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Dark Orbit - finally a "real world" application for math

Discussion in 'General Archive' started by El_Burro, May 19, 2014.

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  1. El_Burro

    El_Burro Old Hand

    1. Galaxy Gate Generator
    1.4 Why dont I get 13% gate parts from the GGG?


    For two reasons:

    1) "Da rules"
    Most of you surely know this, but often complaints about not getting enough gate parts are based on ignoring the following rule: Multipliers are gate parts. Each time a gate part you already have is produced again you get a multiplier instead.

    2) Statistics (again)
    So you took a paper and a pencil and actually wrote down how many parts (and multipliers) you got from lets say 100 or even 1000 turns.
    Now you divide the number of gate parts by the number of turns and get a percentage. You expect to get 13%? Well you probably wont...
    The reason is that the number of parts (and multipliers, I will omit this from here on) you get from a certain number of turns is RANDOM to some extent. The percentage you get is probably closer to 13% if you count more turns, but only for an infinite number of turns you will get 13% in probability. That is one possible definition of a probability.

    Can we evaluate quantitatively how many parts I can expect from a certain number of turns? Yes we can.
    This number follows the so-called binomial distribution. I wont bother you with the math, interested readers are referred to the surprisingly well-written wikipedia article about this topic. From this binomial distribution for the number of parts we can derive the percentage of gate parts we get in our paper and pencil experiment.

    I did this for four different sample sizes (number of turns): 10, 100, 1000 and 10000.

    [​IMG]

    On the horizontal axis we have the percentage of gate parts calculated by dividing the number of parts by the number of turns we made.
    On the vertical axis we have the probability to get this percentage.
    Especially for small sample sizes like 10 there is only a limited number of possible outcomes of the experiment. We can either get 0, 1, 2, 3... gate parts resulting in probabilities of 0%, 10%, 20%, 30% and so on.
    Getting a value of 10% is represented by the second black impulse (counted from the left). The probability for this outcome is around 37.1%.
    Now here what it all boils down to: Even for a sample size of 1000 turns, there is still a fairly high possibility that you only get 10% or even less gate parts, ALTHOUGH THE PROBABILITY FOR GATE PARTS IS IN FACT 13%.

    Again, only for an infinite sample size you can expect to get the "correct" number of gate parts. With sample sizes smaller than infinity you wont get 13% gate parts. This has nothing to do with fraud, it is just math.


    Here is an example
    For this analysis I built 5 Kappa gates in total using only Extra-Energy, performing 100 turns at a time. The first 1000 turns of every gate were recorded (I used single turns to complete the gates afterwards because I didnt want to waste my hard-earned energies).
    From every of these 50 samples consisting of 100 turns, I calculated the yield for gate parts.

    [​IMG]

    See how the values for the single samples vary between 6% and 22%...
    There is a streak where I get more than 13% 8 times in a row...
    The running average after 32 samples (3200 turns!) is 14%...
    But all of this is completely normal for the underlying random process.
    In fact it would be rather suspicious if things like that didnt occur.
    In the end, the average yield from all 5000 turns is 13.2%. (Small note: the estimated standard deviation for this mean value still is quite large: 0.57%)
    There is absolutely nothing that could make me believe that the probability for gate parts is not 13%.
    Unless someone comes up with a similar analysis to prove a different statement about the probability for gate parts do not believe it.

    Here are the screenshots I took to "prove" that I didnt make the numbers up:

    [​IMG]
     
    Last edited: Sep 26, 2014
  2. Omega

    Omega Old Hand

    well thx for ur hard work .so it turns out that me and many others were right when we said its not 13% and that's really weird when i was getting 7.7 % and 10% proves my point .
     
  3. El_Burro

    El_Burro Old Hand

    What? No!
    The point I was trying to make is that the probability for gate parts is indeed 13% although you usually get different results with a limited sample size.
     
  4. Omega

    Omega Old Hand

    I was sarcastic lol :) I should have mentioned that , I know what u said but I responded with sarcasm because it takes a much large sample size to get the 13% which is not that fair most of the time but whatever
     
    Last edited: May 28, 2014
  5. El_Burro

    El_Burro Old Hand

    You should have figured out by now that i am immune to sarcasm;)

    Did I get that correctly that the few screenshots you posted were the results of making 100 turns at a time? Since these are not from consecutive tries I hardly believe that they are representative samples. No offense, but it looks like you actually posted a selection of screenshots where you got the smallest amount of parts.

    If you really want to convince me that you dont get enough parts even though your sample size is sufficient do the following:
    Post the same screenshots for one of the single gates like Kappa where we can see from the number of parts in the gate that they are from consecutive tries.
    Somewhere between 10 or 20 consecutive tries with 100 turns each should be enough.

    I will do the same this weekend using Extra-Energy instead of Uridium to disprove the myth that you get less parts from EE than from Uridium.
     
  6. Omega

    Omega Old Hand

    didn't select them . it happens all the time actually .. and it was with 100 spins at a time , and I don't do kappa .I'm ufe on all my acc all I do is alfa beta gmma .kappa's a waste for me now
     
  7. =[sputnik]=

    =[sputnik]= Forum-Apprentice

    Good thread, it's always nice to find like-minded people attempting their best to demystify DO's galaxy gate generator! I particularly liked your explanation of why the infamous 13% isn't always necessarily observed.

    I did a similar study some 3 years ago (
    here), and so did †TIBΞЯIUS† afterwards (here). Unfortunately, most of the results in my original thread have mysteriously disappeared, but I still find it's a very good read, as it prompted a really nice debate at the time. That's where you can find the reference to the 45/30/25 distribution of gate parts in the alpha/beta/gamma generator. I don't play DO that much these days, and haven't spun a gate in a while, but I wouldn't imagine they changed that, especially not to benefit the construction of gamma!

    One small comment: while you are absolutely correct that the probability distribution functions are not normal, providing the standard deviations is still very useful to obtain an approximate range of where most of the gates will fall. Especially the +/- 3 sigma, as that will give some 99% of all gates (if you're really picky, you can even calculate the precise range!). You should check your code for the calculation of sigma, though - if I remember correctly, subtracting 3 sigma shouldn't even come close to the minimum cost.

    All in all, good work, keep it up!
     
    sirpwnsalot34 likes this.
  8. El_Burro

    El_Burro Old Hand

    =[sputnik]= thanks for the kind words.
    Although it is no problem to calculate the standard deviation in the code or afterwards from the pdf, I demonstrated in post #23 why it is not particularly useful to describe the expected range. See the figure with the indicated ranges of +-sigma pointing to unrealistic values.
    Instead, I added the table at the end of post #5 with the percentiles of the distribution.
    The 0.5 and 99.5 percentiles give you exactly the 99% range you were searching for.

    For the Alpha/Beta/Gamma problem I already have some data that suggests that the breakdown was changed to 33% for all gates. Maybe I can gather some more data this weekend to be sure.

    Edit: small update with some real data to 1.4
     
    Last edited: Sep 26, 2014
  9. =[sputnik]=

    =[sputnik]= Forum-Apprentice

    Ah, yes, I didn't notice that your example was using the x6 multiplier. In that case, the standard deviation is quite high and the distribution functions deviate a lot from a normal curve - as seen very clearly in your plots. For x2, you do get a better approximation from just the mean and standard deviation. But I agree, your percentile tables provide a much accurate range, nicely done!

    Also, fantastic addition on 1.4 above - I don't think I've ever seen more convincing evidence that DO's galaxy gate generator isn't somehow rigged, as many would like to believe! That's exactly what we need to do to get the right distribution between alpha, beta, and gamma parts.

    Of course, it would be nice if the developers just disclosed that information from the outset. Along with the odds for booty box items and epsilon/zeta rewards - I'd really like to know the average cost of an lf4! Keeping it secret only feeds conspiracy theories.
     
  10. El_Burro

    El_Burro Old Hand

    I totally agree that BP should give more information, but that would deprive us of the satisfaction to unravel the mysteries:rolleyes:

    A while ago when I was still in their "Top Gamers Club" and the new gates were released I asked the support for the probabilities of Epsilon and Zeta. The surprising answer: 25% probability for LF4 as a reward from epsilon, 33% probability for Havoc designs from Zeta.
    Arent all the gate reward percentages somehow official?

    Concerning LF4 from Boxes, I made an analysis a while ago in the german forum.
    Its all in german and the images got removed...
    Based on a poll how many Keys had to be opened to find the first LF4 in a box I figured out that the probability must have been somewhere around 0.6%.
    Needless to say that this was years ago and would be impossible to repeat, especially for the other good stuff in the boxes.
     
  11. MyNameIsHawk1

    MyNameIsHawk1 Junior Expert

    thanks El_Burro, this thread will help a lot of people asking why they never get some pieces of gates
     
  12. whoeva

    whoeva Forum Duke

    I glossed over the information in the first page about distribution but was thinking about this today. All we are told is that the % chance for a gate part is 13%

    Well there are 34 alpha parts, 48 beta parts and 82 gamma parts for a total of 164 parts.

    That means when hitting a gate part there should be a (34/164x100) 21% chance it's alpha, (48/164x100) 29% chance it's beta and (82/164x100) 50% chance it is a gamma part.

    Now am I doing something wrong here because this suggests to me that I should build all 3 gates at roughly the same rate and as I'm sure anyone can confirm the ratio is not 1:1:1

    It's not the 13% chance of a part I am questioning; it's the breakdown of the part given that is concerning me since the maths seems to show 1:1:1 and my own stats show alpha (130), beta (98) and gamma (59) which is more like 2.2:1.66:1

    Let's just round it off and say that for each gamma I make 2 alphas and 1.5 betas but if I have 50% chance of getting a gamma part why am I getting 140 alpha and beta parts for every 82 gamma parts? :confused:
     
  13. El_Burro

    El_Burro Old Hand

    Your premise is wrong.
    A probability proportional to the number of parts in the gate is just one of many possible breakdowns. There is no "right" or "wrong" for the breakdown of parts.

    The data I am currently collecting suggests that the probabilities are evenly distributed among the 3 gates. That is why you build more Alphas than Betas and more Betas than Gammas.
     
  14. whoeva

    whoeva Forum Duke

    Ok that makes sense, thanks for the reply. So it looks like from the 13% chance of hitting a part it then gives you a 33% chance of it being a,b or y and then randomly selects the part number.

    I would really like to assist in providing some data but I don't have the patience to do the spins 1 at a time I'm afraid. Thanks again for this thread though and the charts :)
     
  15. SpudnicK

    SpudnicK Someday Author

    Ok seriously it sounds like you are all trying to work out some kind of highly advanced alien technology !! This is bigpoint we are talking about ! The coders they have working for them are still trying to figure out how to open an email . I would bet that the people at bigpoint do not even know how the GGG works as someone from 8 years ago wrote it . If its so complicated to try and work out how it runs then i would imagine that they are to scared to even try and make any sense of it or fiddle with it to rip us off on gate parts .
     
    -Pacman2- likes this.
  16. yellowsubmarine

    yellowsubmarine Commander of the Forum

    What erks player(s) the most is the 'multiplier'
     
  17. =[sputnik]=

    =[sputnik]= Forum-Apprentice

    Yes, there is great satisfaction in unravelling DO's inner workings, but for the sake of transparency they should provide all the odds. I also took great pleasure in coding my galaxy gate simulator, and finding out the average costs of building each gate (my main motivation at the time), along with the best building strategy (always activate on x2!). The same can be done for the costs of lf4, full havocs, and so on, but without knowing the handout probabilities it will lack the rigour I'm after.

    I believe those numbers are the general consensus, but apart from kappa there are no official quotes on gate reward probabilities. Not that I know of, anyway.

    There was some data in the old forums that pointed to a probability between 0.5-1%, but the variability on a random process with such low handout yield must be huge! You need maybe 10.000 keys to reach some sort of reliable conclusion, which is nothing short of obscene!
     
  18. Okapi32

    Okapi32 Forum Freak

    For the sake of interest, is this the post you are referring? Posting encase others might find it useful to look at :)
     
  19. =[sputnik]=

    =[sputnik]= Forum-Apprentice

    That was definitely one of the sources, thanks Okapi32! But I remember another thread where a lot of people were contributing their findings. There was a post by Rooster which was immensely helpful. I'll try to find it and post the link.
     
  20. El_Burro

    El_Burro Old Hand

    The participants in the poll I am referring to must have opened something in the order of 25000 Boxes. I am well aware that not everybody gave correct information, but the way the results were analyzed compensated the influence of faulty information to some extent.
     

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