Math question and yes I need help


Advice


Suppose you have the option of rolling xd6 or xd8-x dice for damage. Which one do you take and why?


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1d6=1d8-1

A d6 has an average value of 3.5, a d8 has an average value of 4.5.

Since 1d6=1d8-1, 2d6=2d8-2, etc. there technically would be no statistical difference.

Since this is a damage roll however, a value of 0 would be equal to 1 point of non lethal damage making the xd8-x the better choice.

There is also a greater max value which can be preferable when trying to overcome DR/hardness.


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You'll get greater variance with the xd8-x. If x is high enough though the variance will still be mostly insignificant.


Gallant Armor wrote:

1d6=1d8-1

A d6 has an average value of 3.5, a d8 has an average value of 4.5.

Since 1d6=1d8-1, 2d6=2d8-2, etc. there technically would be no statistical difference.

Since this is a damage roll however, a value of 0 would be equal to 1 point of non lethal damage making the xd8-x the better choice.

There is also a greater max value which can be preferable when trying to overcome DR/hardness.

Yeah that's what I was thinking. Its such a weird alchemist ability because all it does is increase the variance of the bombs. Thematically appropriate for the First World Innovator but still weirdly odd.


xd6 is better for a player character. xd8-x is a better choice for an NPC.

Generally speaking, PCs are helped more by the more stable option, while NPCs are helped more by the more random option.

This is because PCs have to win (or at least survive) every fight, while NPCs are expected to die. It's the improbable, random possibilities that tend to change that.

A PC only has to get unlucky for one fight. An NPC only has to get lucky for one fight.


I made a test spreadsheet to check 2d8-2 vs. 2d6.
The spreadsheet shows 2d8-2 is better at beating DR.
DR 2d8-2 2d6
01 6.01 6
02 5.06 5
03 4.15 4.02
04 3.31 3.11
05 2.54 2.27
06 1.87 1.55
07 1.31 0.97
08 0.87 0.55
09 0.54 0.27
10 0.31 0.11

/cevah

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