## Calculating the area of star shaped region by four partially overlapping circles

``            I want to calculate the white area enclosed by four circles (as indicated by the arrow). Spacing between the center of circles 'd' and radius is 'r'.            x1^2+y1^2=r^2 and also that (xβd)^2+(yβd)^2=r^2 ``

## Am I correctly calculating the difficulty/XP for this encounter for a 15th-level party of 5 PCs?

I am putting together a campaign and have been experimenting with the guidelines for creating encounters and managing difficulty. I’ve done the math for quite a few encounters at each of the "tier" levels (5th, 11th, 15th) just to get a feel for how it works. One example is below. Does my method look correct?

``15th level party, medium difficulty, 5 PCs  XP Threshold: 5(2800) = 14,000 xp 4 monsters so 2x Encounter Multiplier:  1 fire giant 1(2)(5000 xp) = 10000 xp 1 ogre       1(2)( 450 xp) =   900 xp 2 ettins     2(2)(1100 xp) =  4400 xp                              --------                              15300 xp ``

So a wee bit more than the medium difficulty threshold but still less than the hard difficulty threshold. There are a lot of other factors to take into account when designing encounters and this is just back of the cocktail napkin math. A fire giant figures prominently in the campaign and I’m trying to figure out "when" to bring him in should it come to blows.

## Calculating Modified V5 Dice Probabilities with AnyDice

My game uses 5th edition rules with a house rule where 1s subtract successes and 10s count as two successes. 2s through 5s count as no successes and 6s through 9s count as single successes as normal.

I’d like to compare the specific probability ranges to V5’s normal rules. What function can I use to do so over AnyDice?

## Calculating the critical hits damage [duplicate]

I’m the new person in the D&D and I’ve got a polish version od Player’s Handbook. I’ve got some weird feeling that I do not understand well the Critical Hits mechanics or that paragraph is written in a weird style. Also, Mathew Mercer is saying something strange in one of his video.

One of my players is a 4 level Half-Orc Barbarian, and he uses a great axe (d12). He got funny passive from being the Half-Orc that makes him got one more dice on Critical Hits.

And there we got some problem.

If he rolls natural 20 on the attack test:

A) He has to roll 3d12 and add his strength? I mean that he has the first dice from a great axe, the second from the half-orc passive and the third from the natural 20?

B) He has to roll 4d12 then add his strength? I mean that he has the first dice from a great axe, the second from being half-orc and he has to double it cause he doubles all dices?

C) He has to roll 2d12, double that and add his strength? I mean that he has the first dice from a great axe, the second from the half-orc passive and doubling the damage not the dices? I have this idea cause Matthew is saying in one of his videos: "Critical means the damage dice you double. Roll for damage, double that, and add your modifier."

I know guys, that is a kinda stupid question but I’m starting being GM and after a couple of hours of doing the option "A", I’ve got some feeling that Critical Hits doesn’t matter.

## Calculating Wizard spell casting ability and spell attack bonus

How do you determine the Spellcasting ability and the spell attack bonus? I’ve tried searching for it in the player’s handbook and searched for answers here, but I haven’t found anything.

## 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?

## Calculating caster level when stacking metamagic feats for spell like abilities

Level 6 warlock is able to maximize as well as empower their eldritch blast in separate rounds. If a warlock wanted to stack empower and maximize in single round, how would you calculate required caster level. Also, what would be the earliest level a warlock can cast empowered-maximized eldritch blast in a single round?

## Hep calculating skills and abilities for level 1 Horned Lizard Familiar

Making a level 1 witch with a horned lizard familiar. My witchβs skill ranks are perception, three knowledges, linguistics, perform, spellcraft, and heal. What are the horned lizards racial skill point ranks?

What special abilities does the horned lizard get? The run feat? Camouflage? Puff up? Blood spurt? Whatβs the attack modifier on that?

## Calculating distance on a map

I’m running a campaign in the Sword Coast, and like to provide consistent travel distance and time to my players. As far as I could find, there are no distance charts. And even if there were, they are unlikely to provide all locations (but I might stand corrected!).

A solution could be a piece of software which can open the high resolution Sword Coast map, in which I can draw lines, and which then tells me the length in pixels of the lines, so I could covert that back into miles, and ultimately derive a travel time.

Does anyone know of something to do this in?

Related:

• Travel Chart for the Forgotten Realms

## An efficient way of calculating π(π(p*q)) where p and q are prime

Let p and q be prime numbers and π Euler’s totient function. Is there an efficient way of computing π(π(p*q)) = π(π((p-1)(q-1)), that is not simply based on factoring (p-1) and (q-1)?

Obviously, if p and q do not equal two, (p-1) and (q-1) are even and consequently their prime factorization is entirely different from the prime factorization of p and q. Therefore I assume that no such shortcut exists.

Do I overlook something?