Moving average over time on data entering stochastically

The examples for using MovingAverage mostly refer to data evenly spaced in time,such as stock values. In typical physics data, events arrive random in time (e.g. radio active decay events, but also if acting in day trading on the stock market). I do not see how I can use the apparatus of MovingAverage and associated evaluations in this case. Do I not understand the function, or should I go ahead and invent my own functions?

Is it possible to turn a monster into a humanoid without giving them average physical ability scores?

Savage Species lists some rituals through which a creature can–in one example given–transform from an ogre into an elf.

If nothing else, it’s an interesting and evocative idea: a 6th level ogre barbarian who tires of racial prejudices and transforms into an elf. His RHD disappear, and he becomes a 6th-level elf barbarian. His lower effective level means he can no longer travel with ECL ~12 parties, but he decides to do it anyway. Heck, maybe he did it partly because he was tired of that +2 LA that Savage Species likes to pretend isn’t a big deal.

Unfortunately, losing all those hit dice is far from the worst thing that happens to him. Doing any of the book’s major rituals means his physical ability scores become, at best, 11/13/9. Considering his ogre-born mental scores aren’t picking up much slack either, this is pretty much unacceptable for a barbarian in all but either very silly or very gritty games.

Is there any printed way around this, or to compensate for this beyond things like wishing for inherent bonuses and equipping magic items (which any high level barbarian is going to get anyway, so the transformed elf barbarian still finishes with noticeably poor scores)?

How would optional re-rolling of all hit dice on leveling up affect average hp?

I am considering a homebrew rule that would give players the option on leveling up to re-roll all of their hit dice (excluding their first level) instead of only rolling their new hit die when determining their maximum hit points.

For example a Wizard levels up to level 3. When they leveled up to level 2 they rolled a 2 and they have +0 CON so they had a maximum hp of 8. Instead of rolling their new hit die for possible outcomes of 9-14 hp they can choose to also re-roll their level 2 hit die for possible outcomes of 8-18.

I have been trying to figure out how this would affect average hp outcomes at different levels but I only play with probabilities as a hobby and I am having issues with the math once it gets to higher levels.

How would allowing players to re-roll all hit dice when leveling up affect average hp, assuming that players will always re-roll if their former max hp was below average?

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How to include successful saves when calculating Fireball’s average damage?

I want to know how to calculate the average damage of a spell that also deals half damage on a successful save. For this example, I’ll be taking the most popular evocation spell, Fireball.

As far as calculating damage goes, I know how to calculate the expected damage of attacks using an attack roll, using the following formula:

Expected damage = Probability x Damage + Crit chance x Additional damage on crits
Probability = (21 – target’s AC + attacker’s attack roll modifiers) x 5%

Now I would assume that you just need to reverse the probability formula to calculate a spell that forces a saving throw’s chance of success, like so:

Probability = 1 – (21 – your save DC + target’s save modifiers) x 5%

However, calculating Probability x Damage (omitting the crit chance in the process) using the above formula does not take into account the half damage dealt on a successful save. So how to take this into account when calculating expected damage of spells like Fireball?

What is the most (average) damage one character can do in one Round on its own to a Tarrasque?

Rules/Restrictions:

Any race published is allowed you can use the Customize Your Origin feature from Tasha’s Couldron of Everything.

Any officially published Class by WotC is allowed as well as Optional Class Features.

If there is a circumstantial bonus, such as Assassinate or Haste, please show each step in damage calculation.

No magic items, charms, blessings, or epic boons.

No, the "damage done" can’t be to yourself.

You are on your own no other PC or NPC.

Take into Account that you might not surprise the Tarrasque.

You do not have advantage by default. If you can generate some advantage for yourself, then you may do so.

Consider your target to have AC25; Skill Checks str(+10), dex(0), con(+10), int(-4), wis(0), cha(0); Saving Throws Str +10, Dex +0, Con+10, Int +5, Wis +9, Cha +9;

Damage Immunities Fire, Poison; Bludgeoning, Piercing, and Slashing from Nonmagical Attacks Condition Immunities Charmed, Frightened, Paralyzed, Poisoned Senses Blindsight 120 ft., Passive Perception 10

Since we are talking LV 20 for the purpous of overcomming immunity your weapons may count as magical

You may have one non-combat round of setup outsite the blindsight range of the Tarrasque. Longstride can be cast in advance

What is the highest average charisma skill check a solo character can get, without using magic?

I was building a character that had levels in Feywanderer ranger, that gains Otherworldly Glamour which allows you to add wisdom to charisma checks, and then I noticed Samurai fighters get Elegant Courtier which has the same bonus.

Emboldened by the fact they stack, I started to look for other class features that let you reroll failed intimidation checks or gain advantage.

It made me wonder, what is the highest possible charisma skill check by a solo character?

(This means no spells, or magic items and no outside assistance except by summoned/created creatures, e.g. a familiar using the help action is ok, but a party member using flash of genius is not.).

A average Mark overall for all of one student subjects

Lets say i have a student table , a enlistment table that shows SubjectId and Results for each student how would i get the overall average mark for a student that has more than 3 subjects

Create table  a_Student( StudentId int(5) Not null, StudentForename varchar (30) Not null, StudentSurname varchar (45) Not null,  PRIMARY KEY(StudentId) ); Create table a_Enlistment( StudentId int(5) Not null, SubjectId char(6) Not null, results char (2), primary key (SubjectId,StudentId), foreign key (SubjectId) references a_Subject(SubjectId), foreign key (StudentId) references a_Student(StudentId) );   insert into a_Student (StudentId,StudentForename,StudentSurname) values ("33447","Alan","Burns"), ("33672","Mark","Harrison",);     Insert into a_Enlistment (StudentId,SubjectId,Results) values           ("33447","TMP243","78"),          ("33447","AWD169","45"),          ("33447","IIA887","48"),         ("33672","TMP243","57"),        ("33672","AWD169","67"),       ("33672","IIA887","48"), 

So i want lets say Alans overall mark for his 3 subjects how would i do that? Any help is welcomed thanks a lot