D&D General Sandbox style: Rumors say a +1 sword is in a cave nearby. Go get it?


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I would never refer to an item as “+1” in game. And unless the item is mook loot or bought from a store I would always give it a minor fluff power and some history.

But a sandbox should provide choices. Does the party want to follow up rumours of the magic sword, the magic glaive or the magic bow?
 


Eh.
If you roll a 1 on that d8, a +1 doubles the damage.
If you roll an 8 on that d8, the +1 is 12.5%
On average, a d8 weapon does 4.5 damage. The +1 is then 22.2222%

Do you all now see why I didn't get into damage?
1 pip on a d8 is always 12.5%; and +1 merely increases the range* by one pip from 1-8 to 2-9. Hence, the overall net damage goes up by 12.5%.

* - assumption for these purposes is that the range is closed-ended.
 




1 pip on a d8 is always 12.5%; and +1 merely increases the range* by one pip from 1-8 to 2-9. Hence, the overall net damage goes up by 12.5%.

* - assumption for these purposes is that the range is closed-ended.

Oh boy.

Ok, I'll break it out....

If you can roll 1-8, the average is (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8) / 8 = 4.5
If you can roll 2-9, the average is (2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) / 8 = 5.5

Which is the same thing as adding +1 to the average of a d8.

1/4.5 = 0.222...

Therefore the increase is 22%.

But note that if you have other bonuses, such as +3 for strength, then the +1 is less significant and you get a lower % increase.
 


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