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Message: <blockquote data-quote="-Eä-" data-source="post: 281289" data-attributes="member: 471">Greetings people! Although this discussions seems and have seemed a bit agitated, I just wanted to contribute with some probability distributions, which may be appropriate for determining the reliability of metamagic feats.First:2x Empowered Fireball (to use THE example) does not equal an Enhanced Fireball.The latter is the more reliable, due to the fact that the probability distribution for each sum is narrower, according to this formula (I won't derive the formula here, as that would do nothing to further the discussion):Probability for p, points, throwing n s-sided dice:(1/s^n)*Sum[k=0,Int[(p-n)/s],(Gamma[n+1]*Gamma[p-s*k])/(Gamma[k+1]*Gamma[n-k+1]*Gamma[n]*Gamma[p-s*k-n+1)]People earlier have spoken of the reliability of Intesify Spell and Maximise spell, but given that you use over 20 dice, this is hardly an issue, as the probability of getting far less than the average is diminutive. For example, getting a sum of 80 or higher using 25 8-sided dice, the probability is 0,998, which is a quite a large number.Given as such, a combination would ultimately be preferable, as caster level may not be on par with the new and Enhanced Spell dice cap. As such, Improved Metamagic, Enhance Spell, and Empower Spell is the most lethal combination, especially at higher levels. The procedure is to Enhance a spell so that you get maximium potential of it, then Empower it. I believe many has said so before, but here it goes again.When throwing many dice, the distribution approximates that of a gaussian distrubution, and the standard deviation when throwing n s-sided dice is: SQRT(n*(s^2)-n)/2*SQRT(3), and the average is (n+n*s)/2, and from here it might be beneficial to use the inverse gaussian distrubution for randomising the results, which is easier than throwing 40 dice if you have a calculator.</blockquote>

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