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Message: <blockquote data-quote="Keenath" data-source="post: 4427704" data-attributes="member: 59792">Yes, but a brutal d12 has a smaller chance of rolling a 1 to 2 than a d10 does.That they're equivalent can be proven using many methods; you could produce a limit equation; you could use probability mathematics; I chose monte carlo -- I wrote a quick computer program to run ten thousand tests, rolling a d12 and rerolling any result of a 1-2.The average damage output was, as expected, 7.5.  A standard d12 roll has an average damage of 6.5, so that represents an average damage increase of +1, just like all superior weapons.  (For example, a rapier is equivalent to a shortsword with a bigger damage die, which gives it an average +1 damage.)The damage distribution was a straight line across 3 to 12 -- thus there is no bias towards a particular value*.  An average 7.5 with an even distribution of values is identical to 1d10+2.  It just IS.  I'm sorry.Think of it this way:  If you converted all 1s and 2s into 3s, you'd have a 25% chance of getting the lowest possible damage for your weapon.  That method would produce a huge bias towards small damage rolls.When you reroll the d12, you have an equal chance of all the values coming up -- and if you roll a 1 or 2 again, you reroll again, STILL with an equal chance of all 12 values.  That's mathematically equivalent to simply removing the 1 and 2 from the pool of possible values, effectively turning your d12 into a d10, and then adding 2 to the damage rolls.* A single die roll has a flat distribution curve -- all values have an equal chance of coming up.  Rolling more dice will produce a bell curve that becomes sharper with each additional die.  For example, 2d6 is not an even distribution between 2 and 12; it's heavily biased towards the center of the range.  You have a 45% chance of getting a 6, 7, or 8, and only a 16% chance of a 10, 11, or 12.Simply incorrect.  I just can't explain any more clearly.  You're wrong.  It's exactly as powerful as a +1 average damage, or a +2 with a smaller damage die.  They're mathematically equivalent, period.  There's not even a variation in the distribution of values.</blockquote>

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