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Technicus Broken

For a while now, I have avoided the technithief (haha) because intuitively it always felt "broken" to me. Allow me to explain.

When the technicus says the chance of success (COS) to upgrade is 10%, it should take an average of 10 clicks. Let's assume that the COS is independent from click to click i.e. repeated, independent Bernoulli trials. Then, we can ask some questions that can be answered using the geometric distribution like what is the mean, or average number of trials needed, for the first success? The mean is simply the inverse of the COS. So in this example, a 10% COS results in a mean of 1 / 0.1 = 10 clicks. We can also ask, what is the cumulative probability that we get a success in less than 50 clicks? Here again, the geometric distribution is appropriate and the answer is P(X<=50) = 1 - 0.9^50 = 99.5%.

I was sitting on a large sum of gold coins and I thought, let me try the technicus again to see if these probabilities feel right. The particular set I was working on had a COS was 6% for all four pieces. So, what is the average number of clicks before I see the first success? Answer: 1 / 0.06 = 17. Also, what is the probability I will see a success in 50 clicks or less? P(clicks <= 50) = 1 - .94^50 = 95.5%. Hmm, obviously not 100%, What about 100 clicks? P(X<=100) = 1 - 0.94^100 = 99.8%. OK, now we are talking about some serious bad luck if it takes more than 100 clicks. Well, just as I thought, of the four pieces I was trying to upgrade, it took me more than 50 clicks on 3 of the 4 pieces and one piece over 100 clicks before I gave up.

Now, it is well known that computers aren't capable of generating truly random numbers. It is probably even more likely that computer programmers are incompetent when it comes to implementing random number generators. Having experience in this field, I am always skeptical or curious to see just how a particular program or algorithm behaves. Does it exhibit truly random behavior? I have upgraded many, many pieces to +10 and I always count the clicks for each upgrade to get a sense if the probabilty is obeying the mean of a geometric distribution. And, for the first 10 levels they do i.e. my variances are small. But then something happens at the higher levels once the COS drops below 10%. Now, I am not saying it should NEVER take more than 50 or 100 clicks to upgrade an item when the COS is 6%, but that should be an outlier, not the norm. For example, what is the COS required to click unsuccessfully 50 times in a row 75% of the time? The answer is 0.6% which is more 10X less than the 6% advertised. So something is clearly wrong. But what?

The algorithm that GGS uses could be broken. The technicus could be reporting the wrong COS. The COS is not truly static or independent. But whatever is wrong, at the end of the day, whether or not the technicus algo follows the basic laws of probability is irrelevant because humans will quickly adapt their expectations to the true expected probabilities versus the reported probabilities. This is known as Bayesian statistics. I have never upgraded an item to +20. But, I have read other forum posts, and the fact that it takes literally hundreds of clicks on average to upgrade to +20 implies conditional probabilities on the order of only 1 to 3 in a thousand, and I would go as far to say that the true probabilities drop to below 10 in 1000 much sooner than +20. Maybe as early as +14. Which is fine. I understand that GGS prefers players to buy rubies versus clicking their way to +20.

But in case you were wondering, yes, the technithief is broken. Those reported chance of successes at the higher levels are actually a factor of ten less.

Comments

  • Wasso (INT3)Wasso (INT3) INT3 Posts: 3,332
    I had 2 pieces of the Shadow Sorcerer left at level 18.  I decided to go ahead and record my results.

    1st item
    Level 18 = 3% = got it on 7th click
    Level 19 = 2% = got it on 69th click
    2nd item
    Level 18 = 3% = got it on 16th click
    Level 19 = 2% = got it on 64th click

    So, you tell me what my results mean compared to yours and the % they were at.  Seems to work ok.

    Just watched over 4M coins go away, but it was worth it.  Thanks for getting my set to full power...…..
    Good night.
    Sleep well.
    I'll most likely kill you in the morning.




  • bernhardt (US1)bernhardt (US1) US1 Posts: 978
    I too always do a count and have found that the numbers are definitely off.  For me lvl 8 consistently has a high number of clicks, while 14 or 15 seems 'good'.  Once past lvl 9, I just expect about double the clicks the theif's percentage says and that seems to be about the top of the bell curve from a seat of the pants record keeping methodology.
  • Sorth121 (US1)Sorth121 (US1) US1 Posts: 215
    Key is just to click in the right spot. If you do you can get to level 13 without failing at all, makes the losses on higher levels easier to take. 
    MUFU Member




  • bernhardt (US1)bernhardt (US1) US1 Posts: 978
    That's with the various click sheets I have.  Even worse when I try the just click.
  • Crom CruachCrom Cruach Community Manager Posts: 1,362
    I think Wasso went a long way to confirm that things are working fine. 
    Forum SignatureDiscordFacebookTwitter
  • Wasso (INT3)Wasso (INT3) INT3 Posts: 3,332
    Thanks for the vote of confidence.  However, my experience being different than that of others just proves that Anecdotal Evidence isn't reliable.  ;)

    As for HOW I could have gotten those level 18's so quickly, got me to thinking.  (I know, dangerous pastime for me)  What if I had clicked 50 times before on those pieces and gave up.  Now, going back to them and clicking the extra 7 and 16 times go me to the "success"?  Does the system know how many times you have attempted on each piece, and use some formula to determine when you will be successful?   Or even simpler than that - instead of being random - the number of attempts is predetermined from a pool of 1000s.  When you get your piece, it comes with the corresponding amount of attempts it will take to Tech them up each level.  This would make the attempts easy to track on system, AND be a process that GGS could point to and KNOW that the COS is actually correct for the whole - if not the individual.

    Like I said, a dangerous pastime for me...……. 
    Good night.
    Sleep well.
    I'll most likely kill you in the morning.




  • StrongCommander (US1)StrongCommander (US1) US1 Posts: 442
    edited 27.03.2020
    Thanks for the vote of confidence.  However, my experience being different than that of others just proves that Anecdotal Evidence isn't reliable.  ;)

    As for HOW I could have gotten those level 18's so quickly, got me to thinking.  (I know, dangerous pastime for me)  What if I had clicked 50 times before on those pieces and gave up.  Now, going back to them and clicking the extra 7 and 16 times go me to the "success"?  Does the system know how many times you have attempted on each piece, and use some formula to determine when you will be successful?   Or even simpler than that - instead of being random - the number of attempts is predetermined from a pool of 1000s.  When you get your piece, it comes with the corresponding amount of attempts it will take to Tech them up each level.  This would make the attempts easy to track on system, AND be a process that GGS could point to and KNOW that the COS is actually correct for the whole - if not the individual.

    Like I said, a dangerous pastime for me...……. 
    Since it works with a % setting you have x% each time to upgrade the item.
  • Wasso (INT3)Wasso (INT3) INT3 Posts: 3,332
    Thanks for the vote of confidence.  However, my experience being different than that of others just proves that Anecdotal Evidence isn't reliable.  ;)

    As for HOW I could have gotten those level 18's so quickly, got me to thinking.  (I know, dangerous pastime for me)  What if I had clicked 50 times before on those pieces and gave up.  Now, going back to them and clicking the extra 7 and 16 times go me to the "success"?  Does the system know how many times you have attempted on each piece, and use some formula to determine when you will be successful?   Or even simpler than that - instead of being random - the number of attempts is predetermined from a pool of 1000s.  When you get your piece, it comes with the corresponding amount of attempts it will take to Tech them up each level.  This would make the attempts easy to track on system, AND be a process that GGS could point to and KNOW that the COS is actually correct for the whole - if not the individual.

    Like I said, a dangerous pastime for me...……. 
    Since it works with a % setting you have x% each time to upgrade the item.
    That is how it is supposed to work, yes.   But, people question if it is really happening that way.  

    For example. it was quite fortuitous that I was able to get not one, but TWO level 18 pieces (with a 3% chance of success) in less than 20 clicks each.  Then, on BOTH of my level 19's they were successful within 5 clicks of each other.  69 vs 64.  

    I agree, that odds and probability can look "odd" at times.  :)  But, COULD there be more to the way GGE does the Technicus than meets the eye?

    Inquiring minds want to know...…….
    Good night.
    Sleep well.
    I'll most likely kill you in the morning.




  • bernhardt (US1)bernhardt (US1) US1 Posts: 978
    @Crom Cruach  Wasso's results are anecdotal too since the sample size is so small.  I just haven't used the tech of late to come with another sample to support the other side that double the predicted clicks happens far more often than it should as the OP shown.  Do your own research using statistics, and short of that ask other players in the game.  There's a reason the tech is called the ripper, theif ect by a very large percentage of the players.  People have been saying for years the numbers are off but it has never been taken seriously by GGE.


  • Thanks for the vote of confidence.  However, my experience being different than that of others just proves that Anecdotal Evidence isn't reliable.  ;)

    As for HOW I could have gotten those level 18's so quickly, got me to thinking.  (I know, dangerous pastime for me)  What if I had clicked 50 times before on those pieces and gave up.  Now, going back to them and clicking the extra 7 and 16 times go me to the "success"?  Does the system know how many times you have attempted on each piece, and use some formula to determine when you will be successful?   Or even simpler than that - instead of being random - the number of attempts is predetermined from a pool of 1000s.  When you get your piece, it comes with the corresponding amount of attempts it will take to Tech them up each level.  This would make the attempts easy to track on system, AND be a process that GGS could point to and KNOW that the COS is actually correct for the whole - if not the individual.

    Like I said, a dangerous pastime for me...……. 
    Since it works with a % setting you have x% each time to upgrade the item.
    That is how it is supposed to work, yes.   But, people question if it is really happening that way.  

    For example. it was quite fortuitous that I was able to get not one, but TWO level 18 pieces (with a 3% chance of success) in less than 20 clicks each.  Then, on BOTH of my level 19's they were successful within 5 clicks of each other.  69 vs 64.  

    I agree, that odds and probability can look "odd" at times.  :)  But, COULD there be more to the way GGE does the Technicus than meets the eye?

    Inquiring minds want to know...…….
    A good way to test this is upgrade items and record times/ successful upgrade/ succession per cent.

    And then compare them somehow...
  • Damaden (US1)Damaden (US1) US1 Posts: 69
    edited 10.07.2020
    Thanks to everyone for the great replies in this thread that I haven't visited in a while. Also, thanks to Wasso for posting his/her results. I think that if we want to really add some meat to this thread, players should post their results. Let's be honest though. Don't just post your bad results.

    I will start keeping track of a Master Summoner set that I am trying to upgrade to +20. I wish I had more results to post at this point, but I am feeling more than a little defeated after the first piece. I wish I had Wasso's results. But, alas here is my first Level 18 upgrade ever:

    Level 18 (3%) => 105 clicks

    Assuming each click can be accurately modeled as an independent, Bernoulli trial, the expected number of clicks before the first success with a 3% COS is 1 / 0.03 = 33.3. The implied probability from 105 clicks is 1 / 105 = 0.95%. This is a discrepancy of more than 3 times!

    At this point, it is useless to assume anything. Rather, we are much better off using Bayesian inference. The Bayes estimator for a binomial model is the Beta distribution, B[a,b]. The posterior distribution and expected mean are given as:

    p (theta | y) = Beta [theta | a + y, b + n - y]
    E [theta | y] = (a + y) / (a + b + n)

    where y is the number of successes over n clicks, or y = 1 and n = 105.

    Let's use the advertised Technicus COS to inform our prior. A Beta distribution of B[1,33] seems reasonable and:

    p (theta | y) = Beta [1 + 1, 33 + 105 - 1] = B[2, 137]
    E [theta | y] = (1 + 1) / (1+33+105) = 1.4%

    So, the posterior observed Technicus COS after one Bayesian update is at least a factor of two lower than the advertised COS. I have three more pieces to upgrade in my Master Summoner set to update the Bayes estimator three more times. At this point, it would literally take something like Wasso's results to bring this in line with the advertised COS. But bear in mind, the expected number of clicks based on the result above is 70 which intuitively seems much more in line with expected and observed results than the 33 implied from the advertised COS. I will be using 70 as my expected number of clicks for the remaining three pieces. If I see something less than 70, I will of course be happy. But I feel I am just as likely to see something higher than 70 which is why it is called the expected mean.

    EDIT: I have to admit after pondering Wasso's Level 18 results along with mine, I am nonplussed why the results aren't congregating in the 30s and instead seem all over the map. The implication is that the true distribution has a wide variance thus rendering the mean almost meaningless. Very troubling indeed. I seriously doubt GGS would ever reveal their algo, so let's keep going. We need more results!
    Post edited by Damaden (US1) on
  • I don't count the clicks - i can usually gain a fully upgraded piece for about 5m coins , it seems to work better if you can get the pointer in the exact centre of the icon - and have seen threads / posts in the past showing guarenteed results if positioned correctly !

    dandelion1958 @ en 1

    Am still playing 8 years on ! - hi lvl 800 on new yrs eve (2017/18) !

    Leading the Targaryens - PS interested in joining - PM any officer in Game :-)
    taking a more relaxed role:-)
    PS in top200 on uk 1 never botted or used a VPN - that's why it took 5 yrs to get to leg 800
  • saywhat (AU1)saywhat (AU1) AU1 Posts: 5
    It is not as simple as saying I have a 2% chance to win so that means I should get it in 50 clicks or less.
    Each click independently has a 2% chance. The easiest way to calculate your actual odds are to look at your failure rate. at 2% your failure is 98%. To calculate your chance of success for 50 clicks you do 98% ^ 50 which would show a failure chance of 36.5% which means you have a 63.5% chance you will get success on the 50th click. But still means there is a chance not to succeed. 

    Even at 100 clicks there is still only an 87% chance you will have succeeded. It is possible you have not.
    and at  150 you still only have a 95% chance of success. So there are some people who may still have not successfully reached the level by here.

    There is no point where you get to 100% and as each click is independent there will never be consistent results. some days you will get lucky some you won't.

  • eibbed62 (AU1)eibbed62 (AU1) AU1 Posts: 383
    Back in the days when I was still using technothief, I found that positioning the cursor in the right spot on the upgrade button greatly improved the chances of success. I had plotted the optimal positions for each level and found I could often get to level 12 or 13 with maybe only a couple of fails. For the higher levels there were more fails, but my successes were always achieved when I found the exact spot for that level (of course I was only clicking in the vicinity of my previous successes for that level)  I was never 100% sure whether this was intended, or purely coincidental, but it seemed to work for me. I upgraded many pieces using this method before the introduction of the red sets, and then later, the relics, made them worthless.
    These days I don't bother wasting my coins. I just sell them off when they fill up my equipment storage.

    Regards,
    Debbie
    eibbed62 @ au 1
  • Damaden (US1)Damaden (US1) US1 Posts: 69
    edited 13.07.2020
    Some interesting responses. I appreciate the discussion.
    I don't count the clicks - i can usually gain a fully upgraded piece for about 5m coins , it seems to work better if you can get the pointer in the exact centre of the icon - and have seen threads / posts in the past showing guarenteed results if positioned correctly !

    Back in the days when I was still using technothief, I found that positioning the cursor in the right spot on the upgrade button greatly improved the chances of success. I had plotted the optimal positions for each level and found I could often get to level 12 or 13 with maybe only a couple of fails. For the higher levels there were more fails, but my successes were always achieved when I found the exact spot for that level (of course I was only clicking in the vicinity of my previous successes for that level)  I was never 100% sure whether this was intended, or purely coincidental, but it seemed to work for me. I upgraded many pieces using this method before the introduction of the red sets, and then later, the relics, made them worthless.
    These days I don't bother wasting my coins. I just sell them off when they fill up my equipment storage.

    Regards,
    Debbie
    This could potentially explain the difference in results between mine and Wasso's. But then, how do we interpret the advertised 3% COS? Is it the mean across all pixels? Or, is it the mode while one or two isolated pixels operate like honey pots? And if so, what is their COS?

    It is possible to infer the true, underlying probability (or probabilities) via Bayesian inference. We just just need people to post their trials. This much I am 100% confident in.

    I will be posting mine as soon as I save up enough coins to upgrade my 2nd Master Summoner piece to level 19.
    Post edited by Damaden (US1) on
  • Damaden (US1)Damaden (US1) US1 Posts: 69
    edited 13.07.2020
    It is not as simple as saying I have a 2% chance to win so that means I should get it in 50 clicks or less.
    Each click independently has a 2% chance. The easiest way to calculate your actual odds are to look at your failure rate. at 2% your failure is 98%. To calculate your chance of success for 50 clicks you do 98% ^ 50 which would show a failure chance of 36.5% which means you have a 63.5% chance you will get success on the 50th click. But still means there is a chance not to succeed. 

    Even at 100 clicks there is still only an 87% chance you will have succeeded. It is possible you have not.
    and at  150 you still only have a 95% chance of success. So there are some people who may still have not successfully reached the level by here.

    There is no point where you get to 100% and as each click is independent there will never be consistent results. some days you will get lucky some you won't.

    saywhat, in your analysis you are tacitly assuming that each click can be modeled as independent, Bernoulli trials thereby comprising a Bernoulli process (q.v. my above comments on the potential veracity of this). In the realm of statistics, this process has been rigorously analyzed, and the expected number of trials (clicks) is analytically determined as:

    E (clicks) = 1 / p, where p is the probability of each success

    So, in your example, where p = 2%, the expected number of clicks is 50. Now, this is not the same as saying how many clicks are required to guarantee success. Rather, it is a statistic that says you are just as likely to click fewer than 50 times as you are to click more than 50 times. Think of it like the fulcrum of a see-saw. If the see-saw represents the number line between 1 and 1000, where would you put the fulcrum so that it balances perfectly? The answer is 50. Hopefully, that makes sense.

    And, while you are correct in pointing out that you never have 100% COS, even for 150 clicks, I think this is where we get into some of the nuances of statistics. You seem to imply that because the possibility of 150 clicks exists, it is just as likely as 50 clicks, and this is the source of inconsistent results. But in actuality, if we get enough people to post their results, we should 100% see some consistency in the results. We would observe that 50% of the results are below 50 and 50% are above 50. The results would also exhibit an underlying variance. IOW, we would see the results congregate around 50 +/- some reasonable variance versus results all over the map. We could see one or two results of 150 or more clicks, but these should be outliers.

    But, it is possible to avoid all this discussion by just taking a Bayesian view of the world which I have done. As of now, my Bayes' estimator is 1.4% versus the 3% shown in the Technicus dialog box. Therefore, I have recalibrated my expectations to 70 clicks (1 / 0.014). As I stated before, that means I am just likely to click fewer than 70 times as I am more than 70 times. But, what I didn't say is, I no longer harbor the naive view that I am just as likely to click fewer than 33 times as I am more than 33 times. Nor, do I expect the results to congregate around 33. I fully expect my results to congregate around 70. That may seem like a strange view, but that is how Bayesian statistics work.
    Post edited by Damaden (US1) on
  • Damaden (US1)Damaden (US1) US1 Posts: 69
    I promised to post my results. Here they are:

    Trial 1: +19 (3%) -> 105 clicks
    Trial 2: +19 (3%) -> 44 clicks

    Updating the posterior distribution after the second trial from the Bayesian inferred Beta distribution of B[2, 137]:

    p (theta | y) = Beta [2 + 1, 137 + 44 - 1] = B[3, 180]
    E [theta | y] = (2 + 1) / (2  + 137 + 44) = 1.6%

    Therefore, the Bayesian inferred chance of success after 2 trials is 1.6%. I would also point out that this is more generous than the non-Bayesian method of estimating the COS after two trials which is simply 2 / (105 + 44) = 1.3% (for any of you non-Bayesians out there).

    Seeing that this cost me less than half of the first trial, I will hopefully be back sooner with the third trial.
  • Damaden (US1)Damaden (US1) US1 Posts: 69
    I am back:

    Trial 1: +19 (3%) -> 105 clicks
    Trial 2: +19 (3%) -> 44 clicks
    Trial 3: +19 (3%) -> 11 clicks

    Recall that the Bayesian inferred COS after the second trial via the Beta distribution of B[3, 180] was 1.6%. Now updating after the third trial:

    p (theta | y) = Beta [3 + 1, 180 + 11 - 1] = B[4, 190]
    E [theta | y] = (3 + 1) / (3  + 180 + 11) = 2.1%

    Therefore, the Bayesian inferred chance of success after 3 trials is 2.1% putting the posterior expected number of clicks at 49.

    Now, this is a significant improvement over the first two trials, and I still have one more piece to upgrade to +19. However, my experience with the Technicus at these high levels is that upgrading several items at once results in really bad outcomes.

    Recall from my OP, I was upgrading all the pieces of this set at once when the COS was 6%. The first 3 pieces took more than 50 clicks, and the last piece took more than 100 before I gave up. I didn't record the exact number of clicks, but using a conservative 50, 50, 50, and 100 clicks results in a Bayesian inferred posterior COS of 1.9%. This is why I took to the forums. Something clearly was up.

    However,, the game had a major update a couple of days ago. Could it be that GGS read my post, looked into the algo of the Technicus, found a bug, and fixed it? I just tried a legendary piece I had sitting in my inventory and upgraded it from +1 to +10. I have done this many, many times building out fire castellans, so I am well acquainted with about how many total clicks it takes. I am not going to lie, it went significantly better than usual, and the +10 upgrade succeeded on the first click which I think is a first!

    I know GGS will never admit to anything being broken, but it doesn't take a genius to recognize that the behavior is suddenly different. And I'm not complaining. If my last piece takes less than the reported expected number of clicks (33), then I will be ecstatic and much more confident going into the final, +20 upgrade at the daunting 2% COS. Stay tuned.
  • Damaden (US1)Damaden (US1) US1 Posts: 69
    Fourth and final update:

    Trial 1: +19 (3%) -> 105 clicks
    Trial 2: +19 (3%) -> 44 clicks
    Trial 3: +19 (3%) -> 11 clicks
    Trial 4: +19 (3%) -> 49 clicks

    Recall that the Bayesian inferred COS after the third trial via the Beta distribution of B[4, 190] was 2.1%. Now updating after the fourth trial:

    p (theta | y) = Beta [4 + 1, 190 + 49 - 1] = B[5, 238]
    E [theta | y] = (4 + 1) / (4  + 190 + 49) = 2.1%

    As you can see, the Bayesian inferred COS after four updates is unchanged and has converged on 2.1%. For you frequentists out there, the inferred COS is 1.9% which is slightly lower. I find this quite troubling and so should you.

    Unfortunately, I don't have any more pieces to upgrade to +19, so fellow Lords and Ladies, it is now up to you to post your results.
  • Wasso (INT3)Wasso (INT3) INT3 Posts: 3,332
    Fourth and final update:

    Trial 1: +19 (3%) -> 105 clicks
    Trial 2: +19 (3%) -> 44 clicks
    Trial 3: +19 (3%) -> 11 clicks
    Trial 4: +19 (3%) -> 49 clicks

    Recall that the Bayesian inferred COS after the third trial via the Beta distribution of B[4, 190] was 2.1%. Now updating after the fourth trial:

    p (theta | y) = Beta [4 + 1, 190 + 49 - 1] = B[5, 238]
    E [theta | y] = (4 + 1) / (4  + 190 + 49) = 2.1%

    As you can see, the Bayesian inferred COS after four updates is unchanged and has converged on 2.1%. For you frequentists out there, the inferred COS is 1.9% which is slightly lower. I find this quite troubling and so should you.

    Unfortunately, I don't have any more pieces to upgrade to +19, so fellow Lords and Ladies, it is now up to you to post your results.
    Please add in my numbers from WAYYYYYYYYYYYYYYY up there, and report what you get.

    To help out, here they are..............

    Wasso (INT3) said:
    I had 2 pieces of the Shadow Sorcerer left at level 18.  I decided to go ahead and record my results.

    1st item
    Level 18 = 3% = got it on 7th click
    Level 19 = 2% = got it on 69th click
    2nd item
    Level 18 = 3% = got it on 16th click
    Level 19 = 2% = got it on 64th click

    So, you tell me what my results mean compared to yours and the % they were at.  Seems to work ok.

    Just watched over 4M coins go away, but it was worth it.  Thanks for getting my set to full power...…..

    Good night.
    Sleep well.
    I'll most likely kill you in the morning.




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