## dnd 5e – After the game tests: Planescape Inspired Lady of Pain Patron, is it balanced?

A couple of weeks ago I tried a subclass inspired by Planescape for the sorcerer.
Since then, I have been able to incorporate the comments offered by the community, as well as play the tests with the player who asked me to make this character possible for her. For a bit of context, our campaign has become a kind of adventure for planar rangers. We have an evocation assistant, a forester from Horizon Walker and now the sorcerer from LoP. We started the campaign at 5th level and since then we have progressed to 9th. The initial goal of the subclass was to provide another front-line option other than Hexblade that is more defensive when the Hexblade is offensive.

For this we have simplified the central function, The shadow of serenity to offer the same CA bonus while exchanging the ability to make creatures vulnerable to damage by a few Hellish Rebuke castings.

I still worry about the actual wording of certain features to maintain consistency with the published materials, as well as the overall balance of the Subclass at the highest levels.

You made a silent pact with the Lady of Pain and her cage. As a shadow of His serenity, you have been accused of maintaining the balance between the planes and preserving the privacy of the Lady. As part of this agreement, you have the following restrictions and benefits:

• You should never disclose the nature of your covenant, even under penalty of death.

• You must protect Dabu and the city of Sigil, and never cause harm.

• Alcohol and other intoxicants do not have a diminished effect on the pain you feel. On the contrary, their tolerance to pain has increased twice that of most mortal creatures.

• You can understand the strange visual language of Dabu, but you can not communicate using it.

Expanded spell list

1st: Shield, inflict Wounds.

2nd: Cloud of daggers, silence.

4th: stone skin, death room

5th: binding planar, Geas

Features

Starting at the first level, you can like an action project a sinister shadow that hides your enemy form within a 10-foot radius centered on you for 8 hours, which gives you several benefits:

• You gain a bonus to your CA equal to half of your Charisma modifier,

• In reaction to being hit by a creature within your aura, you can
launches a version of the Hellish Rebuke spell. The level of the spell is
equivalent to the amount of Serenity & # 39; s Shadow charges that
spend. This spell can not exceed the 5th level (6d10) and you must have
The ability to cast the spell to the corresponding corresponding.
level. The damage by this reaction is considered a magical touch.
and use your spell to save DC.

• You can spend 1 charge of Serenity & # 39; s Shadow to take the Hide or
Undock the action as a bonus action.

Dexterity (stealth controls).

The Shadow of Serenity has a number of charges equal to your wizard level +1. Once the Duration of the Shadow ends, you end it soon as an action, or if you use all the Serenity Shadow charges, you must finish a long rest to use the Shadow again.

At level 10, the aura of the shadow grants CA bonus to the allies within the range equal to half of your Charisma modifier rounded down (minimum of +1). The radius of the Serenity Shadow expands to 30 feet.

At level 14, the shadow aura gives you twice the Dexterity skill bonus (stealth controls) and allows allies on your radio to take the Unlink or Hide action as a bonus action.

Breaking off

On the sixth level, your body has adapted to recover from frightful injuries. You have an advantage in saving death shots. Also, if you have hit points equal to or less than half of your maximum hit points, you can use an additional action to throw a Hit Die to recover hit points, the number of hit points retrieved is equal to the Hit die roll. given more your Charism. modifier

Planar goalkeeper

At level 14, you can cast the plane change spell once without using a spell slot or material components as long as you address Sigil. You can use this function to travel to another place if you own the cost of the material component and the spell slot does it normally. In reaction to the plane change spell cast by another creature, you can counteract that spell immediately by using a level 7 spell slot. Once you use this function, you must finish a long rest before using it again.

Lady of Pain Patron Eldritch Invocations

The radius of the Shadow feature of your Serenity expands 30 feet. Also, while the shadow is active, you can cast the Dark spell by spending 3 charges from the Shadow of Serenity.

Berk & # 39; s Bain

Prerequisites: Level 5, Lady of Pain Patron

You are becoming more cruel to your enemies, since you now have a critical hit with an attack roll of 19 or 20, while the Serenity Shadow feature is active, in addition, if you are not, you acquire the ability of Intimidation .

Tormentor

Prerequisites: Level 10, Patron of the Lady of Pain, Covenant of the Leaf

You have learned to foster a fear of abnormal and persistent pain in your enemies.
Once per turn, you can inflict additional psychic damage of 5d6 on a creature that you hit with an attack if you have an advantage on the attack roll. The attack must use your covenant weapon.

You do not need an advantage in the attack roll if another enemy of the target is within 5 feet of it, that enemy is not incapacitated and you have no disadvantage in the attack roll.

I thought you were dead for sure!

Prerequisites: Level 12, Lady of Sorrow Patron

Injuries are a daily occurrence in your line of work, allowing you to obtain more information about anatomy and medicine. You gain skill in medicine ability, in addition, when you use the Separation function, you can now add twice the Charisma Modifier and you can reattach a cut limb by holding a cut body part (other than your head) in the place where it fell. Once you use this function to reposition a limb, you can not use it again until you have finished a long rest.

Prerequisites: Level 18, Lady of Pain Patron

You gain mastery of the specific dimensions of the pocket in which the Lady of Pain fills Berks who dislike it. You can cast the maze spell once without using a spell slot. The labyrinth seems to be a circular series of platforms, roads and portals. The labyrinth can also be cast on a group of willing creatures, just like your Charisma modifier. The objects and inanimate objects that remain in the labyrinth will remain there. If the maze is used in this way, you must complete a DC 20 Intelligence test to finish the spell before. Once this Invocation has been used for any of the functions, you must take a long break to regain access to the maze.

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## A graph theory question inspired by a question about Morse functions in \$ mathbb {S} ^ 2 \$

This question arose from my attempt to solve the problem posed in this fascinating question about the gradient of a soft function in $$mathbb {S} ^ 2$$.

Fix a finite set, $$P$$, of an even number of points $$p_1, ldots, p_N in mathbb {S} ^ 2$$. Leave $$C (p_i) = {q in mathbb {S} ^ 2: q cdot p_i = 0 }$$ Be set of large circles with axis of $$p_i$$.

We make the following assumptions

• $$C (p_i) neq C (p_j)$$ for $$p neq j$$
• $$C (p_i) cap C (p_j) cap C (p_k) = emptyset$$ for different $$p_i, p_j, p_k$$.

Now let $$V = {q in mathbb {S} ^ 2: q in C (p_i) cap C (p_j), mbox {some} p_i neq p_j }$$. This is the set of {vertices}.
Leave
$$Gamma = bigcup_ {p in P} C (p)$$
and let $$E$$ be the set of components of $$Gamma backslash V$$. This is the set of edges. Clearly, $$(V, E)$$ It is a flat graph. Finally, let's go $$F$$ be the set of the components of $$mathbb {S} ^ 2 backslash Gamma$$. This is the set of faces. We can think of $$(F, E)$$ as the dual chart for $$(V, E)$$.

Keep in mind that the antipodal map $$A: mathbb {S} ^ 2 to mathbb {S} ^ 2$$ Induces an involution in the sets. $$V$$, $$E$$ Y $$F$$ which we will also denote by $$A$$.

Now suppose we have a map $$sigma: F to {0, ldots, N }$$ with the property that

• $$sigma (f) + sigma (A (f)) = N$$
• Yes $$f_1$$ Y $$f_2$$ they are adjacent faces, then $$| sigma (f_1) – sigma (f_2) | = 1$$ (that is to say., $$sigma$$ Jump through one through an edge.

Look at the construction ensuring that each vertex. $$v$$ It limits four edges and thus one has four faces. $$f_1$$, $$f_2$$, $$f_3$$ Y $$f_4$$ meet in $$v$$, then, until the re-labeling $$sigma (f_1) = sigma (f_2)$$, $$sigma (f_3) = sigma (f_2) -1$$ Y $$sigma (f_4) = sigma (f_2) + 1 = sigma (f_3) + 2$$.

Now let $$F_e = {f in F: sigma (f) mbox {even} }$$ and y $$F_o = {f in F: sigma (f) mbox {odd} }.$$
Leave
$$F_o & # 39; = {f in F_o: sigma (f) geq 3 mbox {y} sigma (A (f)) geq 3 }.$$
As $$N$$ it's even, we have $$A (F_e) = F_e$$ Y $$A (F_o) = F_o$$.

by $$F_o & # 39; & # 39;$$ some unspecified subset of $$F_o & # 39;$$, we are interested in the following problem:

Issue: Determine if $$F_o & # 39; & # 39; cup F_e$$ contains a connected path (in the dual graph $$(F, E)$$) connecting antipodal faces.

When $$N = 2$$ or $$N = 4$$, $$F_o & # 39;$$ it is empty and it is easy to see any path between the antipodal points in $$F_e$$ must go through $$F_o$$ – That is, there is no route as requested by the problem. I have no idea what can happen when $$N = 6$$. My suspicion is that for $$F_o & # 39; & # 39;$$ big enough one can have such a way.