So, few days ago, I finally gathered all the materials needed to craft 96 dragon shiner bows. Materials needed for crafting 96 Dragon Shiner Bows: • [2400] Dragon Scales • [1920] Dragon Spirits • [480] Dex Crystal Refines • [288] Power Crystal Refines • [96] Bow Production Stimulators • [96] White Nisrocks • [11,520,000] Mesos Market Value Cost of the Items: • [2400 * 1m] = 2.4b • [1920 * 500k] = 0.960b • [480 * 1.2m] = 0.576b • [288 * 4.2m] = 1.209b • [96 * 1m] = 0.096b • [96 * 500k] = 0.048b • [96 * 120k] = 0.01152b Total Cost = 2.4 + 0.96 + 0.579 + 1.209 + 0.096 + 0.048 + 0.01152 Total Cost = 5.30352b in materials. In this one session, I decided to craft all at once. Total Dragon Shiner Bows Crafting, n = 96. Total Variations possible, v = 17. Using Bow Production Stimulator, you have a possible chance of failure that can occur. and then, 95~110 is 16 variations, thus totaling to 17 variations. As follows is the math based on this thread: https://royals.ms/forum/threads/forging-weapons.22424 variable 1 = using stim, 90% chance to succeed [understood through item description] variable 2 = pre-godly stats being w.att of 95~105 [11 variations, because 105 is also considered normal] variable 3 = 10% chance of triggering godly 'roll' variable 4 = any of the 6 godly variations [+0, +1, +2, +3, +4, +5, +6] (90/100)*(1/11)*(10/100)*(1/6) = 0.00136363636 * 100% = 0.136363636% So I would apparently have a 0.136363636% chance of making a godly weapon with perfect stats. However, after crafting 96 attempts, below are the results. The Results Are As Follows: [0] W.Att 110's [0] W.Att 109's [0] W.Att 108's [0] W.Att 107's [0] W.Att 106's [5] W.Att 105's [7] W.Att 104's [13] W.Att 103's [5] W.Att 102's [9] W.Att 101's [9] W.Att 100's [7] W.Att 99's [9] W.Att 98's [5] W.Att 97's [12] W.Att 96's [6] W.Att 95's [9] Complete Exploding Failures While it's not possible to see the exact bow stats of all of them, the image below though edited, shows an existing amount of 96 - 9 = 87 bows. Spoiler: 87 Dragon Shiner Bows In terms of my results, I agree crafting a perfect dragon shiner bow is about 0.136363636% chance. However, I find it incredibly strange that I did not get even one weapon attack of 106~110 bow. Was hoping if the admins can look into this! References Used: https://royals.ms/forum/threads/forging-weapons.22424 https://royals.ms/forum/threads/godly-items-explained.1312 https://royals.ms/library/?page=items&search=shiner+bow
@sounaa , Complaining is defined as express dissatisfaction or annoyance about a state of affairs or an event, so I suppose I am. However, incorrect you are on the aspect of crafting specifically a perfect bow. I would be lying if i said that i'm not happy I didn't get a perfect weapon, but rather that's irrelevant. Primarily, astonished at not receiving any out of the 96 shiners within 106~110 w.att, which is why this thread was created. @sounaa , your response provided no relevant information, please refrain from doing so as well as anyone else, thanks! ^_^
Not sure if your godly section calculation is right. Godly is applied as almost an extra stat (like a free chaos scroll). That means that getting a godly stats item isn't linear. If a bow ranges from 95-105, here is the summation of the godlies items. 95 + (0-5) 96 + (0-5) 97 + (0-5) 98 + (0-5) 99 + (0-5) 100 + (0-5) 101 + (0-5) 102 + (0-5) 103 + (0-5) 104 + (0-5) 105 + (0-5) That gives an effective probability of each number out of all 11 attacks * 6 outcomes of godly 95 (1/66) 96 (2/66) 97 (3/66) 98 (4/66) 99 (5/66) 100 (6/66) 101 (6/66) 102 (6/66) 103 (6/66) 104 (6/66) 105 (6/66) 106 (5/66) 107 (4/66) 108 (3/66) 109 (2/66) 110 (1/66) Adding the probability of what you want as godly items, that is 15/66 (22.72%) that it is godly, instead of what you would perceive as 5/11 (45.45%) godly. Please double check this math, since I could very well be wrong.
This is exactly how Dimitri explained to me. There is a 1/10 chance that an item is affected by the godly system but the item must have perfect stats itself. A 100 att shiner bow affected by the godly system giving a result of 105 may not seem as godly but it actually is affected by the godly system
I really doubt an admin would say anything else than 'the godly system works, you just got unlucky'. There's no real proof here for it not working; 96 is a pretty small sample size.
To finish my math calculation up, the probability of getting a 106-110 bow should be (0.9) * (0.1) * (15/66) = 2.045% chance Getting a 110 bow should be: (0.9) * (0.1) * (1/66) = 0.136% (which is what you got) Using a binomial calculator to see the probability of getting 0/96 godlies: Although unlucky, the 13.8% chance of getting no godlies in 96 pulls is well within a, say 90% or 95% confidence interval which means that it is unlikely for the system and coding to be incorrect.
Hmm good work but one thing I don't understand is the confidence interval part. Isn't a confidence interval built around a sample mean, like in this case the measured sample p is 0/96=0? So I guess we have to do 1-sided test so z=1.65, but also sample standard deviation (sqrt(pq/n)) is also 0 because p is 0 so... It doesn't make sense. Idk really but I found on google that confidence intervals with a sample p near 0 or 1 are highly inaccurate but sometimes people use as an approximate (3/n) for 95% CI or in this case 0.03135. So, maybe an estimated confidence interval is (0.03135). I'm not sure what conclusion can even be made from that, lol. I followed your probability math and you got there is a 13.8% chance that he gets no 106 to 110 att bows in 96 tries. Good work and I agree. But my confusion is, is this really a problem that can use a confidence interval? I think it's purely probability.
Ok but you're just angry you couldn't craft a perfect bow. Idk what you want the admins to do about it. Get luckier?
I think you missed his point. From what I've read, what he's saying is that its odd out of all the bows he crafted, none were affected by the godly system. You don't need a perfect bow for it to be affected.
oh, totally wrong as to how I thought it worked then. I forgot that it could only increase certain stats. @Buccaneer Question then, the 15/16 (22.72%), that represents the sum of effective probability of godly outcomes. So, that's the multiplier for the 'godly' roll variable. I guess I don't follow the reasoning why it is combined as 11*6 = 66. Was it / is it possible to separate them into multiplier terms such as the calculation i've done in the original post? @sounaa lol believe me, not angry at all considering the history of my book success rate + scrolling success rate. i've already come to terms with that, just thought at least this would be different, but apparently not true! as @Shnang clearly pointed it out in 3 letters, RNG. learn to say more than those 3 letters! Anyway, objective of this thread, again, was to figure out I crafted no weapons within the attack range of 106~ 110. As my statistical math skills failed, I think @Buccaneer figured it out correctly from what I understood so far at least. Although unlucky, the 13.8% chance of getting no godlies in 96 pulls is well within a, say 90% or 95% confidence interval which means that it is unlikely for the system and coding to be incorrect. I suppose then, it was a ~2% chance that a godly was rolled and I was affected by it from understanding as @87Karlos also said, "A 100 att shiner bow affected by the godly system giving a result of 105 may not seem as godly but it actually is affected by the godly system" As of this moment, I am statistically satiated by the figures given in this analysis! However, lol realistically speaking, I dont know if it's possible, but i'm still wondering from the admin's end, if something can be done to test it / verify!? Thank you ALL for your feedback! more to some than others! f3
When I think about it more, I was thinking about confidence interval wrong and getting confused. Confidence intervals are used to estimate an unknown mean. So, it's not really used here. In this problem we actually want to do hypothesis testing. This might be redundant, as the probability alone might be enough to accept. Hmm I'm busy will look at later lol
Welcome to the club! If it makes you feel any better I crafted a max inventory of knuckles aswell & each takes..... 5 mithril plates ea to make. On the bright side you have a bunch of bows to scroll for $$$ Spoiler: Sucks
I found you can do the following hypothesis tests: 1-sided Hypothesis test (n>40): p = 0.02045, n = 96 σ = sqrt(pq/n) = 0.0144 α = 0.05 H0: p = 0.02045 H1: p< 0.02045 z = ((0/96)-p)/σ = -1.416 z' = z at α=0.05 = -1.645 Since z > z', fail to reject the null (this evidence is not statistically significant with 95% confidence level) Alternative 1-sided Hypothesis test (n>40): p = 0.02045, n = 96, μ = pn = 1.967 σ = sqrt(pqn) = 1.387 α = 0.05 H0: μ = 1.967 H1: μ <1.967 z = (0-μ)/σ = -1.416 z' = z at α=0.05 = -1.645 Since z>z', fail to reject the null. Note, this set of z and z' is exactly the same as before. P-value Hypothesis test: H0: p = 0.02045 H1: p< 0.02045 X~bin(96, 0.02045) Reject H0 if P(X<=0) <= 0.05 P(X<=0) = (1-p)^n = .13751 Since P(X<=0) > 0.05, fail to reject the null. By Inspection: All that needs to be done is realize 13.8% chance for OP's outcome is not too unlikely. This raises the question, at what percentage would you think something is wrong? 5%? 1%? This is basically what a hypothesis test does for you. Normal Approximation: Since a binomial distribution has known probability distribution, approximating it as normal distribution to calculate Z value of sample data is unnecessary. Using a P value is superior to avoid error. For instance, Z value of -1.416 as calculated earlier has a P value of 0.07839 as opposed to .1375. I guess this is the error of approximating a normal distribution. Maybe as Since a binomial distribution has known probability distribution, approximating it as normal distribution to calculate Z value of sample data is unnecessary. What I did is inaccurate Conclusion: I had a feeling I was making it too complicated but I'm happy the statistics go along with intuition. Also, there probably is nothing wrong with the system lol Extra things I made because I was bored Spoiler: Extra things i made because i was bored i should be doing hw... fml
