How to determine if using the Great Weapon Master feat will increase DPR?

If I have the Great Weapon Master feat, how do I work out if using the -5 to hit and +10 damage gives more damage overall, given a certain AC, to hit, and damage bonus?

For example:

  • I’m an Aasimar with Mounted Combatant feat for advantage and Great Weapon Master feat for -5 to hit and +10 to damage.
  • My opponent has an AC of 16
  • I have a normal “to hit” of +10 (thus +5 with GWM)
  • My average damage bonus of +13 once the Aasimar racial hits (so +23 with GWM)

How do know what will do more damage overall? I know there is a way in Any-Dice to do this, but I’ve not found it.

Is it complicated by the fact that I get an entire extra attack (until Polearm Mastery) if I get a critical hit also?

How to use Master Theorem with strange format of $b$ parameter?

I have a funcion $ T: \mathbb{N}\to\mathbb{N}$ defined as:

$ $ T(n)=\begin{cases} 6 &\text{ if } n=0,\ T(n-1) + 6n + 6 &\text{otherwise.} \end{cases}$ $

How can I apply the Master Theorem to this problem? I have only seen the M.T. in one of these two formats:

$ $ T(n) = aT(n/b) + f (n)$ $ $ $ T(n) = aT(n/b) + \Theta(n^c)$ $

So I’m wondering how to transform the $ T(n-1)$ to something usable. Is it even possible to apply the theorem to this kind of problem?

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Master theorem: When a $f(n)$ is smaller or larger than $n^{log_b a}$by less than a polynomial factor

I was revising master theorem from https://brilliant.org/wiki/master-theorem/ and I was trying to solve a question.

Which of the following asymptotically grows faster.

(a) $ T(n) = 4T(n/2) + 10n $

(b) $ T(n) = 8T(n/3) + 24n^2 $

(c) $ T(n) = 16T(n/4) + 10n^2 $

(d) $ T(n) = 25T(n/5) + 20(nlogn)^{1.99} $

(e) They all asymptotically the same

My calculation says, (a) is $ \theta(n^2)$ (b) is $ \theta(n^2)$ (c) is $ \theta(n^2logn)$ . Now how can I evaluate (d)?

If $ f(n)$ is smaller or larger than $ n^{log_b a}$ by less than a polynomial factor, how can I solve T(n)?

Can’t Edit Master Pages

Can anyone help me. Every time I click the master pages edit menu, edit the display template and edit the page layout, an error always appears as follows

Server Error in ‘/’ Application. Runtime Error Description: An application error occurred on the server. The current custom error settings for this application prevent the details of the application error from being viewed remotely (for security reasons). It could, however, be viewed by browsers running on the local server machine.

Details: To enable the details of this specific error message to be viewable on remote machines, please create a tag within a “web.config” configuration file located in the root directory of the current web application. This tag should then have its “mode” attribute set to “Off”.

Notes: The current error page you are seeing can be replaced by a custom error page by modifying the “defaultRedirect” attribute of the application’s configuration tag to point to a custom error page URL.

thank you for the solution

Does a +1 shield allow me to add 3 to my Dex saves when using the second benefit of Shield Master?

If I have a +1 shield and the Shield Master feat (PHB, p. 170), can I add 3 to my Dex saving throw when I use the second benefit of Shield Master?

If you aren’t incapacitated, you can add your shield’s AC bonus to any Dexterity saving throw you make against a spell or other harmful effect that targets only you.

Does a +1 shield allow me to add 3 to my Dex saves when using the second benefit of Shield Master?

If I have a +1 shield and the Shield Master feat (PHB, p. 170), can I add 3 to my Dex saving throw when I use the second benefit of Shield Master?

If you aren’t incapacitated, you can add your shield’s AC bonus to any Dexterity saving throw you make against a spell or other harmful effect that targets only you.