical probability, seems legit to me.

After all, this is for fun with binomial distribution in general (and next time, maybe with Poisson distribution once I get around it).

Besides, I could manipulate the percentage to be lower or higher to make it more applicable. I chose 99.9% because I ran a RNG program I made myself that helps me to determine a random number, and it gave me 99.9, so I used that.

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Statistics are ALWAYS just for fun in my opinion XD

Getting an absolutely complete data set is pretty much an impossible ideal in pretty much every application of statistics. You are not measuring what is, only what is observed. Consider flipping a coin.... pretty easy to say it's a 50-50 chance (I'm not even going to acknowledge the chance of landing on the edge) but also pretty easy to perform an experiment where you get 9 head and 1 tail side, and if you analyzed that data set you would see a clear 90% probability of getting the head side up. Kudos for putting in the first steps of data collection, no need to scoff at the results.

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Getting an absolutely complete data set is pretty much an impossible ideal in pretty much every application of statistics. You are not measuring what is, only what is observed. Consider flipping a coin.... pretty easy to say it's a 50-50 chance (I'm not even going to acknowledge the chance of landing on the edge) but also pretty easy to perform an experiment where you get 9 head and 1 tail side, and if you analyzed that data set you would see a clear 90% probability of getting the head side up. Kudos for putting in the first steps of data collection, no need to scoff at the results.

You know, there are actual calculations to predict whether a coin will land on heads or tails.

And someone built a machine just for flipping coins to always show only one side.

So, the 50-50 chance for flipping coins is actually just due to human interaction with flipping the coin.

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I'll just throw in my two cents and say I ran the mission at least 50 times and never got an egg. I just gave up and bought the darn thing.

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I'll just throw in my two cents and say I ran the mission at least 50 times and never got an egg. I just gave up and bought the darn thing.

I gave up around 25-30 tries myself, lol. Too bad that means we can't contribute our numbers to help determine a closer approximation of the drop chance.

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• 2 months later...

i attained 2 eggs in~ 90 runs, about 6 dens each run. Honestly I think this is a pathetic thing way to go about things on DE's end. 45 runs for an egg? If my runs are accurate to the % chance(which by no means am i saying they are) that's a .37% chance of an egg dropping (45runs*6dens per run=270dens, 100/270=.37.....%) Seriously? I mean I get that its not supposed to be a walk in the park but is a 1% drop chance too much to ask for? or perhaps a capped pseudo random distribution system rather than the abusive monster that is RNG?

An example of pseudo random distribution is if you have a 1% chance to get something, and don't, you now have a 2% chance to get it the next time, and a 3% the next if you don't again, but if you do then you have a .5% chance, then if you don't get it again it sets back to the default 1% and starts all over again.

What i suggest is that it is capped at the 2nd or third step (2 or 3% in that last case) that way It isn't as brutally ruthless as RNG but still no walk in the park.

You don't want the game to be a walk in the park, but RNG makes me HATE this game sometimes, that's not good.