[Guide] How Negotiator (Pro) and Treasure Hunter Works

Discussion in 'Guides' started by Kivanc, Dec 11, 2014.

  1. Cel

    Cel Well-Known Member

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    Humans tend to try to find pattern in randomness, which is what you're trying to do. From a statistics point of view, it fits in the randomness.

    In case you're wondering, I run 20-1 a lot and I see all types of drops. One recent run, all I got was 1 Animaton. Just 1, and nothing else. There's about 120 enemies in 20-1, and each, on average, has a 6% chance to drop one item (approximately). So a normal run without treasure hunter, it's probably about 7.2 items (plus 0.8 for rare ores + moon tears), you're expected about 8 items. You're getting more than that, on average.

    Do a few more runs, and keep track of the results, and I'd like to know if you feel like you aren't getting drops. Good luck!
     
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  2. sendru

    sendru Active Member

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    All we know is that those drop events are never independent, so large number theory is not applicable.
     
  3. Kivanc

    Kivanc The Data Keeper

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    What do you mean that drop events are never independent? The normal (simplest) way to think about it is that they ARE independent of each other. Do you mean something else?
     
  4. efecinc

    efecinc New Member

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    A question, it may sound stupid but do the powe points affect to Nego and NegoPro? I mean, if I cast a Nego with a powerpoint, its effectiveness is still x8 or does it increase?
     
  5. Kivanc

    Kivanc The Data Keeper

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    Same, it just guarantees activation is you have SB less than 70%.
     
  6. naynaybo

    naynaybo New Member

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    [​IMG]
    Just wanted to see if it was a "pattern" unique to my experience, or if others noticed a similar one. Thanks for the input! I'll try and keep track on future runs. I hope that was your last "1 drop" run and you start racking them up :)
     
  7. phario86

    phario86 Active Member

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    The probability that you drop no items from the regular enemies, is about 0.94^120 = 0.06%. You'd see it once every 1700 runs. Damn rare, but within the scope of reason, I suspect, given how often some people run 20-1.

    I've had similar odds, where I had to run one of the stages more than 30 or 35 times to get Koko's legendary weapon. I'm told the odds are 20% of a drop, so the probability this happened is about 0.1%.

    To be honest, I can't comment on how truly random things are because I don't understand the inner workings of the random number generator.
     
  8. sendru

    sendru Active Member

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    Suppose that the drop events (monster, item) are independent to each other, from the large number theory, they will follow the normal distribution with the stardard deviation sigma/square_root(n-1), where sigma is the standard deviation of one single event, and n is the number of events. When 20-1 is applied, the stardard deviation should be small. Since we observe a large variants in the item drop, this is a proof of pseudo randomness. However, since the expection does not need the assumption of independence, we can estimate it as before.
     
  9. Kivanc

    Kivanc The Data Keeper

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    why standard deviation for single event is small for 20-1? Because you face a lot of monsters? Considering that the base drop rate for most of the common items are already as low as 3%, I cannot follow (although I am not very familiar with Math) why you would expect a small standard deviation.
     
  10. Kivanc

    Kivanc The Data Keeper

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    Minor correction, the mobs can drop two different type of items (correct), but each item has a 3% independent drop rate (not 6% combined). So, probability of not getting any item would be:
    0.97^240 ~= 0.07, even slightly higher than your initial computation.
     
  11. Cel

    Cel Well-Known Member

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    Looking at our data, from 20-1, we have 126 enemies. They all have 2 chances to drop 3% items, and 4 bosses who have a 20% chance to drop items. If additional airgrunts are summoned by chargebot, this number can increase to 132. I'm going to use n=250 (approx 125*2), and p=3%. This is a simple binomial distribution. For the large number theory to apply, and for the normal distribution to apply to this set of data, it's normally set that np > 5 or n(1-p) > 5. Since p is small, the former applies, and n needs to be 167 in our case. So our case for one run of 20-1 can be applied and approximated by the normal distribution.

    So let's look at the properties of the normal distribution. The normal distribution (for number of successes, aka drops) has a mean of np = 7.5, and a standard deviation of np(1-p) = 7.275.

    So, if we're checking 2SDs from the mean using our distribution, we're including 95% of possibilities or basically 0 ~ 22.05, and if we want 3 SD's and including 99.5% of possibilities it's 0 ~ 29.325.

    Edit: Because we can use computers these days, I just plugged numbers into Excel: 95% cumulative probability using 127 enemies (one spawned Airgrunt), gives 12 drops. 99.5% cumulative probability gives 15 drops. If you get less than 1 drop, the chance is 0.387% or about 1 in 259. Note of course, there are all non-rare drops. Also it shows that our normal approximation is pretty off.

    I don't know about you, but my drop rate fits within those boundaries quite well. Are you getting more than 22 non-rare drops per run without treasure hunter? And given the discrete nature of drop rolls, I'm not sure one treasure hunter increases the drop rates anyways.

    Lastly, most random number generators are pretty damn good. Unless you're using it for cryptography or other sensitive subjects, the Mersenne Twister works very well.
     
    Last edited: Jan 13, 2015
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  12. Kivanc

    Kivanc The Data Keeper

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    Excellent post @Cel, thanks! I was expecting something along this lines and glad that the actual math also says it.
     
  13. sendru

    sendru Active Member

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    My calculation is here:
    X 0.03 drop, 0.97 non drop
    E(x)=0.03
    Var(x)=0.029
    n=126 mobs *2= 252
    E(nx)=7.56
    Var(nx)=7.308
    Sigma(nx)=2.703
    It is a rare case whose probability is 0.05 that you get 2 times of standard deviation from the mean, which is 1.9 to 12.7, you should reject the hypothesis that drop events are independent, otherwise you can accept it.

    And you should observe in 66.67% cases that the item is between 4.8 and 10.2 and it is not from my personal experience.
     
    Last edited: Jan 14, 2015
  14. sendru

    sendru Active Member

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    correct me if I am wrong, should np(1-p) be the variant instead of stardard deviation?
     
  15. Kivanc

    Kivanc The Data Keeper

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    I believe that you are right about stddev vs. variance.

    That being said, I don't understand the following:

    "It is a rare case whose probability is 0.05 that you get 2 times of standard deviation from the mean, which is 1.9 to 12.7, you should reject the hypothesis that drop events are independent, otherwise you can accept it."

    You say it yourself that there is a 5% chance that you will get lower than 2 items or higher than 13 items (outside that range). We are running this dungeon like hundreds of time. So, isn't it normal that we eventually see drops above 13 and below 2? How does this reject the hypothesis? I would understand that you could reject it if you have seen it back to back many times, but only getting it rarely, doesn't make it outlier?
     
  16. sendru

    sendru Active Member

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    For one single test, you can reject the hypothesis with 95% confident if you see as low as 2 or higher than 13, but you are right that we run 20-1 dungeon hundreds of times, and in that case, it is better to use Chi-square test. Give me a series of number and I can do the calculation.
     
  17. Kivanc

    Kivanc The Data Keeper

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    Oh sorry, I do believe the independence hypothesis (since easier) rather than recording run results :D. Someone could do that experiment though...

    Thanks for the explanation. I agree that for that single data, you reject the hypothesis, but you would never conclude a stats experiment with one single data even if that immediately rejects your hypothesis :D
     
  18. sendru

    sendru Active Member

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    Pseudo randomness means dependence, it is just designed to undetectable. But even if they are dependent to each other, the expectation is still additive. And the independent model can still serve as an approximation. Just keep in mind, you will experience a larger variance in the real game.
     
  19. Cel

    Cel Well-Known Member

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    Yeah that's right.

    But with that, our data is the same, in the 95% confidence interval case: 2 to 12.

    There are specific tests to determine how "random" a particular data stream is. It's not that it's designed to be undetectable, but there is math rigor behind this. I'm not enough of an expert in this area to assess it, but based on what's said on the internet, some implementations of the random number generation are bad (linear congruence generator), but with newer technology, the Mersenne Twister is quite good. Like I mentioned, there are better ones, as it solves certain issues with failing tests of randomness.

    So the question, is that is this implementation of the pseudorandom number generator random enough for drops? Well, it's hard to say, and given the limited abilities to see into the code (unless, one of our data experts knows which implementation of a PRNG we are using), then we can assess it. The rest is just based on guesses at the data, based on what we see, and that requires statistical methods beyond just simple means and standard deviations, since there are multitudes of tests. And even so, more data gets us closer to the answer. Just because one test fails, there's still a chance we are wrong (usually 5%), and you have to decide how confident you are of your answer.
     
  20. Noche

    Noche New Member

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    Apparently I can't post my original long message, so let's cut it short. I have both Rikken and Yukken, double pincer with power point should give me 100% drop rate for apollo, yet on my 4th time I got it (1 of them was a single pincer with power point, should be plenty enough still). I will soon arrive 23-10 for spirit particle (20% drop rate), I will try again and report the results.
     

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