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RPG.SE is currently having a bit of a vigorous discussion about this question about dice rolling (meta thereupon), in which this stack was brought up as a potential migrate target. There is a dice tag here, but is this sort of question on topic to begin with?

(Note: I am not in any way a representative of RPG.SE, just a user of it.)

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    $\begingroup$ I took the liberty of changing the title. The key aspect of the question is not that it came from RPG.SE - as the thread in their meta says, there is no RPG aspect whatsoever in it. Considering what the OP wanted to roll the dice for, they could just as well have posted it in Christianity.SE. Or Mi Yodeya. Conversely, I do think that elementary questions about rolling dice, which this one is, are definitely on topic here. $\endgroup$
    – Stephan Kolassa
    May 4, 2019 at 8:41

2 Answers 2

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TL;DR A version of this question is a good fit for stats.SE, but the question on RPG.SE needs work before migrating to here

I think the question will need to be more clearly stated to get interesting answers. Let's build up from vague to better questions. I hope that this exercise illustrates why asking a clearly-specified question is important.

How can I randomly select a passage from among 150 passages of text?

You can cut out the dice step entirely if you just write the text on the slips of paper instead, and draw random passages that way.

How can I generate uniform numbers from 1 to 150?

Use a computer.

How can I generate uniform numbers from 1 to 150 without a computer?

  • Use your phone and navigate to anydice.com or some dice rolling application.
  • Write the numbers 1 to 150 on identical slips of paper, mix them up in a box, and draw them from the box.

How can I generate uniform numbers from 1 to 150 using dice?

Make a fair d150 and use that.

How can I generate uniform numbers from 1 to 150 using platonic solid dice?

Some answerers will make suggestions similar to those on RPG.SE about using different combinations of polyhedral dice.

Because there are so many ways to do this, it is probably too broad -- everyone will be tempted to post clever, or even cheeky, solutions without regard to practicality. (This is a very common occurrence for "brainteaser"-type questions. See Approximate $e$ using Monte Carlo Simulation and Brain teaser: How to generate 7 integers with equal probability using a biased coin that has a pr(head) = p? for examples.)

Insisting on using physical dice brings some additional complications:

  • Can a good solution require a bit of arithmetic?
  • Are the dice fair? Is compensating for possibly unfair dice part of the task? Some statistical questions assume fair dice, but since you're actually rolling physical dice, we ignore unfair dice at your peril.
  • Can the user consult a table or other apparatus?
  • Is minimizing the number of dice rolled important?
  • Is the efficiency of the procedure in some other sense (such as the number of "rejected" rolls) important?

What's the most efficient way to generate numbers from 1 to 150 uniformly using a fair d6?

This seems like the best question to ask. Pretty much every house has a pair of d6 in some dusty cupboard, and this question generalizes reasonably well to arbitrary ranges of numbers.

Converting base-6 to decimal could be a stumbling block for some people, and if it is for you, then you'll have to state that and ask for an answer that doesn't using base-6 conversions (possibly returning to the domain of rolling several polyhedra.)

On the other hand, you could just renumber all of the texts using base-6 once, instead of doing the math for each dice roll. This will require less work if you’re doing more than 150 rolls.

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  • $\begingroup$ Well, I can't answer that since I'm not the OP of the question in question, but yeah. Base 6 would be a bit of a pain in the neck for me, too. Also, how do I link this answer? It's a very good answer and I want to be able to reference it. $\endgroup$
    – Stackstuck
    May 4, 2019 at 0:35
  • $\begingroup$ This should work (it's the link to this answer from my profile page): stats.meta.stackexchange.com/questions/5652/… $\endgroup$
    – Sycorax Mod
    May 4, 2019 at 1:11
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    $\begingroup$ @Stackstuck: there is a "share" link underneath every answer (and question), which generates a link. The number after "/a/" ("/q/" for questions) references the answer uniquely, and the number after that one is your user number, so if you include the full link, one knows who shared the link. $\endgroup$
    – Stephan Kolassa
    May 4, 2019 at 8:44
  • $\begingroup$ +1 for the first part of your second. Almost-(-1) for the second. As you write, pretty much any household owns dice, but not everyone has a computer or a smartphone at hand. (There are even people who own mobile phones that are not smart.) Rolling dice is a wonderful way of generating random numbers that does not involve some kind of magic you have to trust. ... $\endgroup$
    – Stephan Kolassa
    May 4, 2019 at 8:49
  • $\begingroup$ ... I have used dice frequently to help my kids learn their multiplication tables, and I would not have dreamt of using an app on my phone. Yes, I'm sure such apps exist, but I know what would have happened if I had pulled out my phone instead of my dice. (It would not have involved math, because my kids are smart enough to associate the phone with completely different things than random number generation, and those things are much more interesting.) $\endgroup$
    – Stephan Kolassa
    May 4, 2019 at 8:50
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    $\begingroup$ @StephanKolassa Ah yes, the rarely-seen sidevote $\endgroup$
    – Sycorax Mod
    May 4, 2019 at 14:19
  • $\begingroup$ (+1) Another angle might be to put aside the practicalities of mapping a sample space to a set of integers & to ask how to find out whether or not a particular discrete uniform distribution is obtainable from a given candidate set of dice; if it is, how many of them are needed; & if it isn't, & you need to reject some outcomes & re-sample, what the expected number of rolls is. $\endgroup$
    – Scortchi - Reinstate Monica Mod
    May 4, 2019 at 21:57
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    $\begingroup$ @Scortchi I agree that the efficiency of any proposed scheme should be an important consideration. However, after reading the thread at RPG.SE and in our chat Ten Fold, it seems that this audience would consider any details beyond how to map dice to integers unimportant or even pointlessly arcane. (Apparently converting senary to decimal or vice-versa is simply too much work.) I chose to motivate my answer from the perspective of how to ask a question in such a way that its answers are illuminating to these readers: "If you ask an under-specified question, you'll get poor answers." $\endgroup$
    – Sycorax Mod
    May 4, 2019 at 22:04
  • $\begingroup$ In my view that would go fine -- with small edits -- as an answer on the main site. You just need to reverse engineer the question. $\endgroup$
    – Nick Cox
    May 5, 2019 at 12:16
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    $\begingroup$ @NickCox Fair. I've asked such a question: stats.stackexchange.com/questions/406723/… $\endgroup$
    – Sycorax Mod
    May 5, 2019 at 16:37
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It could be on-topic here, I suppose, if criteria to define the correct answer were explicitly stated. What constraints are there on the types of dice used & the method for combining rolls? What's to be optimized?—the number of dice needed? the number of rolls? As it stands, the question's much too broad.

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    $\begingroup$ I don't think the question is too vague. Except for the request that the numbers be uniformly distributed (not stated, but implied, and obvious enough if you know how non-statisticians think - and this additional requirement would be easily elicited via comments), the question is not vague, but very clear - but simply elementary. Maybe we should discuss whether elementary questions are on-topic here. I would say yes. We might treat them as self-study. $\endgroup$
    – Stephan Kolassa
    May 4, 2019 at 8:52
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    $\begingroup$ @StephanKolassa: I've changed 'vague' to 'broad'. I meant that it's the constraints & requirements that are vague - that's why there are 13 answers already (14 if you count the one given in the question) with nothing to choose between them. $\endgroup$
    – Scortchi - Reinstate Monica Mod
    May 4, 2019 at 9:24

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