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Thread: Definitive Thunderstruck Statistical Inference Thread

  1. #1
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    Definitive Thunderstruck Statistical Inference Thread

    Hello friends,

    My name is Evidence and I am a Statistician. Yes, that means I went through school and obtained 3 University degrees, one being a B.Sc. in pure mathematics, and an M.Sc. Statistics for good measure. I am also an avid gamer.

    As we know, Thunderstruck trees are of major interest to the playerbase of Archeage, due to the fact that they are worth a lot of gold. A lot of anecdotal evidence and a little research has brought us to where we stand today. We know that TS can occur anywhere. We know it can occur at different times in a tree's lifespan. We know it can occur in the wild. We know a little about which trees can become thunderstruck, and which ones seem to be more likely. We believe that trees with longer lifespans have higher chances.

    We are here today to improve our understanding in hopes of finding a strategy to optimize our tree-growing for the best chance to be struck by lightning. I aim to provide you with a clear, concise explanation of how this works, and we will do our best to avoid the ignorance of statistics and probability that seems to pervert every thread surrounding randomness in video games.

    We are going to use the data provided in this thread: http://forums.archeagegame.com/showt...uck-Ratio-Data

    The data here is useful, but does not explicitly tell us what the chance of a tree becoming Thunderstruck over it's lifetime. Instead, it tells us the probability at each stage. I have created a tree diagram (get it?) to illustrate the situation.



    As we can see, the probability of a tree becoming thunderstruck over its lifetime is given by the formula:

    P(T) = a + b(1-a) + c(1-b)(1-a)

    Where a is the probability of success in Stage 1, b the probability of success in Stage 2, and c the probability of success in stage 3.


    So how does it work? Let's do an example. From the aforementioned thread:
    Pine (6x6)
    Small Sapling to Sapling: 6h 51m 30s
    Chance for Thunderstruck: 0.09%
    Sapling to Small Tree: 1d 3h 26m
    Chance for Thunderstruck: 0.14%
    Small Tree to Tree: 1d 10h 17m 30s
    Chance for Thunderstruck: 0.23%

    So for pine trees, a = 0.0009, b = 0.0014, c = 0.0023

    Using our formula, we get:

    P(T) = 0.0009 + (0.0014)(0.9991) + (0.0023)(0.9991)(0.9986)
    P(T) = 0.004593452898

    Therefore, with one Pine tree, there is a 0.459345% chance it will become Thunderstruck.

    You can plant 10 Pine trees on one 16x16 farm, and using the Binomial distribution, you would have a 10*0.00459345*(1-.00459345)^9= 0.04407 or 4.407% chance to get one on your Pine farm.

    Similarly, a Cedar tree has a 0.159921012% chance of getting TS. You can fit 20 Cedars on a large farm, giving you a 0.031026 or 3.1% chance to get a TS on your Cedar farm.

    Theoretically, you can grow 2 and 2/3 Cedar crops in the time it takes to grow 1 pine crop (2 days). Therefore, over a 2 day period, filling your farm with Pine gives you a 4.407% chance to yield a TS, while filling your farm with Cedar over that same period would give you a 8.27% chance.

    These probabilities are for the chance of getting one TS tree on your farm. It is also possible to get more than one. You can use 1-(1-p)^n to calculate the probability of getting at least one.

    You can calculate the same probabilities for any of the trees we have data for, and I invite you to do so. Please feel free to ask any questions, and I will do my best to debunk any junk stats other readers try to throw at us.

    Thank you for your time!

  2. #2
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    Reserved for future additions!

  3. #3
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    The credentials..and his name! You can not distrust what he says!

  4. #4
    If I plant 28 pines and 25 cedars across all my farms, what is the % chance of me getting a thunderstruck if I only harvest everything once the pine trees mature (i.e. not being able to harvest cedars when they full mature due to various reasons) with this batch?

    Thanks

  5. #5
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    Finally. Someone that doesn't get glossy eyed when I start speaking with numbers.
    Casimyr
    <Windward>
    Lvl 50 Paladin | Abolisher
    [Calleil][East]

  6. #6
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    It's a game man...not a math class.

    If you get one.. you get one.

  7. #7
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    I think you are off in your calculations. It seems you are simply taking the chance of a success (.23) and multiplying it by the number of trials (20). That does not seem to follow the formula for binomial distribution. Then again, it has been a long time since I was in stats class and I am frequently wrong, just ask my wife.

    My bad, I swear it said you can fit 20 trees on a farm but you said 10 so the number of trials is 10 and not 20. Also, I see you are using percentages from all three stages.

  8. #8
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    Thanks for the info. I will now do pines on days I work and cedars on days I don't.

  9. #9
    So planting 10 pine trees when each tree has a ~.45% chance to get thunderstruck means you have a 4.5% chance per 16x16 farm? I feel like that's not how probability works but then again I know nothing about this field.

  10. #10
    Quote Originally Posted by Vantwan View Post
    So planting 10 pine trees when each tree has a ~.45% chance to get thunderstruck means you have a 4.5% chance per 16x16 farm? I feel like that's not how probability works but then again I know nothing about this field.
    You are correct. 0.45% chance per tree with 10 trees would be 1 - (1 - 0.0045) ^ 10 chance of getting a thunderstruck. In this case that happens to come out to 4.4% chance.

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