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<blockquote data-quote="EzekielRaiden" data-source="post: 6873669" data-attributes="member: 6790260">Okay,&nbsp; @<a href="http://www.enworld.org/forum/member.php?u=6799649" target="_blank">Arial Black</a>, here's my fundamental point:Do you think that, in the long run, you will get consistently and without fail characters that are indiscernibly different using 4d6k3 than using &quot;4d6k3 reroll 1s ignore results with net mod less than 1/highest stat of 12 or lower&quot;? That because you can generate the same characters with either one, there is no meaningful difference between one method and the other?Because if you think that, you are wrong. If you do not think that, then this entire discussion has been pointless. Because I care about whether the expectation values, and probability of getting certain things, is higher or lower. I don't care about whether there are a bunch of results that get rejected--and I can even excise the &quot;rejection&quot; part, leaving JUST the math, no rules for what is or isn't acceptable (in some cases, anyway).If we consider 4d5k3+3, there is no possible way to parse it as &quot;shifting&quot; away from some other distribution, because there is no other distribution--we're not applying any discarding rules at all. The probability of rolling--since there is not and cannot be a &quot;discarded numbers&quot; aspect, here--straight 18s in that system is (.0272)^6 = 4.05*10^-10, or about 1 in 2.5 million. The probability of rolling such with 4d6k3 is (0.0162)^6 = 1.81*10^-11, or approximately 1 in 55.3 million, a difference of more than an order of magnitude.Does this mean 4d5k3+3 is different from 4d6k3, or the same? If they are the same, why do they have different odds of producing the exact same result? If they are different, why is something mathematically equivalent to 4d5k3+3 (that is, 4d6k3 reroll 1s) not *also* different from 4d6k3?</blockquote>

[QUOTE="EzekielRaiden, post: 6873669, member: 6790260"] Okay, @[I][B][U][URL="http://www.enworld.org/forum/member.php?u=6799649"]Arial Black[/URL][/U][/B][/I], here's my fundamental point: Do you think that, in the long run, you will get [I]consistently and without fail[/I] characters that are [I]indiscernibly different[/I] using 4d6k3 than using "4d6k3 reroll 1s ignore results with net mod less than 1/highest stat of 12 or lower"? That because you [B]can[/B] generate the same characters with either one, there is no meaningful difference between one method and the other? Because if you think that, [I]you are wrong.[/I] If you do not think that, then this entire discussion has been pointless. Because I care about whether the expectation values, and probability of getting certain things, is higher or lower. I don't care about whether there are a bunch of results that get rejected--and I can even [I]excise[/I] the "rejection" part, leaving JUST the math, no rules for what is or isn't acceptable (in some cases, anyway). If we consider 4d5k3+3, there is no possible way to parse it as "shifting" away from some other distribution, because there [I][B]is[/B][/I] no other distribution--we're not applying any discarding rules at all. The probability of [I]rolling[/I]--since there is not and cannot be a "discarded numbers" aspect, here--straight 18s in that system is (.0272)^6 = 4.05*10^-10, or about 1 in 2.5 million. The probability of [I]rolling[/I] such with 4d6k3 is (0.0162)^6 = 1.81*10^-11, or approximately 1 in 55.3 million, a difference of more than an order of magnitude. Does this mean 4d5k3+3 is different from 4d6k3, or the same? If they are the same, why do they have different odds of producing the exact same result? If they are different, why is something [I]mathematically equivalent[/I] to 4d5k3+3 (that is, 4d6k3 reroll 1s) not *also* different from 4d6k3? [/QUOTE]

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