I’m trying to figure out whether I want a D&D character of mine to take a feat that turns all 1s into 2s. It’s most relevant on casting fireball, which does 8d6 damage. The calculation is normally trivial, as the average for that roll is 28. However, if I treat 1s as 2s, that means the odds of rolling a 2 is 1:3, while the odds of 3 to 6 are 1:6 each. My die roller stats calculator can be set to a minimum value. As expected, setting the minimum roll to 2 gives the proper distribution. A 2d6 roll gives the same probability distribution as a fair roll for all totals except 4, which is doubled as expected. The average increases from 7 to 7.11. Calculating out to 8d6, setting a minimum result of 16, the average is still only 28.01.
This seems intuitively lower than it should be, but that doesn’t mean I’m right. Which is why I’m asking here.
So, three questions. First, am I doing the calculation right (or setting the software correctly)? Second, does this mean that on average the gain really is negligible and with enough trials the feat is worthless? (If so, sneaky, sneaky game designers). And third, as the number of possible trials is much less due to the rules of the game, is the shift to doubling the minimum damage worth it, as it only reduces the odds of something less than 16 by less than half a percent?