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Thread: R stones probability

  1. #1
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    R stones probability

    Just a quick calculation whilst I was thinking about it because I (and everyone I have talked about R stone revisions to) is favouring increased chance over double chance and now I gave it some thought I think that is sub-optimal.

    If the odds of getting an R stone are fixed at 1%. - assumption

    Would it be better to put points in increased chance or double lotto or even in both?

    We have enough SP to put 50 points in one or the other (to make calculation quick and easy)

    With 10% increased chance, our expected value of 100 waves becomes 1.1 stones. (as each individual wave has an exclusive chance increase of 10%)

    With 10% double chance of a stone our expected value of 100 waves also becomes 1.1 stones. (Our expected 1 stone return as a 10% chance of being 2 stones.)

    Conclusion - To pick either one or the other, it makes no difference.

    Now, what if we mix them?

    With 5% chance of both, our increased chance to get a stone would give an expected value of 1.05 stones per 100 waves, now with 5% chance to double we get (1.05*1.05 = 1.1025).

    With 7.5% increased chance and 2.5% double chance we get (1.075*1.025 = 1.101875)

    With 2.5% increased chance and 7.5% double chance we get the same obviously 1.075*1.025 == 1.025*1.075)

    When we take into consideration points are not equally valued, it is more likely we could get roughly 35 points in each rather than 50 in one. (1.07*1.07 = 1.1449)

    Conclusion - The optimal way to split points is completely even. As the price increases, the optimal input of points is to put the next point into whichever of the two is cheaper as every additional point in each is multiplicative of the number of points in the other.


    tl;dr - Put equal points in both

  2. #2
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    "Just a quick calculation whilst I was thinking about it because I (and everyone I have talked about R stone revisions to)..."

    There's been some discussion about this on NA but I've heard no one make a judgement on it, except me.

    The specialties are equal in value, that is to say 100 points in double is equivalent to 100 points in increased chance.
    I can tell that at a glance because 100 points in double gives a 20% chance to get 2 stones instead of one, and that's another way of saying an extra 20% stones.

    The best way to distribute the points is to do it evenly.

  3. #3
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    Quote Originally Posted by psycodiver View Post
    "Just a quick calculation whilst I was thinking about it because I (and everyone I have talked about R stone revisions to)..."

    There's been some discussion about this on NA but I've heard no one make a judgement on it, except me.

    The specialties are equal in value, that is to say 100 points in double is equivalent to 100 points in increased chance.
    I can tell that at a glance because 100 points in double gives a 20% chance to get 2 stones instead of one, and that's another way of saying an extra 20% stones.

    The best way to distribute the points is to do it evenly.
    You actually just made the assumption which was the reason I said it was a quick calculation and why I noted a couple of things were assumptions

    I am glad to see someone else has taken an interest in it though, if we had more data to build a more complex model, I suspect we would find that double stones would be valuable on lower diff/score (therefore lower chance) games and increased chance would be more valuable on higher difficulty with a lot of torment games.

    Although it may seem obvious to make a quick calculation on the numbers, there are actually a lot of factors at play here. Things like the guaranteed stone on 300 give a slight edge to double stones and dependant on how the increased chance is calculated in the code, this could give a much better expected value than our face value assumptions the higher the score gets.

    Would be interesting if anyone gets to speak to Han to ask him increased chance calculates in the code, three ways of doing this in the code immediately come to mind and the way increased chance would improve as score got higher would vary between them.

  4. #4
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    "Things like the guaranteed stone on 300 give a slight edge to double stones ..."

    You are right there, assuming that double stone works on the guaranteed stone at r300.
    I haven't seen it work yet on the guaranteed stone. I assume it does though.

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    Quote Originally Posted by psycodiver View Post
    "Things like the guaranteed stone on 300 give a slight edge to double stones ..."

    You are right there, assuming that double stone works on the guaranteed stone at r300.
    I haven't seen it work yet on the guaranteed stone. I assume it does though.
    Confirmed, it can proc on the r300 stone

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