Are there any tools or tricks to quickly level characters multiple levels at once?

I’m in the process of writing a short sci-fi campaign which is based on D&D 5e, in which the player classes, weapons, and skills are effectively just sci-fi reskins of their magical counterparts. I’m avoiding guns through lore, and players will instead have body modifications that constitute skills and weapons. In order to keep things simple, the players will select from a small pool of pre-made characters and apply some personal flair.

The campaign will be fairly short, so something I’d like to do is give the players the full range of experiences in terms of being squishy, then gearing up, then jumping into some serious (CR20+) world-ending battles. The campaign will be played by some seasoned players, so I’m not really too worried about character complexity spikes, but I also don’t want to get to one of my “level up” points and have the players doing 8 levels worth of decisions in one go. Instead, what I’d like to do is have the character stats and skills roughly figured out ahead of time, so they can reach the level-up point and carry on without too much of a stall in gameplay. The problem is that I’m not really sure what the best way to go about this is.

Are there any tools out there that can help me figure out the correct stat ranges and skills progressions for various classes? Are there any tricks to doing this kind of pre-levelled setup in a game?

Can you do blood-bond related activites without incurring blood-binding penalties with Tzimisce tricks?

There is a certain Tzimisce power that allows you to take in foreign blood without incurring Blood Bond penalites – a combination discipline of Vicissitude and Auspex called “The False Drink”.

From what I can discern, to learn an out-of-clan discipline (say, Protean), the student must find a capable mentor and drink one point of their blood, which would normally result in a level 1 Blood Bond.

Would The False Drink prevent the Blood Bond resulting from this procedure, or is it inevitable?

I would love to hear versions from both V20 and V5 on this one.

Are illusions just mind tricks or do they produce physical images and sounds?

Do illusions exist as images and sounds in the world, like holograms, or do they exist only in the beholder’s mind, like mass hallucinations? There are paragraphs in the PHB that can support both assumptions.

Clarification: the question primarily concerns illusions produced by Minor Illusion, Programmed Illusion, Silent Image, Major Image, Disguise Self spells. Spells like Fear or Phantasmal Killer explicitly says they affect creatures, so they are out of the scope.

Illusions as actual images and sounds

Spell description explicitly says that the caster “creates a sound or an image”:

You create a sound or an image of an object within range

When casting an illusion, the caster have to specify a location, not a creature. Anyone who looks at the location perceives the illusion.

Many obviously mind-affecting spells like “friends” or “charm person” are enchantments, not illusions.

While there are creatures immune to charm, there is no creatures immune to illusions. Even a construct can perceive an illusion.

Illusions as mind tricks

The wizard’s arcane tradition describes the School of Illusion as

magic that dazzles the senses, befuddles the mind

Being revealed, an illusion looks different to the perceiving person only:

If a creature discerns the illusion for what it is, the illusion becomes faint to the creature.

When does it matter

There are several cases when the outcome might depend on where the spell effect is located:

Antimagic Field – to be negated, should the illusion “itself” be in the field, or does any creature in the field become immune to illusions?

Detect Magic – assuming that Detect Magic spell can detect illusions, what exactly should be in the 30 feet range to be detected?

Also there are ambiguity with light, vision and line of sight:

Block light – A caster tries to use an illusion to cover a window, or conceal a lit torch.

Block vision – Many cases. A caster tries to hide an object “under” an illusion, but the spell description says it can only “create an image” and not “hide an object”. If we assume an illusion actually can cover an object or a creature, Disguise Self would protect from all LoS-dependent spells, etc.

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Do warhorses know the combat riding tricks? Can they be changed?

I reckon not many DMs or players would ever waste time into arguing about this, I would rule it as “do what’s best for your character”. But let’s assume I’m playing with a very nitpicky DM which wants to play as RAW as possible.

The “combat riding” entry in the handle animal skill says

Combat Riding (DC 20): An animal trained to bear a rider into combat knows the tricks attack, come, defend, down, guard, and heel. Training an animal for combat riding takes six weeks. You may also “upgrade” an animal trained for riding to one trained for combat riding by spending three weeks and making a successful DC 20 Handle Animal check. The new general purpose and tricks completely replace the animal’s previous purpose and any tricks it once knew. Warhorses and riding dogs are already trained to bear riders into combat, and they don’t require any additional training for this purpose.

From this answer What happens when a mount is trained for combat riding using the handle animal skill I know what happens to a normal horse which is trained to bear a rider into combat and what being trained to bear riders into combat means (as per the riding skill).

But when I get a Warhorse must it already know the tricks given by combat riding (since Combat Riding says animals trained to bear a rider into combat know those tricks and then says warhorses are already trained to bear riders into combat) or can i chose?
That is, is bearing riders into combat tightly tied to knowing those tricks or are warhorses able to bear riders into combat without being forced into having exactly those tricks?

What puzzles me is that if whenever you got a warhorse they always had those tricks it’s very likely this would’ve been written on the creature entry in the monster manual.

In the case the answer to my question is that all warhorses come with those tricks, can you change the tricks without making your warhorse less “warhorsey”?

Tricks for getting a creative idea

Caveat: I fear that people will criticize me for asking this potentially inappropriate question here, but I guess that the community here is quite unique in the ability of potentially answering my question (if you don’t have an answer, then probably there is no), and that there is some (little) chance of getting some good answers to the question – and not asking this question here or banning it right away would reduce the chance of getting a good answer to 0.

The question is: If one tries to prove something, are there some tricks for getting a creative idea? Ok, I now what you think, yes, there is no algorithm to finding a creative idea, otherwise the idea wouldn’t be creative. However, there are some general “tricks”: if for minutes one stares at ones sheet of papers with no new ideas, just moving in the same thought cycles, it certainly helps to go and talk to a colleague, because somehow talking awakes the creative ability of the brain (and, additionally, together with a colleague one can mutually pick up an idea of the other and think it a bit further). Also, forgetting the problem for a moment and go and attend talks (even if they are about another topic) or even just rest helps. Do you have any other general “tricks” for getting creative ideas for solving mathematical problems?

To make the question a bit more concrete, do you know of any tricks for finding or looking for a good lemma (or several lemmas)? I have the feeling that often the most creativity in proving a theorem lies in finding the right lemma (not even the proof of it, but just the statement). I noticed that whenever I see a proof about which I afterwards say “wow, that’s genius, I don’t even rudimentally see how one could have come up with it”, the crucial point was a lemma (or several lemmas). This also seems to me to be one difference between doing research and doing like homework problems: in homework assignments the proofs usually require only one or two main ideas, and if it requires a lemma, this lemma often is stated in the task as a subtask – while in research, one doesn’t even know how much one has to “go down”, how many levels of lemmas one has to show.

Mathematical card tricks

For quite some time I have taken interest in analyzing card tricks that make use of a deep knowledge of advanced mathematics and there’s been some progress. However, all the tricks I’ve tried decoding seem to be based on elementary math which any serious high school number aficionado can understand and appreciate if not decipher. Is there a card trick that’s so outlandishly brilliant that mathematicians need to wreck their heads over it? P.S: I’m after the holy grail of card tricks that require minimal sleight of hand

Mathematical tricks

This question asks for examples of “tricks”, with “trick” defined as a mathematical statement with the following properties:

  1. It was used in a proof of a major theorem (major is somewhat subjective; for example, a theorem solving a long-standing open problem or opening a new direction of research).
  2. It is pretty short/easy to state.
  3. It looks like a red herring (i.e. does not look particularly natural when you first learn about it). For example, it may involve some arbitrary-looking numbers. Optional: it is really not clear how to generalize it in a useful way.

In short, it is something that would probably annoy Grothendieck. Some candidates:

  • Zarhin’s trick about abelian varieties (e.g. see here).
  • In Weil I, there were two statements that might qualify, one is a Rankin-style power trick, the other is about rational functions with $ l$ -adic coefficients (e.g. see here).

P.S. This is not a duplicate of this question (that one asks for a common characterization) and not a duplicate of this question (ours is less ambitious).

Is there a general theory of when certain polynomials are integrable due to symmetry tricks?

Consider the functions $ x^2$ and $ x^4 + 2x^2y^2$ on the unit sphere $ S^2$ . The surface integral of these functions over the sphere can easily be calculated by symmetry via $ $ 3 \iint_{S^2} x^2 \mathrm{d}A = \iint_{S^2} (x^2 + y^2 + z^2) \, \mathrm{d}A = \iint_{S^2} \mathrm{d}A = 4\pi$ $ and $ $ 3 \iint_{S^2} (x^4+2x^2y^2)\, \mathrm{d}A = \iint_{S^2} (x^2 + y^2 + z^2)^2 \, \mathrm{d}A = \iint_{S^2} \mathrm{d}A = 4\pi.$ $

However, I suspect (although I cannot prove) that the function $ x^4$ cannot be integrated without direct parameterization of the sphere and evaluation of the surface integral.

My question is: in general, given any symmetries and polynomial relations on a manifold (in this case $ (x, y, z) \mapsto (y, z, x)$ and $ x^2 + y^2 + z^2 = 1$ ), is there a general theory to determine what functions are integrable over the manifold by symmetry and relations alone?

A reference (or definitive statement of lack thereof) would be greatly appreciated.