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Rolled character stats higher than point buy?
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<blockquote data-quote="Arial Black" data-source="post: 6867358" data-attributes="member: 6799649"><p>There you go. <img src="https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f642.png" class="smilie smilie--emoji" loading="lazy" width="64" height="64" alt=":)" title="Smile :)" data-smilie="1"data-shortname=":)" /></p><p></p><p>To clarify, character creation by rolling ability scores does <strong>not</strong> involve finding the average rolls for a particular method and using them. It involves rolling (in our example) 4d6k3 six times. The average for those rolls might be interesting, but <em>the average plays no part in the actual rolls you just made!</em> Any discarding of an unsuitable set has absolutely no impact on the set you keep! Any discarding is done <em>after</em> those rolls (with the mathematical average associated with that method) has already been completed. Any later discarding does not alter the probabilities of that method to get those results.</p><p></p><p>Let's try an analogy: let's say that the average height of an adult human male is, say, six feet. Let's say that you have a six-foot tall adult human male standing in front of you. Do you have a male of average height in front of you? Yes.</p><p></p><p>Now, shoot every adult male who is <em>less</em> than six-foot tall. (note that I'm not actually advocating this in real life; it's just a thought experiment. Put the shotgun down and back away from the 2nd amendment!) Now that there are no adult males less than six feet, the guy standing in front of you can truthfully be said to no longer be 'average height'; he's now the joint shortest guy in the world! <em>But his actual height has not changed one iota!</em> He's still six foot tall, no matter the heights of other people alive or dead!</p><p></p><p>And if that guy has kids, the average height of those kids when they grow up will conform to the pre-culled population, not the post-culled population. Their heights will lie along the <em>original</em> bell curve of heights, not the bell curve of heights post-culling.</p><p></p><p>And when you discard the first (or second or third) set of rolls, the next set will be generated by the same mathematical rules of the first, and won't take any discarding (and that effect on the final average) into account. The next set will have the same bell curve as the original, and that curve will be unaffected by any discarding.</p><p></p><p>So the set of scores that you do keep are the same (and use the same bell curve) whether or not you are allowed to re-roll.</p></blockquote><p></p>
[QUOTE="Arial Black, post: 6867358, member: 6799649"] There you go. :) To clarify, character creation by rolling ability scores does [b]not[/b] involve finding the average rolls for a particular method and using them. It involves rolling (in our example) 4d6k3 six times. The average for those rolls might be interesting, but [I]the average plays no part in the actual rolls you just made![/I] Any discarding of an unsuitable set has absolutely no impact on the set you keep! Any discarding is done [I]after[/I] those rolls (with the mathematical average associated with that method) has already been completed. Any later discarding does not alter the probabilities of that method to get those results. Let's try an analogy: let's say that the average height of an adult human male is, say, six feet. Let's say that you have a six-foot tall adult human male standing in front of you. Do you have a male of average height in front of you? Yes. Now, shoot every adult male who is [I]less[/I] than six-foot tall. (note that I'm not actually advocating this in real life; it's just a thought experiment. Put the shotgun down and back away from the 2nd amendment!) Now that there are no adult males less than six feet, the guy standing in front of you can truthfully be said to no longer be 'average height'; he's now the joint shortest guy in the world! [I]But his actual height has not changed one iota![/I] He's still six foot tall, no matter the heights of other people alive or dead! And if that guy has kids, the average height of those kids when they grow up will conform to the pre-culled population, not the post-culled population. Their heights will lie along the [I]original[/I] bell curve of heights, not the bell curve of heights post-culling. And when you discard the first (or second or third) set of rolls, the next set will be generated by the same mathematical rules of the first, and won't take any discarding (and that effect on the final average) into account. The next set will have the same bell curve as the original, and that curve will be unaffected by any discarding. So the set of scores that you do keep are the same (and use the same bell curve) whether or not you are allowed to re-roll. [/QUOTE]
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