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Thread: FiveThirtyEight: D&D Riddle
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2020-05-15, 02:10 PM (ISO 8601)
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FiveThirtyEight: D&D Riddle
This week's "Riddler Classic" feature on fivethirtyeight is D&D-related (5th ed, in fact). Have at it, all your crazy mathematicians!
Last edited by Telonius; 2020-05-15 at 02:11 PM.
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2020-05-15, 06:32 PM (ISO 8601)
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Re: FiveThirtyEight: D&D Riddle
About the Riddler Express I can do a sum of 6
is there a lower option?Spoiler(use 4 1s to limit the possible places for the one in a square to the middle and put a 2 in the middle)
About the d&d oneSpoilerdisadvantage of advantage is the better one for average values, here https://statmodeling.stat.columbia.e...e-probability/ this give the probabilities for advantage/disadvantage. for advantage you have an 75.1% chance of getting 11 or higher, which give you an 56.4% chance to have neither of two advantages be below 11. Other way around for advantage of disadvantage. (I guess to do this properly mathematically I would have to show that it isn't weirdly skewed but I did simulate it and got a 13.8 avg for dis of ad, and 7.17 for ad of dis.)
About the extraSpoilerif I am not doing it wrongfor 14 and higher normal is better than disadvantage of advantage, and for 8 and lower ad of dis is better than normal.
I don't think adof dis is better than dis of ad for any value.Last edited by Ibrinar; 2020-05-15 at 06:54 PM.
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2020-05-16, 02:34 AM (ISO 8601)
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Re: FiveThirtyEight: D&D Riddle
I don't think your proposal would have a unique solution which I understood to be a requirement or this.
For the D&D one I brute-forced it in Excel, and you are not doing it wrong.
Adv of Dis and Dis of Adv are indeed mirror distributions
And needing a 14 or better is indeed the point where Dis of Adv becomes better than a single dice.
There is another option he did not consider for having both Advantage and Disadvantage at the same time - roll three dice and discard the highest and lowest. I haven't run the numbers, but it will make for a very centered distribution - both high and low rolls being very unlikely.Last edited by Khedrac; 2020-05-16 at 02:34 AM.
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2020-05-16, 08:30 AM (ISO 8601)
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Re: FiveThirtyEight: D&D Riddle
That's my easy solution too upper bound, that 3 is insufficient I think is equally trivial.
Anything doable in 5 has to involve "5*1" or "3*1+2" which I think don't work but there might be something clever.
Ah, it's the success we're changing for the AoD DoA dice. I couldn't see why my intuitive feel was dice size dependent. Although not really thought about it.
Spoiler: thinking further with actual wording and avoiding specifying the dice
For any underlying probability of success P:
The probability of succeeding under advantage is PA=2*P - P 2 (You win if you succeed on either dice)
The probability of succeeding under disadvantage is PA=P2 (You win if you succeed on both dice)
by composition of the functions.
PAoD=2*PD - P D2=2*(P2) - (P 2)2 = 2P[sup]2[/sub]-P4
=P (2P-P3)
while
PDoA=PA2=(2*P - P 2)2 = 4P2-2*2*P3+P4
=P (4P-4*P2+P3
Sanity check if P=0 both are trivially 0. if P=1 then Paod=1, Pdoa=1
So PAoD>P if (2P-P3)>1 which graphing is when P>0.618
And similarly for PDoA, when P>0.382
Which I think almost makes sense with the 14 given earlier, when I remember that a D20 starts at 1. I like the symmetry, but feel I might have a sign wrong.
Finally
PAoD > PDoA if:
(2P-P3)>(4P-4*P2+P3
(-6P-2P3+4*P2)>0
(-6-2P2+4)>0 Which is never the case if P is between 0 and 1
Last edited by jayem; 2020-05-16 at 09:48 AM.
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2020-05-23, 03:55 AM (ISO 8601)
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Re: FiveThirtyEight: D&D Riddle
Does a statistics question based on a fake D&D rule somehow qualify as D&D trivia? Why would anyone care?
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2020-05-23, 12:24 PM (ISO 8601)
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Re: FiveThirtyEight: D&D Riddle
A.) There is no fake D&D rule presented, it's explicitly listed as a hypothetical scenario in which an existing rule is changed.
2.) Who called it D&D trivia? I can't find that claim in either the article or in this thread.
iii.) People interested in puzzles and/or math/statistics would care because it fits their interest.Cuthalion's art is the prettiest art of all the art. Like my avatar.
Number of times Roland St. Jude has sworn revenge upon me: 2
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2020-05-24, 08:33 PM (ISO 8601)
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Re: FiveThirtyEight: D&D Riddle
The answer is in:
Originally Posted by 538