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Message: <blockquote data-quote="Arial Black" data-source="post: 6874799" data-attributes="member: 6799649">We seem to be talking past each other, so permit me to clarify my fundamental point.Imagine that we know are using 4d6k3 six times to generate a set of six ability scores, but we don't know whether or not we can re-roll sets that don't meet a certain criteria. In fact, one of us is allowed to re-roll, but the other is not, but we don't know this! In fact, it will be decided by a flip of the coin which of us would be allowed to re-roll, and this coin will be flipped after we have each generated our set of six.We roll our stats as instructed. We expect the average distribution to be about 16/14/13/12/10/9, because that is what is expected for 4d6k3. As it turns out, neither of our sets would qualify to be re-rolled anyway.At what point is one of us expected to have a higher set than the other, based on a re-roll that was never used?Explain to me how the one that was allowed to re-roll (but never did) has an expectation of a higher stat distribution than is expected for 4d6k3!See, this is the reality of rolling for scores. Sets of six are not generated from some average that is observed after the effect. Time only moves one way, and so does causality. Your possible decision to discard a set doesn't make any rolled set higher than it was before! If you discard one unsuitable set after another, five, ten, fifty times until you finally roll a set that doesn't qualify to be discarded and re-rolled, that final set has exactly the same expectation as every other: 16/14/13/12/10/9 in our case.Re-rolling does not increase any set you roll, discarded or not. This is the Gambler's Fallacy; the idea that if the last seven spins of the roulette wheel have spun a red number, that the next spin is more likely to be black, on the grounds that eight reds in a row only has a 1 in 256 chance. This is bogus! If you're interested, the chances of red/black remain equal, because the sequence '7 reds followed by 1 black' also has only a 1 in 256 chance.With (possible) discarding, the sets you discard have absolutely no effect on the next set you generate. Discarding doesn't give a mathematical expectation of generating higher scores.The fact that you can observe averages of already generated sets and change the average of those by discarding low sets doesn't actually increase any rolled set at all! You increased the average, not by increasing any scores, but by taking low results away! This manipulation of the observed average has no impact on character creation beyond taking low scores away! It doesn't increase any kept set at all!</blockquote>

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