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Thread: A lesson in the negative binomial probability distribution

  1. #11
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    Quote Originally Posted by KoBeWi View Post
    >when you suggest a change to drop rates, which is ignored by Trion, so you give a lecture about probability
    I'll even do them more. I wrote a very simple R script so they can visualize the instability of their RNG system for a given r and p.

    =========

    #Number of required successes
    r = 5

    #Probability of success
    p = 1/3000

    #Number of players (or some large amount to calculate the proportion of players accurately)
    b <- 1000

    #Used to store the results
    S <- double(b)

    for(i in 1:b){

    #a will track the number of successes within an attempt
    a <- 0

    #n is the number of trials within an attempt
    n <-0

    while(a < r){

    #For every iteration, increase the number of trials by 1
    n <- n + 1


    #was a success or not
    y <- rbinom(1,1,p)

    if(y==1){a = a+1}

    }

    #record the number of attempts
    S[i] <- n

    #print every 100 iterations
    if(i%%100 == 0){print(i)}

    }

    #histogram
    hist(S,freq=F,xlab="n",,main=paste("Proportion of people and their required number of trials for p = ",round(p,6), "and r = ", r))

    #plot mean
    abline(v = r*((1-p)/p) +1, col = "red",lwd = 2)

    #plot 2.5% and 97.5% quantiles for the 95% middle
    abline(v=quantile(S,c(0.025,0.975)),col="purple", lwd = 2)

    =====



    From this image, it is very clear that if p = 1/3000 and r = 5, 95% of the players will fall between getting those 5 fragments either within 5000 trials or 30000 trials. Some unlucky players will take excess of 50000 trials. We don't need to be guinea pigs when it takes a couple minutes to do a valid simulation. They don't even need to know any formulas.

  2. #12
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    Even bonus, bonus. Take a look what happens to the stability when when make p = 10 times the amount and r = 10 times the amount. The average value is still the same.


    Now 95% of the players will get all 5 fragments within 11,000 or 20000. The first graph doesn't follow the central limit theorem exactly as indicated by the heavy skew to the right. However, the left side is closer a normal distribution hence the left bound approaches about sqrt(10) towards the middle.

    The theory about the central limit theorem and normal distribution, for something like this, you generally want E[n] * p = r > 20 for a symmetrical distribution. This is another statistics lesson for trove, your RNG is skewed.

    I usually get paid a lot of money to do simple things like this. This is compliments of a frustrated player.

  3. #13
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    Issue is, we have no idea how the 'odds' are calculated behind the RNG system within trove.
    Regardless of the countless number of equations you may throw at it, all the statistical data is meaningless, if nobody can understand how the drop rates even happen.

    This is why the first step is 'gathering' data.

    Look for repeating patterns, or common situations between similar groups of people... and you get an idea of what is happening, despite the 'math' behind the RNG.

  4. #14
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    Quote Originally Posted by High5 View Post
    Issue is, we have no idea how the 'odds' are calculated behind the RNG system within trove.
    Regardless of the countless number of equations you may throw at it, all the statistical data is meaningless, if nobody can understand how the drop rates even happen.

    This is why the first step is 'gathering' data.

    Look for repeating patterns, or common situations between similar groups of people... and you get an idea of what is happening, despite the 'math' behind the RNG.
    '

    I agree with you but we don't need to know the exact odds like you said (no excuse for the developers who do know the exact odds). It's obvious, almost within a few weeks, that their implementation of the RNG was bad. I know I have confirmation bias because I focus on all the bad implementations of RNG, but it's no secret that we are guinea pigs whenever they implement it and usually subject to change within the next updates.

  5. #15
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    Hey,

    You about this way more then me so I'm just wondering can you tell me what it would look like in this situation please?

    Initial rng is .1% of winning prize.
    Every try rng gains a .1% bonus.
    Rng is capped at 20%, one chance out of 5, this is debatable.
    When prize is won, rng is reset to .1%

    What do the stats on this type of rng look like?

  6. #16
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    +1 i hope devs see this

  7. #17
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    Agreed, good info for statistics. Great post. Love it.
    I am really hoping that we get some questions answered during the dev stream regarding whether all players have the exact same numbers within their equations (whatever they may be), or if the probability of success changes based on other factors. Is why I am trying to gather as much data as possible, not only here in the forums, but also in various discords, in game people I know, etc...

    The karma bars and dragonite were put in for a good reason. For those falling within the 1% of the low end of the bell curve "luck", at least there is progression.

    I am really surprised that these fragments were not tradable. They wanted something rewarding in game for the 'miners or gatherers' as a bonus, however so far the results have been that most players have begun to rage/leave and that they typical farmers of these materials are not able to make a profit because the quantity of players farming insane amounts of materials hit the insanity level.

    Regardless, great post.

  8. #18
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    Quote Originally Posted by Jsm View Post
    Hey,

    You about this way more then me so I'm just wondering can you tell me what it would look like in this situation please?

    Initial rng is .1% of winning prize.
    Every try rng gains a .1% bonus.
    Rng is capped at 20%, one chance out of 5, this is debatable.
    When prize is won, rng is reset to .1%

    What do the stats on this type of rng look like?
    I will create a simulation with this. Fortunately something like this doesn't need to use anything complicated since it caps off at 20% and you have a well defined probability calculation

  9. #19
    Senior Member TheLazyCanadian's Avatar
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    i like you friend this whole explanation is just savage we need this ingame asap

  10. #20
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    Quote Originally Posted by Cytosine View Post
    I will create a simulation with this. Fortunately something like this doesn't need to use anything complicated since it caps off at 20% and you have a well defined probability calculation
    Awesome, the shape matters! I will be all eyes on this.
    Also, if you look for my post in the 'devs question' thread, I think that you would be one of players who would understand what those questions 'equate' to

    Matlab?

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