Is this homebrew variant of True Strike too strong to be a cantrip?

Lethal Strike
Enchantment cantrip

Components: V S
Casting Time: 1 Bonus Action
Range: Self
Duration: until the end of current turn

When you roll a 19 on a weapon attack, that attack is also a critical hit, then this spell ends.

This spell is brewed for my players’ Arcane Trickster, who would like a combat cantrip that will enhance his sneak attack. He does not like true strike because it wastes one full turn before he can attack, thus I make this one requiring bonus action instead.

I’m worried that making it requiring bonus action instead of action will make this overpowered.

Is this homebrew spell overpowered as a cantrip? If yes, what is the suggested spell level for this? What can be modified so this can stay as a cantrip?

Why can’t the “Variant: Imp Familiar” be found with the Find Familiar spell?

The Find Familiar spell describes a familiar

The Find Familiar spell description explains what a “familiar” is. It describes its properties — acts independently, can’t attack, can deliver spells, can be dismissed into a pocket dimension, etc.

The PHB uses “familiar” as a term, expanding its properties in some cases, e.g. Pact of the Chain:

Pact of the Chain
You learn the Find Familiar spell and can cast it as a ritual. The spell doesn’t count against your number of spells known. When you cast the spell, you can choose one of the normal forms for your familiar or one of the following special forms: imp, pseudodragon, quasit, or sprite.
Additionally, when you take the Attack action, you can forgo one of your own attacks to allow your familiar to make one attack of its own with its reaction.

So the Warlock’s familiar can be an imp, pseudodragon, quasit, or sprite, and it can attack.

“Variant: Familiar” describes additional familiar properties

Notice that imp, pseudodragon and quasit all have the “Variant: Familiar” block and there are no other creatures in the MM with the “Variant: Familiar” block. That block describes additional familiar features: first one is the 1-mile telepathic link, and second one depends on the creature type (for instance, Imp gives its master the Magic Resistance trait). That block does not describe any other familiar’s properties. It doesn’t explain anything that is already described in the Find Familiar spell, and it still uses the “familiar” term. It is logical to assume that it is the same “familiar” as the PHB describes.

From my understanding, “Variant: Familiar” expands base familiar description, like the Pact of the Chain does:

  1. General familiar properties are given in the Find Familiar spell description.

  2. If the spellcaster is a Warlock and they chooses the Pact of Chain feature, the familiar properties are expanded, giving more potent familiar as a result.

  3. The familiar properties might be expanded even more, if the familiar is Imp/Quasit/Pseudodragon and the DM uses the “Variant: Familiar” optional rule.

It goes well with the “specific beats generic” rule:

  • Familiar can’t attack (generic) but it can with the Pact of Chain (specific).

  • The spellcaster can share familiar’s senses within 100 feet (generic), or 1 mile with several kinds (specific), providing the DM uses the variant rule.

So why in fact does it not?

Several answers (like this one) assume that in fact “Variant: Familiar” rule describes a sort of “another” familiar with completely different properties. It can attack, but can NOT deliver spells, and if it dies — it’s gone forever. How to obtain this familiar remains a mystery. It is still called a “familiar” though.

That seems purely homebrew for me, but is treated as official rulings. It is also being said these creatures cannot be found with the Find Familiar spell. What is the source of this assumption? What are the properties of this “another familiar”, and where they are described?

@SevenSidedDie mentioned that all “Variant: X” in the MM mean a somewhat special creature:

… a variant is just an alternative stat block for a given creature, so that it works slightly differently from the common variety of that creature.

The idea of “variants” is that, just like not every human is identical

A familiar variant of a creature is just the stat block to use for a creature that has somehow agreed to serve as a familiar for a spellcaster.

That actually supports the idea that Warlock should have the magic resistance trait from the imp, not contradicts it.

The Warlock summoned an imp as a familiar — therefore, that particular imp agreed to serve as a familiar. The DM uses the variant rule. Why shouldn’t the imp give the magic resistance trait, as the “Variant: Imp Familiar” describes?

It is just a spirit that takes a particular form

That answer explains it that way:

the Warlock’s familiar isn’t any sort of pseudodragon, let alone one with the variant. It’s a spirit that takes the form of a pseudodragon

But that reasoning does not work with the imp. Find Familiar implies that the imp familiar is an imp:

the familiar has the Statistics of the chosen form, though it is a celestial, fey, or fiend

So a fiend can be a familiar, and Imp is a fiend.

multiset variant of subset sum problem known algorithms

I have been working in the time analysis for a solver I designed for the subset sum problem (multiset variant), and determined its time complexity to be dependent on the count of repeated elements in the input.

The time complexity is $ O(2^{n/2} \cdot 0.75^{\frac{d/2}{n}})$ where $ d=$ # of duplicates in the input instance (assuming both $ n$ and $ d$ are even)

For example, when $ d=n/2$ then:

$ O(2^{n/2} \cdot 0.75^{\frac{n/4}{n}}) \approx O(1.4142 \cdot 0.93) \approx O(1.316^n)$

Besides to ask for comments, I am looking as well for other known algorithms with a similar behavior to compare approaches (looked for them but found nothing so far…)

Would Epic Heroism be an acceptable rule variant for a small, first-time group?

I’m DMing a group with 4 players. For all of us, this is our first D&D experience. We’ll be playing Lost Mines of Phandelver.

I’m concerned about the survivability, especially given how green the players are. At first level, they’ll have 10 or 12 hit points, facing groups of goblins that can hit for 1d6+2. I’m adjusting the number of monsters in each encounter, but still worry.

Healing seems to be very rare. At first level, the spellcasters will have the ability to cast two spells in an entire dungeon.

Epic Heroism (DM Guide p267) seems like it could help, but might tip the balance too far the other way into easy mode:

This variant uses a short rest of 5 minutes and a long rest of 1 hour. This change makes combat more routine, since characters can easily recover from every battle. You might want to make combat encounters more difficult to compensate.

Spellcasters using this system can afford to burn through spell slots quickly, especially at higher levels. Consider allowing spellcasters to restore expended spell slots equal to only half their maximum spell slots (rounded down) at the end of a long rest, and to limit spell slots restored to 5th level or lower. Only a full 8-hour rest will allow a spellcaster to restore all spell slots and to regain spell slots of 6th level or higher.

Am I missing some element that would make the party more likely to survive the first dungeon, or would this rule variant be a good way to introduce the mechanics of the game?

How do the activity limitations for a long rest work in the Gritty Realism variant?

In my current campaign (in which I am a player) we are considering switching over to the Gritty Realism rest variant in the DMG so that the party would have to expend more resources between resting. The variant says:

This variant uses a short rest of 8 hours and a long rest of 7 days.

But we are confused at how this variant interacts with the normal rules for resting.

A normal long rest has this description:

A long rest is a period of extended downtime, at least 8 hours long, during which a character sleeps for at least 6 hours and performs no more than 2 hours of light activity, such as reading, talking, eating, or standing watch. If the rest is interrupted by a period of strenuous activity – at least 1 hour of walking, fighting, casting spells, or similar adventuring activity – the characters must begin the rest again to gain any benefit from it.

How do these rules transfer over to the variant? Is it true that you must spend 7 full days only in a single long rest and that you may not perform more than 2 hours of light activities over the entire 7 day (168 hour) period? It seems like over 7 days you could easily spend at least 2 hours eating and talking.

Would the long rest be invalidated if they take are interrupted by a single hour of strenuous activity over the entire 7 days? Even for a “gritty” variant that seems really extreme.

How are the activity limitations supposed to work in this variant?

PF-1e Can you variant multiclass as your primary class?

Can you VMC into the same class you’re taking as a primary class to ‘focus on your class’ at the expense of feats and gain increased benefit or uses from class features, or to be able to choose from two options of a class ability you would otherwise have to make choices against?

The example in mind is a Wizard VMC Wizard. At the expense of some feats you can choose a school as your main wizard, and specialize in a different school on the VMC ‘side’. Likewise you could choose an arcane bond with your primary levels, and then pick up a familiar at level three. The arcane school powers you get from the VMC side are slower than you’re primary, but this would (in theory) allow you to double dip on some class abilities.

Many VMC combinations like this are somewhat useless, such as a Ranger VMC Ranger would gain nothing they don’t already have and things which don’t really stack (except, maybe, having more favored enemies.) But a Paladin could have more lay on hand and smite uses per day.

The Character Advancement rules don’t expressly prohibit it. They do prohibit taking levels in your VMC class, but only in the context of blending normal multiclass with VMC; avoiding builds like Fighter VMC Cleric 3 / Cleric 2.

Conversely, there is no way to take the 1st level in a class twice. You cannot be a Sorcerer 1 / Sorcerer 1 and choose two different bloodlines. Curious if there was any rule or guiding principle I’m unaware of giving a hard line on if this is a legitimate option or not.

TSP Variant – Ordered Path

Recently I came up with a traveling-salesman-esque problem. As usual, we have n vertices, and a weighted edge between any two vertices. However, each vertex is associated with a color, which may be repeated. Then, you are given a sequence of colors, and you want to find the shortest path that follows this sequence. If all vertices are the same color, this is the same as TSP. However, if all vertices are different colors, there is only one solution.

Is this variant at all studied? Let $ c$ be the most vertices of any given color. Is the decision problem this variant NP-complete for some fixed, c, or alternatively is there a simple way to solve the decision problem polynomially for any finite $ c$ ?