Conspiracy Theory: Blueprints from GB rewards are not actually random for the Arc

Discussion in 'Forge Hall' started by Jovian 702 the Wise, Dec 5, 2018.

  1. Jovian 702 the Wise

    Jovian 702 the Wise New Member

    Dec 5, 2018
    Setting the scene:

    You've been motivating your friends, guildmates, strangers everyday and plowing all the FPs you can into random people's GBs, all in the pursuit of blueprints. You are meticulous. Day after day you motivate and plow, motivate and plow. You are a motivated, plowing machine. You plow so hard your girlfriend can't keep up, and leaves you, but still you motivate and plow on. Eventually, coworkers start to take notice of your unkempt looks and constant plowing at work. One day, HR takes you aside to tell you that the workplace is safe space and your constant plowing is making people uncomfortable... and also... you're not doing your job. But what do they know? They are not motivated and do not understand the thousands of medals you've received for your constant plowing. But alas, they will never understand. You lose your job, but that just means more time to motivate and plow. Days turn to weeks, weeks turn to months. You lose track of how many nights you've spent lying awake in a bed of empty ramen wrappers, fueled by caffeine and an itch that cannot be scratched. Nothing can satisfy. Drugs, women, Jesus, none of it. Your family tries an intervention, but even they know hopelessness when they see it. You just can't... stop... motivating... and plowing... searching... for that one... last... F'ING... BLUEPRINT FOR YOUR ARC.

    Too close to home? Yes, with the scene set, I introduce you to my theory: FoE intentionally changes the probability of getting a BP for a given square when it is the last square needed to make a BP set for building or leveling a GB, especially when the GB is an Arc.


    Before I dive into proof, "why would FoE do this" you ask? If you're here (and still reading this rant), you already know. Diamonds = money and money = ramen and the people at FoE LOVE RAMEN.


    1. We should expect to need to collect 25 BPs to get at least 1 complete set

    The problem of collecting all of a set when the probability of collecting one of each of the set is the same at each opportunity is called the "Coupon Collector's Problem". Generally speaking, people use the example of solving for the minimum number of expected rolls it takes to roll all 6 numbers of a fair dice (the answer is 15). The problem can be solved using a geometric distribution formula which can be applied to "how many BPs should we expect to have to collect in order to collect a full set?" There are online calculators that will do this for you.​

    2. We should expect to need to collect less than 25 additional BPs to get the 2nd set, and less for the 3rd, etc.

    The problem of figuring out the number of "opportunities" required to collect multiple sets is called the "Double Dixie Cup Problem" ("DDCP"). While it's much more complicated formula, the proof indicates it should take less "opportunities" to complete a set than it did the previous time. So if it takes 25 to get the 1st set, it should take less than 25 more for the 2nd set, and then less again for the 3rd set. Unfortunately, I don't have the math chops to calculate what this means for FoE and I couldn't find any online calculators out there to do it for me.

    3. My 8, non-Arc, 1 BP remaining, GBs are representative of #1 and indicate that BPs are indeed applied at random

    Of the 8, non-Arc GBs I have with only 1 BP remaining for a set, I've collected an average of 28 BPs all time and an average of 1 complete set for each. This is a little freaky, but goes to back up the probability in #1 (should expect 1 set in 25 BPs). This supports that FoE is using random probability for collecting BPs.


    4. I've collected a total of 57 BPs for the Arc while only accumulating 2 full sets. The probability of this scenario is much lower than it should be it BPs were being applied randomly

    **This gets a little complicated so I'm attaching a screenshot of my calcs**
    While we can't get to an exact probability using the Double Dixie Cup Problem, we can use a binomial distribution equation to determine the probability of getting "k" amount of BPs in 1 square given "n" amount of total BPs collected. I applied this formula to each of my GBs where I have 1 BP remaining to determine the probability of ending up in that scenario for that specific GB.

    • The probability of getting 0 BPs in a single square of Alcatraz given collecting 11 total Alcatraz BPs is 27% (pretty likely)
    • The probability of collecting 1 or less BPs in a single square of CDM given collecting 32 total CDM BPs is 11.5% (less likely, but still relatively likely).
    • The probability of ending up with exactly 1 BP in a square given collecting 25 total BPs is 21.7%
    • The average probability of where I ended up for each non-Arc GB is 20.0%
    • The probability of my Arc scenario is 4.0%

    WHY is the probability of my Arc situation so much lower than expected at 4.0% when the rest of the GBs I analyzed are nearly perfectly aligned with the expectation-based probability???

    Screen Shot 2018-12-05 at 12.28.14 AM.png


    • does not take into account BP trade-ins however, taking this into account would increase "n" and decrease the overall probabilities therefore this is a conservative estimate
    • Assumes all BP sources apply a BP in a truly random way for each individual event (1/9 chance each time)
    Caveat: sample size of 1 (me). Need more data!
    Last edited: Dec 5, 2018
  2. Emberguard

    Emberguard Active Member

    Oct 27, 2018
    Sample size me:

    Disclaimer: All views expressed are my own and are no way indicative of anything from the companies viewpoint

    Before I ever got an arc for some reason some sets in the end game ages was spread out reasonably even to the point where Arctic Orangery I had one BP in each spot for the first 8 BPs before anything doubled up. Anything low age *cough* lighthouse *cough* kept stacking BPs so it took a long time before I actually got my lighthouse without trading BPs. Had somewhere between 10-20 BPs in a single spot before getting the final BP I needed.

    So basically what's happening on your Arc BP hunting is exactly how my Lighthouse of Alexandria BP hunting was going: every spot but the one spot I needed

    Conclusion: Everything random in this game tends to go through stages of clumping and not clumping. As a player I've noticed this negotiating and spending event currency. It's still random overall. Just within that randomness you will get times that seem less random. Which is why when negotiating if I've got a final option left and I don't know the answer I'll go for something that's already given a green
    Last edited: Dec 5, 2018
    Stephen Longshanks and Graviton like this.
  3. Agent327

    Agent327 Well-Known Member

    Jan 22, 2018
    Your girlfriend was right.
  4. Graviton

    Graviton Well-Known Member

    May 22, 2015
    Not the first time this theory has been presented, although I believe you've spent more time on it than anybody else has. I still think it's a conspiracy theory born of confirmation bias and small sample size.
  5. Antiochos 1337 the Lucky

    Antiochos 1337 the Lucky New Member

    Dec 5, 2018
    I suspected the same conspiracy... so I created a spreadsheet, applied a Chi-Square test and entered my data and some friends data
    With 1542 bp spread on 6 GB (4 of them being Arc) I got a 94.35% chance that the distribution _is_ random.
    but if one look at individual GB with small number of bp the result look way more skewed.... my CdM, for example show a 7.09% chance of being a random distribution. Iow just like Graviton said above:
    [...] it's a [...] theory born of confirmation bias and small sample size.

    PS: I started that spreadsheet with the intent to confirm with hard data what I felt was some non-randomness at play. The data do not fit the hypothesis, the hypothesis is wrong.
    PS2: Randomness is hard and non intuitive.
  6. Roxana 1184 the Wise

    Roxana 1184 the Wise Active Member

    Oct 16, 2018
    Just got the last BP for my Arc on the 20th BP. If it is skewed, I really hit the jackpot. On the other hand, I got my last BP for CoA on the 43rd.
  7. Stephen Longshanks

    Stephen Longshanks Well-Known Member

    May 8, 2015
    Apparently your former girlfriend realized that your sample size was much smaller than you thought it was.:)
  8. amiar

    amiar Active Member

    Jan 7, 2018
    I posted something on this a while back with my CF. One BP spot was legit 30 BPs lower than anything else. All other 8 spots were within +/- 8 BP of one another. It was crazy. I'd put 1st on a friends CF, get like 28 BPs and would get all 8 but the bottom center...over and over again.

    Happened as well with my voyager. The center spot was so much lower than all the others!

    The only solution is to grit your teeth and keep collecting BPs!
    Sir Brandon Starr likes this.
  9. Sir Brandon Starr

    Sir Brandon Starr Member

    Sep 6, 2017
    The golden rule whenever there is RNG within a game is to always anticipate the worst. Delete all your expectations (which believe me is really difficult to do) and just play on. For example:

    -I will not get the last BP I need for a GB. If I do a 2 for 1 trade, I am going to get another duplicate.
    -I see a lot of incidents on my map. They will all be coins or coin boosts which I have an enormous surplus of.
    -I will not get the prize I want on the winter event. I will hit shuffle before I get the prize I want.

    I bring this up because I constantly need to remind myself this rule as I myself like to believe in conspiracy theories when my luck turns sour. It even happened last night when I got a researcher chest and thought I was going to get a good prize because the last one was 5 FPs. Nope, good ole law of averages failed me again LOL.

    In the end it is all random and as humans we are probably going to focus more on our bad luck streaks than our good luck streaks. Keep playing and your persistence will pay off!
  10. Sir Brandon Starr

    Sir Brandon Starr Member

    Sep 6, 2017
    With regards to my previous post, I can also share my experience on Sinerania. I don't remember the exact numbers but around lv 15 on my ARC I started getting a surplus of all BP slots except the top middle slot. I even remember asking myself if that slot was rigged because I'm certain I had about 6-7 BPs on all other slots. However, about 15 levels later it started becoming the middle left slot that I started running out on...and then the top right slot a few levels later...

    Emberguard made a very good point regarding clumping. Think of flipping a coin 100 times and getting 50 Heads and 50 Tails. One thing we never really consider is the order. What if 10 of those heads were consecutively? There is an interesting theory called Poisson clumping
    Last edited: Dec 6, 2018
  11. RazorbackPirate

    RazorbackPirate Well-Known Member

    May 29, 2018
    I doubt that it's truly rigged. Keep in mind that when you get to that last blueprint, there is an 8 to 1 chance you will not get the print you need. That can easily mean needing 12 - 16 additional prints just to fill that last spot.
    Sir Brandon Starr likes this.
  12. Mustapha00

    Mustapha00 Well-Known Member

    Aug 27, 2015
    Yes, but shouldn't that be true of all GBs? Assuming, for the sake or argument, that it is not of course.

    I've read posts such as this on more than one occasion, and I'm not sure if there is legitimately a problem with only the Arc or if the problem seems more prevalent due to the overwhelming popularity of and fixation to level the Arc. It might well be that Notre Dame has the same issue, but no one cares.
  13. Josar

    Josar Active Member

    Jan 27, 2018
    It would not surprise me if the randomness was weighted somehow. I could see an scenario where the longer you go without geting one square you would see a slight increase in a chance to get that square, but it hardly matters in any case.
  14. freshmeboy

    freshmeboy Well-Known Member

    Jul 17, 2017
    Don't listen to these guys..It is actually as random as it can get but being based on programming it will never be truly random....And remember, if you have bad luck it's because INNO hates you...
    Stephen Longshanks likes this.
  15. Emberguard

    Emberguard Active Member

    Oct 27, 2018
    It's not the Arc. I've had the same "problem" over just about every GB across 10 worlds - while also having times when getting a near perfect run for completing a set on a world over multiple GBs over those 10 worlds.

    Collecting Arc BPs so I can get to lvl 80 the spacing difference between spots has had moments when it's been quite a large gap, and other times where it's been fairly even.

    If it's truly random you can't expect every time to be evenly spaced. It wouldn't be fully random then. The argument would be more around what's the nature of that randomness. Is everything 11%~ chance or is each spot a different chance? Based on my results I don't see a weighted system.
    Stephen Longshanks likes this.
  16. Agent327

    Agent327 Well-Known Member

    Jan 22, 2018
    Start on a new world and see what it takes to get a full set of BP's of the Oracle :p
  17. Emberguard

    Emberguard Active Member

    Oct 27, 2018
    Haha. Love your sense of humour

    I already did get a full set without the quests :D Noarsil never received the Oracle because I built an Inno before that.


    ^ results of hunting Oracle BPs
  18. Konrad the mediocre

    Konrad the mediocre Well-Known Member

    Nov 13, 2014
    That is not how you calculate the probability. You use all the bps you've ever received for the arc and use the chi-square test to determine the probability that the bps are not evenly distributed. It's been done several times in the forums. That said, it does look odd, but with tens (hundreds?) of thousands of players have arcs, someone's likely to be on the short end.
  19. SomeGuyTed

    SomeGuyTed New Member

    Apr 29, 2018
    I have only two cities. My primary is where I try hard to plan and optimize. I did everything I could to accumulate Arc BP there and finally after a lot of effort I got it.

    My second(ary) city's job is to make diamonds for my primary. I don't even bother with RQs there after they cough up diamonds. Well - I got a full Arc BP set there after only collecting 17 of them.

    Literally, go figure.
    Stephen Longshanks likes this.
  20. RazorbackPirate

    RazorbackPirate Well-Known Member

    May 29, 2018
    It is. I've had this issue with various GBs in both of my cities.
    It's called confirmation bias. You're hyper fixated on it, so all you remember are the times it takes forever. Find mid-level 50+ Arcs to take 4th or 5th on. It goes much faster when you're getting 4-8 prints at one time.