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<Greys> egg, can you think of any combination of dice that when summed together create a probability distribution which is an asymmetric bell curve?
<Iskierka> rather than combination, method of combination? Multiplying them should approach a maxwell-boltzmann distribution
<Iskierka> or at least the same kind of asymmetry, probably not the same actual shape
<Iskierka> other than that any dice with an asymmetric distribution should do that (1, 1, 1, 2, 2, 3 on sides) but I don't think you can by adding up regular dice
<Greys> hmmm, multiplication should be workable, with a sufficiently high ratio, say d20 * d4
<Greys> this distribution actually seems to be too irregular
<Iskierka> I believe the drop highest/lowest method also gives irregular, though I don't know by how much
<Greys> 1d3+(1d3*1d3) looks pretty good, if I could reverse it
<Iskierka> huh, nifty.
<Greys> I guess if the game was low rolls = good this would be great, but you'd need 3 differently colored d3, which are already non-standard
<Greys> d4s don't work with this formula
<Greys> this would be used in a FATE like system that normally uses 2d6; I don't love that because 7 is significantly more probable in a 2d6 roll, and you need to roll at least an 8 to get what you want
<Greys> what does this syntax on output 2 mean?
<Iskierka> access items 2 and 3 from the collection of 3 dice, which are ordered from highest to lowest, so is effectively "drop 1 highest"
<Iskierka> use 1,2 to drop lowest and invert the curve
<Greys> inverted is best, and this is an easy roll to perform
<Greys> great, so then the players are more likely to succeed
<Greys> roughly 1/3rd chance of failure, almost 30% chance of mediocre succeess, more than 1/3rd chance of full success, and 20ish% chance of critical success
<Iskierka> This is why D&D uses the drop lowest for stats, and effectively also does for advantage, though it words it differently
<Greys> any idea on how to smooth that down a bit?
<Iskierka> Not hugely without irregular dice, unless you just want to use a fixed +- number to reduce crit or something
<Greys> I just want to make the min and max likelihoods slightly closer together, maybe get the min to 2% and bring the max down to more like 14%, with the same proportional shape
<Greys> but this works
<Greys> d8 is a bit nicer
<Iskierka> http://anydice.com/program/c17d might be a bit aggressive and makes 1 possible but is another option with any even-sided dice
<Greys> {3}@(d8) seems wrong
<Greys> maybe I'm not good at statistics
<Iskierka> I'm not sure what result that should return as you're asking for the third die of a collection of exactly 1 d8
<Greys> {3}@(3d8)
<Iskierka> That looks right to me; it's selecting the lowest of 3 d8s
<Greys> right, this is the probability of the other two being equal or higher than N
<Iskierka> of rolling N and the other two being equal or higher
<Iskierka> which does make it somewhat different
<Greys> so there's a .2% chance in rolling 3d8 of getting 3 8s
<Iskierka> !wa (1/8)^3 as decimal
<Qboid> Iskierka: N[(1/8)^3] = 0.001953125
<Iskierka> yep
<Greys> eh, maybe I don't need to think about this
<Greys> rolling a 20 on a d20 is a 5% chance, rolling a 16 on {1,2}@(3d8) is just under 5%, that should be fine
<Greys> but rolling 3 8s should maybe be a super crit
* Iskierka was trying to match the 12 maximum but doesn't know the rules so fair enough if that works
<Greys> 12 is already a fairly arbitrary number
<Greys> I just don't like how sharp and straight the 2d6 distribution is
<Greys> !c 100/16.666
<Qboid> 6.00024000960038
<Iskierka> it's a perception thing from the datatype. Put it on "at least" or "at most"
<Greys> so basically a 1 in 6 change of rolling a 7
<Greys> keep in mind 7 is a failure
<Iskierka> by definition a 1 in 6 chance; no matter what you roll on the first dice, there's exactly 1 number (of 6) on the other that can make it 7
<Greys> you're better at numberoception than I am
<Greys> so you have a 58.33% chance of rolling 7 or less
<Greys> in 2d6
<Greys> which means just on a standard roll with no bonuses, you're probably going to fail
<Iskierka> And I don't know how common the system wants failures to be so *shrug*
<Greys> with the fancy d8 that I'm not going to type out anymore, the "even chance" line is between 11 and 12
<Greys> experimenting to try and get the even chance a bit lower, I tried 1,2 of 2d8+1d6, why does this go up to 22
<Greys> what combination of a single 8 and a single 6 results in 22
<Iskierka> I'm unsure how it decides to combine but it may be adding 1d6 to each d8 then selecting the two highest (of those two)
<Greys> that makes sense
<Iskierka> or actually, adding it to one of them then selecting the two highest. To both would be able to reach 28 (as 8+6 + 8+6)
<Greys> (8+8)+6
<Iskierka> yes, though it's seeing d8 & d8 + d6 and changing it to (d8+d6) & d8
<Iskierka> I can't see an obvious way to create a collection of dice that includes differing dice
<Iskierka> though as it has programmatical methods there's definitely other ways to select the two highest from two collections
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