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. -Pacman2-

    -Pacman2- User

    Apologies I miss read your chart and what it was displaying I'll remove my last posts :)
    I accept that the 124 data points are not conclusive and I do not suggest anywhere that they are, but the results so far are well below 13%.

    When I started my investigation into gate part yield I had similarly small amounts of data, but it was enough for me to put the effort in to evaluating ( new / duplicate) part yield. As you see my earlier recorded A,B,Y result it would appear that the GGG was returning less than the 13% specified probability.

    Now with the same level of limited data I will be more focusing on multiplier yield.
    Last edited: Jun 8, 2014
  2. El_Burro

    El_Burro User

    Great, now it looks like i have been talking to myself;)
    No need to apologize for not seeing it, this happens to everyone from time to time.

    Small teaser: apparently, there is one thing we can do to reduce the cost for building some of the gates even further. The difference is not high compared to using every multiplier instantly on level 2, but it is there.
    I will check this thoroughly and let you know how it works.
    But I dont think I will change all the tables and charts I made so far because of the minor difference.

    If someone else comes up with another smart idea for reducing the cost, I can check if it works.
    Last edited: Jun 9, 2014
  3. Okapi32

    Okapi32 User

    If you use a ship that has full nano hull whilst using the galaxy gate generator you will not get any nano hull at all, so could in theory have a very small chance of receiving a part instead.
    Maybe this is already what you have heard and are teasing? ^^
  4. El_Burro

    El_Burro User

    Nope. Of course this is what I always do when I operate the GGG because anything is better than nano hull.
    If the probabilities were distributed evenly among the other possible outcomes when the nano hull is full, this would increase the chances from 13% to 13.5%. This would reduce the cost significantly especially for Alpha, Beta and Gamma gates. So using a ship hangar with full nano hull is advisable anyway.

    Unfortunately, it would take a huge amount of data to see if this is true or if the chances for nano hull are simply added to ammunition. Spotting a 0.5% difference in probability with some statistical significance is beyond my abilities.
  5. -Pacman2-

    -Pacman2- User

    All we need to do is spend £k thousands on gate spins, then we could work out the statistical significance in relation to the specified probability. Who wants to go first :p:rolleyes::D.
  6. Guys this is some good stuff.Funny thing is I was able to come to these conclusions
    without all the math but it only got me so far. I used to average 1800 to 2400 spins
    to do Kappa using these methods.I added 1 small twist, now my ave. from 1300 to
    1800 as low as 1200 spins.:cool: This is gonna help a lot of people. Nice thread:)
  7. SPSAT99

    SPSAT99 User

    All this argument in the forums about the gg materializer, gate parts, and multipliers getting smashed in this thread! :p:p:p:p:p
  8. El_Burro

    El_Burro User

    1. Galaxy Gate Generator
    1.6 Can we do better than that?

    So far, the cheapest way to build gates was using every multiplier instantly on level 2.
    There is one thing we can do to reduce the cost further. Dont be disappointed though, the improvement is quite small.

    The basic idea is to use different multiplier levels when a gate is almost completed to perform a "precision landing" with the last few parts you get from a multiplier. In other words: if there are 6 parts missing use the multiplier on level 6, if there are 5 parts missing use it on level 5 and so on.
    Unfortunately, this does not work if we start as soon as 6 parts are missing. This will only increase the cost. But if we start as soon as only 3 parts are missing, we need on average 5-6 turns less than when using only level 2 multipliers.
    The following table holds the data for the smallest single gate (45 parts) and the largest single gate (128 parts) to show that the benefit is nearly constant and that starting as soon as 3 parts are missing is the only option for all gates.


    I estimated a 99% confidence interval for the mean values (+-0.09) to show that the results are statistically significant.
    The conclusion is: Use every multiplier you get instantly on level 2 UNLESS there are only 3 parts missing to complete the gate. In this case, use the multiplier instantly on level 3.

    What about Alpha, Beta and Gamma gates?
    For the first 3 gates, we have to change this strategy a bit. Using X3 multipliers whenever any of the gates is missing 3 parts will increase the cost because this decreases the chances for parts for the other 2 gates.
    Based on the results of a thought experiment that using higher multipliers than x2 causes less damage when the gates are nearly empty, I designed the following strategy:
    As always, use every multiplier you get intantly. If any of the gates is missing only 3 parts, use X3 multipliers instantly as long as the other gates are "empty enough".
    To find out what exactly is "empty enough" I ran a series of simulations using both absolute and relative limits. Absolute means that all gates need to have more than the specified number of parts missing, relative means that a certain percentage of the total number of parts has to be missing.
    Here are the results:



    As usual, the error bars show an estimate for the 99% confidence interval of the values to prove that the results are statistically significant.
    As it turns out, using a relative limiter somewhere around 20% of the total gate parts yields the lowest cost. While the lowest cost so far was 437.57 turns per GU, the cost here is 436.98 turns per GU.
    Only 0.59 turns less may sound like nothing, but it reduces the average cost per GU by 41 Uridium or 1%. Still not that much, but it is higher than the reduction of the 5.3 turns less for Delta gate.
    To sum things up:
    Use every multiplier you get instantly unless one of the gates is missing exactly 3 parts. In this case, use X3 multipliers instantly as long as the other 2 gates are missing more than 20% of their total number of parts. In absolute values: 7 parts for Alpha, 10 Parts for Beta and 16 parts for Gamma gate.

    If you come up with a different idea how to reduce the cost, I can check if it works.

    Leaving one or more gates completed -> doesnt work
    The basic idea is to leave one or more of the first three gates completed to get more multipliers for the other gates. As it turns out, this is a particularly bad idea which greatly increases the costs:


    Last edited: Oct 5, 2014
  9. El_Burro

    El_Burro User

    So would you tell us what exactly you do to get an "average" for Kapa gates between 1300-1800? If it really works, I will stop participating in this thread and farm Uridium from doing gates;)
  10. Sure I used to use x2 multiplier immediately 100% of the time, now it's more like
    80% of the time.The rest of the time I'll skip one turn and use on the next or the
    next it kinda depends how the parts are coming.In a lot case's if I get parts back
    to back odds are many parts will come after a skip.With this method I have farmed
    A,B,G gates for uri. In most cases I get 3A 2B and 1G.

    So I'm doing pretty much the same thing everyone else is doing.I spin 5 at a time
    until multipliers start showing up and then it's one spend at a time to have better
    control over multipliers.If you play close attention you may notice when parts skip
    instead of coming back to back I just try to hit the skips too.

    EL_Burro to anyone that's really paying attention to gate spinner can see certain
    patterns emerge that help to build gates quicker.Your post above kinda describes
    the skips I'm talking about:cool: Don't know if this helps statistically but thats how I
    do it.:)
    Last edited: Jun 11, 2014
    heimdall2012 likes this.
  11. El_Burro

    El_Burro User

    I hope you dont get this the wrong way, it is not my intention to offend you. But I have to say that you are mistaken.
    Let me explain why, because I read this kind of argument very often. I hardly think that I can convince you, this is mostly for the other readers.

    First of all, delaying the use of a multiplier is not a good idea, as was clearly shown in post #2. On average, if you dont use multipliers instantly, the average number of turns needed to build a gate increases.

    I cant remember how often I read that when you look close enough, "patterns" emerge from the GGG allowing you to guess what comes next...WRONG!
    It is true that the pseudo random numbers generated by a PC are not random at all. They are deterministic. But only if you know which type of generator is used, what was the seed value and a few other things. But If you dont know all that, the sequence appears to be entirely random to the "naked eye".
    It is also true that the linear congruential generators (LCG) that are used to generate pseudo random numbers in many compilers have their flaws. There may be correlations between the numbers (that is what you call a pattern) but if the LCG is not designed extremly poor, these show up in higher dimensions at most.
    Then these generators have a limited period length after which the sequence repeats itself. But one of the LCGs with the shortest period length implemented in a compiler still has a period length of around 16 million. Usually, the period length is MUCH longer.
    To conclude this excursus about pseudo random number generators: it is plain impossible to find something like a pattern in the outcomes of the GGG.

    Then why is it that some people still claim that they found patterns?
    Psychology and Statistics.
    The range for the number of turns needed to complete a gate is quite large (see post #5). So if you try to do one thing, like e.g. using a multiplier after getting 2 times Xeno in a row, you might complete the gate with a low amount of turns although you did not use the optimal tactic. Now you can fool yourself thinking that you got a cheap gate BECAUSE you used a certain "twist". But in fact, it was ALTHOUGH you used the twist.
    If you would really take an average (by the way: an average is one number, not a range) over a sufficient number of gates (lets say around 20) you would see that you did not perform as good as you were thinking.

    Edit: Before someone comes up with the criticism that I am an egghead who knows all about math and nothing about the game: I am level 22, top 15 in the PvP statistics on my server and I have done quite a few gates myself.
    Last edited: Sep 26, 2014
    mahi919 likes this.
  12. -Pacman2-

    -Pacman2- User

    The expected cost should not have changed, unless you changed the way you do the kappa gates.
    Every thread that discussed how to optimise gate spins has posted use the multiplier at x2

    You do not post what you did before or what you do now. If it is just that you have changed something about what you did and do now, it would be useful to elaborate on that, as the change you are posting is significant.
  13. -Pacman2-

    -Pacman2- User

    Hi El_Burro, I am not a high level mathematician, and struggle to get my head round why it is, that when you need more than 6 gate part, why you get a better yield from using x2 rather than x6.

    Assuming that the multiplier still returns the multiple part/s even if you hit a duplicate part.
    If not, then:-
    A. Unless there is further adjustment to compensate for hitting a duplicate part with a multiplier we would get less than the specified 13% probability.
    B. The probability of hitting the last part would be the same for using the multiplier as hitting it as a new part.

    If I'm getting my head round it correctly;

    to hit 6 parts using x2 when you need exactly 6 part or less it would be 1 in 23 ish multiplier usages on average to get 6 parts from them,

    but if you use the multiplier at x6 when you need 6 part you will get to x6 and hit all the parts until you get to x6, then you would have a 1 in 7.69 chance of hitting any part.

    Could you post the equations that show, even when we need more than 6 gate part it is still better to use x2. Or are your results assuming that hitting a duplicate part does not return a hit.

    I use a x5 spins early on as there is less chance of getting more than 1 multiplier and I struggle to see how using a x2 or x3 early on will make that much difference.

    Last edited: Jun 11, 2014
  14. El_Burro

    El_Burro User

    Neither am I ;)
    It is hard to put this into an equation, but I can offer you a thought experiment that sheds some light on it.

    Suppose you do some number of turns and managed get 100 multipliers in total.
    Using these 100 multipliers instantly on level 2, you have 100 times the chance to get 2 additional gate parts. With the probability of 13% that you get a gate part with an activated multiplier, on average this results in 2*100*0.13 = 26 gate parts from the multipliers.
    If on the other hand you wait until the multipliers pile up to level 6, you need 5 multipliers to get there (1 multiplier -> level 2; 2 multipliers -> level 3...).
    So you only have 100/5 = 20 turns with an activated multiplier. On average, this would return 6*20*0.13 = 15.6 gate parts from multipliers, which is significantly less.

    This is partly what Ρļ€*İŋ*Ŧħ€*§ķ¥ mentioned here.
    Of course the ratio of gate parts returned from multipliers is not exactly 15.6/26 because there are other factors involved, but you get the picture.
    Last edited: Sep 26, 2014
  15. -Pacman2-

    -Pacman2- User

    I had modified my last post while you was replying.

    But I do not get how it would be 100/5 as if you use the multiplier at x2 you have a 1 in 7.69 chance of getting 2 part.

    If you use the multiplier at x6 you hit every part up to when you use x6 then you have a 1 in 7.69 chance of hitting a part and get 6 parts.

    if you use the multiplier with x100 then you will have a 1 in 7.69 chance of getting 100 part

    if you use the multiplier at x600 then you will have a 1in 7.69 chance of getting 600 part. but it will take 6 time longer to get x600

    If indeed there is a difference then surely there must be an equation that show this.

    I understand why using x6 when you have less than 6 part to get is not good, but not before.

    I accept if we only get a hit using the multiplier when hitting a new part then there will be an advantage, but in that case we would not get the specified 13% probability from the gate generator if we were only getting 13% yield for hitting new parts.

    What would then happen when we hit a duplicate part?

    For you to be able to produce your charts you must have had an equation for each instance.

    What was the equations you use to produce your charts?
    Last edited: Jun 11, 2014
  16. El_Burro

    El_Burro User

    That is just how it works. Otherwise, the gates would cost several times more than they do now. And last time I checked, the description was quite clear about this.

    I even posted 2 equations that show it.

    Correct. but this only happens 20 times, because the other multipliers are somehow "wasted" to bring the multiplier to level 6.
    Compare this to 100 times the same chances when you use x2 multipliers.

    Maybe the first thought experiment was a bit too simplistic. Lets try something different:
    Assume we have a gate with an infinite amount of parts. Infinity is to eliminate the complicated effects that happen when parts are produced during the experiment and change probabilities.
    This gate is half filled. So every time you hit a gate part, there is a 50% chance that it is a new gate part and a 50% chance that it is a multiplier.
    Now we do 77 turns. These should on average yield 5 parts and 5 multipliers (77*0.13*0.5).
    Using the multipliers on level 2, we get 5 times the chance to produce 2 additional gate parts with a probability of 13%. That makes for an average of 2*5*0.13 = 1.3 additional gate parts, a total of 5+1.3 = 6.3 parts from our 77 turns.
    Using multipliers on level 6, we only get to use the multiplier once during our 77 turns. From this one time use, we have a 13% chance to produce 6 additional gate parts: 6*1*0.13 = 0.78 additional parts from multipliers. That is a total of 5+0.78 = 5.78 parts from 77 turns. Slightly less than with the x2 multiplier.
  17. -Pacman2-

    -Pacman2- User

    Thank you, I had always been looking at it to simplistically, not considering that each time you get a part, the chance of hitting a duplicate increase. :)
  18. Don't worry no offense taken.I guess all I was trying to say is that x2 immediatly
    works but not all the time. What I noticed over time Is that many spins I would
    hit x2 multiplier immediately only for it to come the next time around so i started
    trying to hit the skip on those parts that don't come back to back. Sure enough
    bam I started hitting them been doing it ever since.I guess it could be luck I don't
    think so.Pac man several months ago told me to try and right it down.After about
    4 or 5 kappas wouldnt do it anymore because with this method i build gates on the low end. one of those gates I wrote down I built for 1269 spins may latest kappa I built for 1721. It's probably been more than a year since I spent 2200 plus for a kappa.

  19. SBT To get these numbers I have second hanger ship with nano hull full.I spend 5 at a time If I get a multiplier 1 at a time use it Immediately I do this until I have about 60 part by the the multiplier start coming more frequently.at this point its 1 spin at a time until close to the end. I used to use x2 multiplier immediately 100% of the time but notice that they tended to skip (it use to piss me off ) so I start skipping to. S0 now about 80% of the time I use x2 immediately. 20% of the time I try to hit the skip also I notice if you get parts 2 or 3 times odds are is about to do a skip. Rarely do you get back to back 4 time in a row that let me know a skip is coming so I try to hit it, not a 100% but it works. Another way you can see it is in the beginning of building gates if you look at the parts you'll see them come back to back all of a sudden they don't come back to back anymore they skip a little while
    the go back to back.
  20. El_Burro

    El_Burro User

    What you describe is a common misconception about independent random events. Their key feature is that future events have nothing to do with what happened in the past. So after you got lets say 3 gate parts in a row, you are still better off using a multiplier instantly, hoping for even a fourth gate part.

    I can illustrate this with a very instructive example: A coin flip with a fair coin that has equal probabilities for "heads" and "tails"
    Imagine you flip the coin several times in a row. Among the first 20 flips, you got only 5 times "heads" but 15 times "tails". Improbable, but it can happen.
    Now many people would suggest that among the following coin flips, we should get more "tails" than "heads" because everybody knows that when you flip the coin very often, the numbers for "heads" and "tails" must be equal to match the probability of 50% for each result. So if they had to bet on one of the results, they would take "tails".
    But that is not how it works. both results are still equally probable during the next flips.

    Calculating the probabilities from the first 20 turns, we get 5/20=25% for "heads" and 15/20=75% for "tails".

    We continue flipping the coin, but from here on each of the two results appears equally often, just as we would expect it. So after 100 flips, we have 5+40=45 times "heads" and 15+40=55 times "tails". This is already much closer to the probability of 50% we expected.

    After 1000 flips, we had 45+450=495 times "heads" and 55+450=505 times "tails". You see where this is going. The probabilities get closer to the expected value of 50% without "heads" having to "catch up" with "tails" because it did not appear often enough during the first 20 flips.
    Last edited: Sep 26, 2014