<h1>TL;DR <a href="https://stats.stackexchange.com/questions/406723/uniform-integers-at-random-from-1-to-n-using-fair-d6">A <em>version</em> of this question is a good fit for stats.SE</a>, but the question on RPG.SE needs work before migrating to here</h1>
<p>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.</p>
<h1>How can I randomly select a passage from among 150 passages of text?</h1>
<p>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.</p>
<h1>How can I generate uniform numbers from 1 to 150?</h1>
<p>Use a computer.</p>
<h1>How can I generate uniform numbers from 1 to 150 without a computer?</h1>
<ul>
<li>Use your phone and navigate to <code>anydice.com</code> or some dice rolling application.</li>
<li>Write the numbers 1 to 150 on identical slips of paper, mix them up in a box, and draw them from the box.</li>
</ul>
<h1>How can I generate uniform numbers from 1 to 150 using dice?</h1>
<p>Make a fair d150 and use that.</p>
<h1>How can I generate uniform numbers from 1 to 150 using platonic solid dice?</h1>
<p>Some answerers will make suggestions similar to those on RPG.SE about using different combinations of polyhedral dice.</p>
<p>Because there are <em>so many</em> 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 &quot;brainteaser&quot;-type questions. See <a href="https://stats.stackexchange.com/questions/193990/approximate-e-using-monte-carlo-simulation/193997#193997">Approximate $e$ using Monte Carlo Simulation</a> and <a href="https://stats.stackexchange.com/questions/354678/brain-teaser-how-to-generate-7-integers-with-equal-probability-using-a-biased-c/354679#354679">Brain teaser: How to generate 7 integers with equal probability using a biased coin that has a pr(head) = p?</a> for examples.)</p>
<p>Insisting on using <em>physical</em> dice brings some additional complications:</p>
<ul>
<li>Can a good solution require a bit of arithmetic?</li>
<li>Are the dice fair? Is compensating for possibly unfair dice part of the task? Some statistical questions <em>assume</em> fair dice, but since you're actually rolling <em>physical</em> dice, we ignore unfair dice at your peril.</li>
<li>Can the user consult a table or other apparatus?</li>
<li>Is minimizing the number of dice rolled important?</li>
<li>Is the efficiency of the procedure in some other sense (such as the number of &quot;rejected&quot; rolls) important?</li>
</ul>
<h1>What's the most efficient way to generate numbers from 1 to 150 uniformly using a fair d6?</h1>
<p>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.</p>
<p>Converting base-6 to decimal could be a stumbling block for some people, and if it is <em>for you</em>, 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.)</p>
<p>On the other hand, you could just renumber all of the texts using base-6 <em>once</em>, instead of doing the math for each dice roll. This will require less work if you’re doing more than 150 rolls.</p>
