Are d20 Future HP comparable to regular old D&D 3.5 HP?

So, for research reasons, I am interested in the explosive yield of the SRD’s Hellball with its 40d6 damage over a 40′ radius. However, I have come up with two wildly disparate results based on the path taken, so I believe there’s a logical issue somewhere, but my math pointed me at an odd result, namely that d20 Future uses a different "scale" of hit point than a regular fantasy D&D 3.5e game would. Is this correct, or have I gone awry somewhere?

Path 1: conversion-by-damage-dice

As pointed out by Hey I Can Chan in an answer to a similar question, the Nuclear Missile from d20 Future, with its said-to-be-1MT warhead, does 16d8 damage, which is roughly equivalent to 21d6 according to his translation of the damage dice. Extrapolating linearly from this datapoint puts us at a Hellball yield of ~2MT, which is certainly hellish enough!

Path 2: conversion-by-effective-radius

However, to try to cross-check this answer, I took the 40′ damage radius provided by Hellball, mapped it to the "nothing survives" fireball radius of a nuclear warhead, and took the NUKEMAP for a spin. However, even with a surface blast from the tiny 20ton Davy Crockett, I get a fireball radius of 20m, or over 60′; getting a smaller fireball than that requires going to a 10-15ton yield, although model uncertainties become limiting at this small scale.

Of course, if you try to plug the Path 1 answer of 2MT into NUKEMAP, you get a far larger fireball of about a mile wide. Furthermore, 16d8 of raw energy damage sounds like a lot…but in the context of anywhere-close-to-upper-level D&D 3.5 characters, even with no saving throw, resists, or SR, the 128 maximum damage it produces is quite tankable. For example, the character that prompted this inquiry has 220HP with only their gear warding them, and still manages 112HP stark naked.

As a result, I am sitting here wondering if I’m barking up the wrong tree somewhere.

How to determine if an animal is a familiar or a regular beast?

As a player (or DM) might use a familiar as a spy, are there ways, magical or otherwise to detect that a cat is a familiar, or just a house cat?

I’ve read the answer to Are familiars considered magical for effects like detect magic? and agree with the accepted answer that they are not. So what might be other methods for exposing the nature of the creature in front of you?

And I mean short of killing it to see if it disappears 😉

Does Elemental Wild Shape work like regular Wild Shape?

A Druid of the Circle of the Moon gets a feature called Elemental Wild Shape which allows them to transform into elementals. I couldn’t find anywhere that said one way or the other, do the usual restrictions of Wild Shape apply to Elemental Wild Shape? For example, can a Druid cast spells while shapeshifted into an elemental?

If not, the Beast Spells feature allows a Druid to cast spells while shapeshifted, but specifically mentions beast forms. Can a Druid with the Beast Spells feature cast spells while in elemental form?

How to add a goal in Google analytics with regular expression such as

I want to add Goal in Google Analytics with the same URL twice with a different regular expression such as 

these are on the same page with different tabs. So how I track user go which tab and other go where because google analytics just track my checkout page, not #shiiping and #payment

Why metamagic feats for spell-like abilities that Warlocks use are so much stronger than regular metamagic feats at early levels?

Warlock is able to stack maximize and empower spell like abilities as early as level 6 without increasing effective caster level, which is not true for maximize/empower spell feat (for Sorcerers and Wizards)

Warlock is able to maximize and empower their magic items with that boost their eldritch blast such as gloves of eldritch admixture, which adds 4d6 to their total damage, but it doesn’t hold true for regular metamagic feats.

How come there is such a power gap between metamagic feats for spell vs spell like abilities?

Automatic-Dodge vs. Regular Dodge Bonus

I’ve been consulting a few RIFTS and Palladium system forums online to try and figure out exactly how the Automatic Dodge system in the games work and have been rather unsuccessful. So I’m turning to the RPG stack to try and come up with a legitimate explanation for the ability and its mechanics.

Automatic dodge is an ability conferred by certain Hand to hand skills, classes such as Juicer, super powers such as Extraordinary Physical Prowess, Super speed, etc. that confers the ability to dodge without using up one of your melee actions for the round.

There are other dodge bonuses in the game systems that confer similar bonuses to dodging. It doesn’t state anywhere in any book I’ve read in the Palladium system whether or not the dodge bonuses from hand to hand, or other skills can be added to automatic dodge bonuses to determine if an attack is dodged.

So my question is thus:

Can Automatic-Dodge Bonuses and Dodge Bonuses added together to determine whether or not an attack is evaded without using up a melee action, and where if any can I find the rules to support said answer?

A regular language derived from another

This is similar to a previous question I asked, but doesn’t seem aminable to the same technique. Given a regular language $ A$ , show the following language is regular: $ $ \{x|\exists y \; |y| = 2^{|x|} and \; xy \in A\} $ $

I’m aware of the notion of regularity preserving functions, and that it would suffice to show that $ f(x) = 2^x$ satisfies the property that for an ultimately periodic set $ U$ , $ f^{-1}(U) = \{m|f(m) \in U\}$ is ultimately periodic. I’m struggling to $ f$ has this property, but the book from which this comes implies a solution not using this is possible. It appears to be looking for a construction.

I can see that by repeated application of the idea behind the Pumping Lemma, if $ A$ has DFL with $ k$ states, that for any $ x$ with $ |x| \geq k$ then $ $ \exists y \; |y| = 2^{|x|} and \; xy \in A\ \implies \exists y \; |y| \leq k \; and \; xy \in A\ $ $

But this doesn’t give anything going in the opposite direction, that shows that some suitably short $ y$ guarantees the existence of a $ y$ of the required length.

Any help in solving this, or hint at how to progress would be very helpful.

Can this language be called regular?

Recently, I was facing some problems in effectively proving the following :

Consider the alphabet Σ ={0,1,2,…,9,#}, and the language of strings of the form x#y#z, where x,y and z are strings of digit such that when viewed as numbers, satisfy the mathematical equation x+y=z.

Is this language regular and why ?

I was trying to apply the Pumping Lemma, but am unsure of how to complete the proof. Could anyone please help ?