How to add the weights to the transition graph of a Markov chain?

The following working program uses Graph and Markov Chain

P = {{1/2, 1/2, 0, 0}, {1/2, 1/2, 0, 0}, {1/4, 1/4, 1/4, 1/4}, {0, 0,     0, 1}}; proc = DiscreteMarkovProcess[3, P]; Graph[proc, GraphStyle -> "DiagramBlue",   EdgeLabels ->    With[{sm = MarkovProcessProperties[proc, "TransitionMatrix"]},     Flatten@Table[DirectedEdge[i, j] -> sm[[i, j]], {i, 2}, {j, 2}]]]  sm = MarkovProcessProperties[proc, "TransitionMatrix"] sm == P 

Since I couldn’t make it work for larger matrices, I clarified in the last two lines that sm is just P. But, if I try to replace sm by P in the first part, all hell breaks loose. So, I tried copy paste changing just P to a larger matrix, but this does not work. Why?

P = {{0, 1/4, 1/2, 1/4, 0, 0}, {0, 1, 0, 0, 0, 0}, {0, 0, 1/3, 0, 2/3,      0}, {0, 0, 0, 0, 0, 1},    {0, 0, 1/4, 0, 3/4, 0}, {1/4, 0, 0, 0, 3/4, 0}}; P // MatrixForm proc = DiscreteMarkovProcess[1, P]; Graph[proc,   EdgeLabels ->    With[{sm = MarkovProcessProperties[proc, "TransitionMatrix"]},     Flatten@Table[DirectedEdge[i, j] -> sm[[i, j]], {i, 6}, {j, 6}]]] 

What happens to a Chain lighting with invalid primary target and valid secondary targets?

This question asks what happens when a single-target spell has an invalid target. (A target that is not legitimately permissible, not a target that is weak from illness or injury).

The answer appears to be: that depends on whether one wishes to implement an older Sage Advice segment of a Dragon Talk podcast, or the more recent but optional written rules in Xanathar’s Guide to Everything.

Assume for this question that I prefer XGtE.

The rule for resolving invalid spell targets states (XGtE 85-86):

If you cast a spell on someone or something that can’t be affected by the spell, nothing happens to that target, but if you used a spell slot to cast the spell, the slot is still expended.

Now consider the chain lightning spell, in which

You create a bolt of lightning that arcs toward a target of your choice that you can see within range. Three bolts then leap from that target to as many as three other targets, each of which must be within 30 feet of the first target. A target can be a creature or an object and can be targeted by only one of the bolts.

Suppose my primary target for the spell is invalid, because it is not a creature or an object. If an example must be given, suppose it is an illusion. However, each of the three secondary targets of the spell are valid, being either creatures or objects.

Do I spend the spell slot with nothing happening at all, or does the slot get spent, the chain lightning impact the illusion but do nothing to it and then leap to the three valid targets with the full effects given in the spell description?

Note: I am assuming that an illusion is not an object, based largely on my interpretation that an illusion is not an "item" and on the text of the 14th-level School of Illusion wizard feature, Illusory Reality. I am open to frame challenges that demonstrate that illusions are, in fact, objects, but such answers will be better if they then either provide a more appropriate example of something that is not a creature or an object, or demonstrate that the question is moot since everything is at least either a creature or an object.

If you use the Investment of the Chain Master Eldritch Invocation, does your familiar get a bonus to its saving throw DC from your own magic items?

The Investment of the Chain Master Eldritch Invocation states:

[…] When you cast find familiar, you infuse the summoned familiar with a measure of your eldritch power, granting the creature the following benefits: […]

[…] * If the familiar forces a creature to make a saving throw, it uses your spell save DC. […]

My question is, if the warlock has a Rod of the Pact Keeper, or Wand of the War Mage or something else which raises their saving throw DC, does the familiar inherit this when it triggers a saving throw? For example: If I had a DC 14 save with no gear and a DC 15 save with my +1 magic item, would the familiar use a 14 or a 15 for its save DC?

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When does a warlock’s familiar make their attack if the warlock has the Investment of the Chain Master eldritch invocation?

So, Tasha’s Cauldron of Everything introduces a lot of new "pet" mechanics in DnD 5e. An emerging trend for some of them is that the master can take a bonus action to command the pet to take a specific action. For example:

Circle of Wildfire Druid’s Wildfire Spirit

In combat, the spirit shares your initiative count, but it takes its turn immediately after yours. The only action it takes on its turn is the Dodge action, unless you take a bonus action on your turn to command it to take another action.

Beast Master Ranger’s Primal Companion

In combat, the beast acts during your turn. It can move and use its reaction on its own, but the only action it takes is the Dodge action, unless you take a bonus action on your turn to command it to take another action.

A Pact of the Chain Warlock with the Investment of the Chain Master eldritch invocation

When you cast Find Familiar, you infuse the summoned familiar with a measure of your eldritch power, granting the creature the following benefits:

  • […]
  • As a bonus action, you can command the familiar to take the Attack action.
  • […]

While it probably won’t matter much for the Wildfire Spirit or the Primal Companion since they both take their turns on or right after the master, a familiar has its own initiative and acts on it own turn. So, if a Pact of the Chain warlock with the Investment of the Chain Master eldritch invocation uses its bonus action to command their familiar to take the Attack action, when does said familiar actually take the Attack action?
Contrast this with the base Pact of the Chain feature, where a familiar can use its reaction to take the Attack action on the master’s turn, should the master forgoes one of their attacks:

Pact of the Chain

Additionally, when you take the Attack action, you can forgo one of your own attacks to allow your familiar to use its reaction to make one attack of its own.

Can the Dimension Dervish chain be use in conjunction with combat, teamwork feats?

Can I string the Dimensional Agility Feat chain (specifically, Dimensional Savant) and Precise Strike feat together? As I read it since I can flank with myself as an ally doesn’t the feat bonus apply as well?

Precise Strike:

Whenever you and an ally who also has this feat are flanking the same the creature, you deal an additional 1d6 points of precision damage with each successful melee attack. This bonus damage stacks with other sources of precision damage, such as sneak attack. This bonus damage is not multiplied on a critical hit.

Dimensional Agility:

While using the Dimensional Dervish feat, you provide flanking from all squares you attack from. Flanking starts from the moment you make an attack until the start of your next turn. You can effectively flank with yourself and with multiple allies when using this feat.

Can a chain of simulacra casting a spell make it permanent?

This is a weird question.
It has been established that a caster could cast Simulacrum on themselves to make a simulacra, then the simulacra can cast Simulacrum on the caster to make a second simulacra of the caster, and son on. Let’s call this a chain of simulacra.

Certain spells can be made permanent by casting them on the same place daily or weekly for a set period of time, such as a month or year. These spells include Mordenkainen’s Private sanctum, druid grove, forbiddance, guards and wards, temple of the gods and mighty fortress.

I am not certain of the wording on these, but could a chain of simulacra make any of these permanent?

Can a Pact of the Chain Warlock summon their familiar in an invisible state?

As a Pact of the Chain Warlock, 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.

The imp, quasit, and sprite all have the power to turn invisible.

Is it possible that when the Warlock calls forth their familiar, that the familiar starts in an invisible state? Or would they have to appear visible, and then immediately take an Action to turn invisible?

Does the Voice of the Chain Master eldritch invocation let me cast a purely verbal spell through my familiar?

In D&D 5e, as a Pact of the Chain Warlock, I can choose an eldritch invocation that lets me speak in my own voice through my familiar called Voice of the Chain Master (PHB 111):

You can communicate telepathically with your familiar and perceive through your familiar’s senses as long as you are on the same plane of existence. Additionally, while perceiving through your familiar’s senses, you can also speak through your familiar in your own voice, even if your familiar is normally incapable of speech.

Healing word is a spell with only a verbal component (PHB 249):

Components: V

[…]

A creature of your choice that you can see within range regains hit points equal to 1d4 + your spellcasting ability modifier.

The description of verbal components in the rules of spellcasting (PHB 203) says the sound of my voice alone is what causes the magic of this spell to happen:

Most spells require the chanting of mystic words. The words themselves aren’t the source of the spell’s power; rather, the particular combination of sounds, with specific pitch and resonance, sets the threads of magic in motion.

Say my familiar is in another room, no matter how far away. Through my familiar’s eyes, I see a target at 60 feet. From my familiar comes my own magic-infused voice. That particular combination of sounds, with specific pitch and resonance, sets the threads of magic in motion that travel to the target and heal it.

Is this possible?

Connecting to SQL Server from SSMA (the certificate chain was issued by an authority that is not trusted!)

I am trying to use SQL Server Migration Assistant for the first time from my home PC. I have SQL Server in one Docker container and Oracle in another. I can connect to Oracle from SSMA, however when trying to connect to SQL Server I see this error:

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I have read plenty of questions on here that explain how to resolve the problem if it is seen when connecting from SQL Studio Manager e.g. this one: The certificate chain was issued by an authority that is not trusted. I have no problem connecting from SQL Studio Manager – just SSMA. How can I connect to SQL server from SSMA?

I have tried unticking ‘Encrypt connection’ on the SSMA SQL Server login window and I see the same error.