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I am playing a fighter in a (heavily homebrewed) D&D campaign. The way the DM and I have created my character she has the option of using her main weapon, a quarterstaff, either one handed or two handed.

One Handed: 1d8 + 6

Two Handed: 1d10 + 4

At the moment the two have an identical +9 to hit. I took dueling as my fighting style so have a +2 to the one-handed attack.

To my (mathematically challenged) eye this seems fairly useless since the two are nearly identical in damage. I'd like to argue for a different setup but I would like some hard numbers to show to my DM to argue my case (or perhaps show me that I'm totally wrong).

What is the average amount of damage each of those attacks will do?

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The average roll of any single die can easily be calculated by taking the the sum of all faces and then divide by the number of faces. Luckily, this always comes to 0.5 × HIGHEST_NUMBER + 0.5. So for a d8, the average will be 4 + 0.5 = 4.5 and the average for a d10 will be 5 + 0.5 = 5.5.

This means for your attacks it's

  • 1d8 + 6 = 4.5 + 6 = 10.5 average
  • 1d10 + 4 = 5.5 + 4 = 9.5 average

Thus, using it one-handed is superior. Using it one-handed also allows you to do other things with your other hand - such as wielding a shield, or a second weapon - making it even more superior.

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  • \$\begingroup\$ Excellent answer! For added information, you could note that expected values scales linearly, so when multiple attacks (or die rolls per attack) come in to play you can simply add together the expected damages of the individual rolls to get the new, correct average. \$\endgroup\$
    – kviiri
    Aug 7, 2019 at 7:06
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    \$\begingroup\$ A second weapon would make the Dueling fighting bonus non-applicable, while the shield would not. However, it would enable the bonus action of off-hand light weapon attack for extra damage without ability modifiers. I would suggest to address these points in your answer to improve its quality. Also some references from the rules would be nice. \$\endgroup\$
    – adonies
    Aug 7, 2019 at 8:48

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