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<blockquote data-quote="Ainamacar" data-source="post: 5921458" data-attributes="member: 70709">In a <a href="http://www.enworld.org/forum/new-horizons-upcoming-edition-d-d/319343-proposal-tiered-skill-training-very-long.html#post5843017" target="_blank">post</a> in my thread about a tiered skill system I made a few charts to demonstrate how multiple dice work out, with I copy here with minor changes.&nbsp; (Some of you may be interested to check out that thread, since characters with the lowest tier of training performing tasks of the lowest tier of difficulty in that system work very similarly to advantage/disadvantage.&nbsp; It's not quite a superset of the a/d system, but it's close.)---The math of multiple dice is pretty straightforward.&nbsp; If p is the&nbsp; probability of success on a single roll, then the probability of getting&nbsp; at least one success over n rolls is 1-(1-p)^n.&nbsp; Here's a couple tables&nbsp; illustrating that.&nbsp; The first one is just the probability of getting at&nbsp; least one success.&nbsp; The second&nbsp; table is the increase in probability compared to a single roll, which is&nbsp; just 1-(1-p)^n-p.<img src="http://www.pa.msu.edu/%7Egranlund/ENWorld/md1.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" /><img src="http://www.pa.msu.edu/%7Egranlund/ENWorld/md2.png" alt="" class="fr-fic fr-dii fr-draggable " data-size="" style="" />As you can see from the second graph, a single extra die gives anywhere&nbsp; makes it anywhere up to 25% more likely to get at least one success.&nbsp; On&nbsp; average it is just under 16%, roughly a +3 bonus, assuming all the p&nbsp; occur equally often during play.&nbsp; Probably checks in the middle of the&nbsp; range are more common in play, so the actual benefit of a single extra&nbsp; die is probably a +4 or so.&nbsp; It is worth keeping in mind, however, that a&nbsp; reroll isn't that helpful on very easy or very difficult checks, and&nbsp; that it can't make a check an automatic success or prevent an automatic&nbsp; failure like a +4 potentially could.The case with rolling 3 dice is very similar, increasing the probability&nbsp; of getting at least one success up to just under 40%.&nbsp; On average (again assuming all probabilities occur with equal frequency in play) the&nbsp; increase is about 24%, about a +5.&nbsp; Again, rolls for p somewhere in the&nbsp; middle are probably more common in play, so the actual improvement is&nbsp; probably closer to a +6.---If one wanted to stack disadvantage the math is even simpler, because using the worst die means all the dice rolled must succeed.&nbsp; That would make the chance of success p^n.&nbsp; Even for large p (but still less than one) this decays rapidly.</blockquote>

[QUOTE="Ainamacar, post: 5921458, member: 70709"] In a [URL="http://www.enworld.org/forum/new-horizons-upcoming-edition-d-d/319343-proposal-tiered-skill-training-very-long.html#post5843017"]post[/URL] in my thread about a tiered skill system I made a few charts to demonstrate how multiple dice work out, with I copy here with minor changes. (Some of you may be interested to check out that thread, since characters with the lowest tier of training performing tasks of the lowest tier of difficulty in that system work very similarly to advantage/disadvantage. It's not quite a superset of the a/d system, but it's close.) --- The math of multiple dice is pretty straightforward. If p is the probability of success on a single roll, then the probability of getting at least one success over n rolls is 1-(1-p)^n. Here's a couple tables illustrating that. The first one is just the probability of getting at least one success. The second table is the increase in probability compared to a single roll, which is just 1-(1-p)^n-p. [IMG]http://www.pa.msu.edu/%7Egranlund/ENWorld/md1.png[/IMG] [IMG]http://www.pa.msu.edu/%7Egranlund/ENWorld/md2.png[/IMG] As you can see from the second graph, a single extra die gives anywhere makes it anywhere up to 25% more likely to get at least one success. On average it is just under 16%, roughly a +3 bonus, assuming all the p occur equally often during play. Probably checks in the middle of the range are more common in play, so the actual benefit of a single extra die is probably a +4 or so. It is worth keeping in mind, however, that a reroll isn't that helpful on very easy or very difficult checks, and that it can't make a check an automatic success or prevent an automatic failure like a +4 potentially could. The case with rolling 3 dice is very similar, increasing the probability of getting at least one success up to just under 40%. On average (again assuming all probabilities occur with equal frequency in play) the increase is about 24%, about a +5. Again, rolls for p somewhere in the middle are probably more common in play, so the actual improvement is probably closer to a +6. --- If one wanted to stack disadvantage the math is even simpler, because using the worst die means all the dice rolled must succeed. That would make the chance of success p^n. Even for large p (but still less than one) this decays rapidly. [/QUOTE]

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