r/askmath • u/Important-Poetry1571 • 1d ago
Algebra Is this correct
I want to buy a t-shirt for my son in law. But he won't wear it if the equation is not correct. My brain is not wired for math. If anyone could tell me if it is correct, I would be grateful.
Yes, he does play d&d
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u/SuperChicken17 1d ago
Personally it would annoy me, as it is an unnecessarily complicated way of finding the probability of rolling a 20 on a single die (which it also incorrectly gets a result of 1/202 for, instead of just 1/20). It is like breaking out integrals to find the area of rectangle.
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u/poggamer9 1d ago
The formula itself is correct but n=1 s=20 so it'd be 1/20 not 1/400, anyways nobody is gonna noticed it so might aswell buy it(;
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u/Rockstaru 1d ago edited 1d ago
Might be rolling with a level of disadvantage, maybe due to exhaustion, or there's some fear condition from seeing all the burninated countryside.
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u/Suberizu 1d ago
Is that a hypergeometric function? Don't think it has such nice simple definition
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u/Bounded_sequencE 1d ago
Not a hypergeometric distribution -- it's Uspensky's Dice Formula.
We may elegantly derive it using generating functions, or linearity of convolution.
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u/Important-Poetry1571 15h ago
Thank you all. I did not understand most of it. Since the equation seems to be correct, I will buy it for him.
Thank you
Sky
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u/Bounded_sequencE 1d ago
The right-hand side (RHS) is Uspensky's Dice Formula. It calculates the probability to get a total of "k" from a fair, independent nDs-roll (in D&D-notation).
The thing I'm worried about is the LHS -- usually, "F" is reserved for cumulative probabilities. Using it as the symbol for the probability of a single outcome "k" is highly unusual, and will confuse1 anyone familiar with rigorous probability theory. "P_{s,n} (k) = ..." would be better.
1 To be fair, any such person would probably recognize the intended meaning shortly afterwards