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<blockquote data-quote="EzekielRaiden" data-source="post: 6623817" data-attributes="member: 6790260">OP: Of course the average for each individual stat hews closer and closer to the mean (which, for 4d6 drop lowest, is 12.24)--that's just the central limit theorem in play. The larger a sample you take, even if it were perfectly ideally random, the more likely each mean will hew to the expected value of the dice.Much more interesting, and worthwhile, is to consider what the expected distribution of stats will be--that is, what we can &quot;typically&quot; expect any given set of six rolls to be. As it so happens, the people at AnyDice have already computed this, and given a nice breakdown of everything! So I'll just link that <a href="http://catlikecoding.com/blog/post:4d6_drop_lowest" target="_blank">here.</a>The relevant information: Approximately 56.76% of all stat rolls, using 4d6 drop lowest, will have their highest stat as a 16, and nearly half (46.16%) will have two 15s.These odds are then further modified by the fact that most DMs will be likely to let someone re-roll if they have low stats, and especially if they have more than one substantially low number (that is, more than one number less than 8). While the OP might not, that is how every DM I've ever had would do it, which means that those probability values are going to go up (we're excluding valid possibilities that aren't &quot;high stats,&quot; so &quot;high stats&quot; become relatively more likely; the exact effect is impossible to gauge because each table's rules are a bit different).</blockquote>

[QUOTE="EzekielRaiden, post: 6623817, member: 6790260"] OP: Of course the average for each individual stat hews closer and closer to the mean (which, for 4d6 drop lowest, is 12.24)--that's just the central limit theorem in play. The larger a sample you take, even if it were perfectly ideally random, the more likely each mean will hew to the expected value of the dice. Much more interesting, and worthwhile, is to consider what the expected [I]distribution[/I] of stats will be--that is, what we can "typically" expect any given set of six rolls to be. As it so happens, the people at AnyDice have already computed this, and given a nice breakdown of everything! So I'll just link that [URL="http://catlikecoding.com/blog/post:4d6_drop_lowest"]here.[/URL] The relevant information: Approximately [I]56.76%[/I] of all stat rolls, using 4d6 drop lowest, will have their highest stat as a 16, and nearly half (46.16%) will have two 15s. These odds are then further modified by the fact that [I]most[/I] DMs will be likely to let someone re-roll if they have low stats, and especially if they have more than one substantially low number (that is, more than one number less than 8). While the OP might not, that is how every DM I've ever had would do it, which means that those probability values are going to go up (we're excluding valid possibilities that aren't "high stats," so "high stats" become relatively more likely; the exact effect is impossible to gauge because each table's rules are a bit different). [/QUOTE]

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