Reply to thread

Message

<blockquote data-quote="Ovinomancer" data-source="post: 7245919" data-attributes="member: 16814">Well, no, because you're forgetting the effect on the standard deviation.&nbsp; 20d6 does have an average of 70, with an SD of 7.6.&nbsp; This means 95% of all results will be between 55 and 85. 20d6 exploding on a 6 has, as you note an average of 84, but has an SD of 14.6, meaning it's 95% probability is from 55 to 113. The probability density function of exploding d6's skews heavily upward, but has a higher variance.&nbsp; It's bottom is still rooted at the same point as non-exploding d6's, but its upper end is much higher than a simple look at the mean would suggest.&nbsp; In fact, the mean of the exploding function is right at the upper 95% boundary for straight 20d6, meaning that, on average, you're at least 50% likely to roll better than the upper 2.5% likelihood on straight 20d6.And this same pattern holds across all xd6.The upshot here is that you have a better than 14% chance on 20d6 exploding to roll over 100 damage, and a much less than 1% chance to do so on straight 20d6.&nbsp; You also have an almost 2% chance on exploding 20d6 to exceed the maximum value of straight 20d6. So, statistically speaking, the chance of better damage is much higher than the means would predict.</blockquote>

[QUOTE="Ovinomancer, post: 7245919, member: 16814"] Well, no, because you're forgetting the effect on the standard deviation. 20d6 does have an average of 70, with an SD of 7.6. This means 95% of all results will be between 55 and 85. 20d6 exploding on a 6 has, as you note an average of 84, but has an SD of 14.6, meaning it's 95% probability is from 55 to 113. The probability density function of exploding d6's skews heavily upward, but has a higher variance. It's bottom is still rooted at the same point as non-exploding d6's, but its upper end is much higher than a simple look at the mean would suggest. In fact, the mean of the exploding function is right at the upper 95% boundary for straight 20d6, meaning that, on average, you're at least 50% likely to roll better than the upper 2.5% likelihood on straight 20d6. And this same pattern holds across all xd6. The upshot here is that you have a better than 14% chance on 20d6 exploding to roll over 100 damage, and a much less than 1% chance to do so on straight 20d6. You also have an almost 2% chance on exploding 20d6 to exceed the maximum value of straight 20d6. So, statistically speaking, the chance of better damage is much higher than the means would predict. [/QUOTE]

Verification