## dnd 5th – How to calculate the dice and bonuses for attack rolls and damage rolls?

All the information presented below is gathered and derived from the rules set out in chapter 9: Fighting, from the player manual for the 5th D&D edition, from page 189. Any additional rules (or effects, like spells) cite their origin.

There are four parts that add up:

• For most melee weapons, this is strength; for most ranged weapons, it is dexterity; for attack spells, it's your ability to cast spells (usually Intelligence, Wisdom or Charisma)
• The notable exception to this rule is the Delicacy , which, when found on a weapon, allows you to explicitly choose between dexterity or strength when you choose to attack, and therefore use the modifier you have chosen to attack and damage rolls. In the main game, this property only appears on melee weapons.
• In addition, the weapons launched typically count as melee weapons, even if they can be used from a distance; check the weapon's statblock for possible exceptions to this rule.
• Another notable exception is the special class features or spells that allow alternative ability modifiers. For example, a druid cast Shillelagh (Player's Manual, 275) gains the ability to use wisdom for both attack and damage, instead of strength or dexterity, but only on certain weapons.
• Likewise, a Hexblade warlock (Xanathar & # 39; s Guide to Everything, 55) uses charisma instead of force or dexterity for his attack attacks and damage, provided that the weapon that they use matches the requirements of their boss.
• This applies if you have mastered the weapon. As simple as that. For martial classes like fighters, barbarians or paladins, this means just about every weapon in the game, which means they always get their skill bonus. For other classes, you need to check the skills that their class bestows.
• There are also, theoretically, "exotic weapons" in which no class gains skill by default, and for which a character would not receive their skill bonus unless they gain skill by certain means; however, the base game does not contain such weapons.
• For spells, you almost always have mastery of spell casting and therefore earn this bonus. There may be a few marginal cases where this might not be true, but they are rare and deserve to be mentioned only as a curiosity.
• Special modifiers on the weapon itself
• Some magic weapons grant bonuses to attack roll, damage roll, or both. A +1 weapon (DMG, 213), for example, gives a +1 bonus to both rolls.
• Buffs / Other Effects
• The spell Bless (PHB, 219), for example, adds a d4 roll to any attack roll from the target.

So, for example, a level 5 hunter brandishing a +1 rapier (has the Delicacy , with a strength score of 16 and a dexterity of 18, would have the following bonus for their attack roll:

• Capacity modifier: +3 if they use Force, or +4 if they use Dexterity
• Skill: Fighters acquire Rapier skills, so +3 for a level 5 character
• Magic weapon: The weapon is a +1 rapier, so +1.
• Total: +7 with Strength; +8 with dexterity
• Same as above: Strength for melee, Dexterity for distance, Either for weapons that have the Delicacy property, Intelligence / Wisdom / Charisma for the features that allow you to replace this modifier with a different statistic.
• Spells do DO NOT Earn this damage bonus unless the character has a specific characteristic that allows their spells to benefit, such as the Evocation Assistant (PHB, 117) or the Scary explosion Function of warlock (PHB, 110); or if the spell says so specifically, as with Green flame blade (Sword Coast Adventurer & # 39; s Guide, 143) by specifically saying that you are allowed to add your spellcast modifier to the damage caused by the spell.
• Special modifiers
• Some magic weapons grant bonuses to the damage roll, attack roll, or both. A +1 weapon (DMG, 213), for example, gives a +1 bonus to both rolls.
• Buffs / Other Effects
• For example, the spell Divine Favor (PHB, 234) allows the target to add 1d4 radiant damage to all of its damage rolls produced by weapon attacks.

So using the Fighter example above, assuming they took the Duel Fighting style (which gives a +2 bonus to damage rolls when a character does not handle more than one weapon and only handles this weapon in one hand), their damage bonus would be:

• Capacity modifier: +3 if they use Force, or +4 if they use Dexterity
• Magic weapon: +1
• Buffs / Other Effects: the Duel Combat style adds +2 to damage rolls for one-handed weapons if the character doesn't handle another weapon, so +2
• Total: +6 for strength; +7 for dexterity

Note that for damage, jurisdiction has not been explicitly added. Skill is generally not added to damage rolls, unless a feature specifically says so.

In addition, it is important to remember that with the Finesse weapons, the fighter has the choice of which modifier to use, but he must use the same modifier for attack and defense. Thus, they could not, for example, choose to use Force for the Attack roll and Dexterity for the Damage roll.

• Level 5 Sorcerer's Throw Lightning bolt, Intelligence 18
• Attack roll: 1d20 + 4 (Intelligence) + 3 (Skill) == 1d20 + 7
• Damage Roll: 2d10 (Firebolt)
• Launch Level 10 Evocation Wizard Lightning bolt, Intelligence 20
• Attack roll: 1d20 + 5 (Intelligence) + 4 (Skill) == 1d20 + 9
• Damage Roll: 2d10 (Firebolt) + 5 (Intelligence, Reinforced evocation (PHB, 117))
• Level 13 thief brandishing a long sword, dexterity 20, strength 10
• Attack roll: 1d20 + 0 (Strength) + 0 (Non-skill) == 1d20
• Damage roll: 1d8 (or 1d10 if you use two hands) + 0 (Strength) == 1d8 or 1d10
• Level 13 thief brandishing a rapier, Dexterity 20, Strength 10
• Attack roll: 1d20 + 5 (dexterity) + 5 (skill) == 1d20 + 10
• Damage roll: 1d8 + 5 (dexterity) + 7d6 (stealth attack for a weapon of finesse and having an adjacent ally) == 1d8 + 5 + 7d6

## trigonometry – How to calculate C (horizontal shift) for a sin function?

I write code to calculate each value that constitutes a sinusoidal function.

I need to calculate C. How do I do this?

``````func A(min: Int, max: Int) -> Double {
return Double((max-min)/2)
}
func B(min: Int, max: Int) -> Double {
return Double(Double(2*3.1415)/Double(max-min))
}
func C(min: Int, max: Int) -> Double {
return ?
}
func D(min: Int, max: Int) -> Double {
return Double((max+min)/2)
}
``````

## geometry – How to calculate the positions of the vertices of icosahedrons in spherical coordinates?

The locations of the vertices of a regular icosahedron can be
described using spherical coordinates, for example as latitude and
longitude. If two peaks are taken to be north and south
poles (latitude $$pm90 °$$), then the other ten vertices are at latitude
$$pm arctan ( frac12) approx pm26.57 °$$. These ten peaks are regularly spaced
longitudes ($$36 °$$ apart), alternating between north and south latitudes.

I understand the first and last parts. I understand having summits at latitude $$pm90 °$$. To understand also to put the other summits to longitudes $$36 °$$ apart, because there are 5 vertices on each of the pentagonal pyramids ($$360 div 10 = 36$$). What I don't understand is why latitudes are at $$pm arctan ( frac12) approx pm26.57 °$$.

Looking at an icosahedron from the side, it certainly looks as the middle section forms a 2: 1 rectangle (depending on the orientation). I'm having trouble proving it mathematically, however.

My question is, how did they get to $$pm arctan ( frac12) approx pm26.57 °$$? How is it derived?

## How to calculate the probability of choosing numbers K among N chosen from a probability distribution whose sum is greater than S?

I work with data sets that are histograms of numbers.
As an example of a

``````1: 4,989 occurrences
2: 1,156 occurrences
3: 285 occurrences
4: 58 occurrences
5: 9 occurrences
6: 4 occurrences
TOTAL: 6500
``````

for example. What is the probability of choosing 8 numbers (1-6) with this probability distribution and making a sum of 33 or more?

On my 1st choice, I can choose a 1 (with a probability of 4989/6500). I can then choose a 6 (with a chance of 4/6500), then a 4, then a 1, then 2, then a 1. So, that would sum up to (1 + 6 + 4 + 1 + 2 + 1) 14 How often do I make 33 or more?

## how to calculate the area of ​​an island

I need to make a program that allows me to calculate the area of ​​an island.
To make the perimeter I divided the island into several parts and I made several interpolations, but to make the surface I have no idea because I do not know how to take it into account heights.
can someone help me?
Thank you

## in PHP how to calculate the full uncompressed public key from a short 02/03 pub key?

in PHP, how to create the full public key from a compressed key?

my test key is

and the uncompressed one is
36b6fbcb60b5b3d4f1551ac45e5ffc4936466e7d98f6c7c0ec736539f74691a6

can this be done via openssl?

thanks for any helpful response !!

## Calculate the discriminant and the conductor of an elliptical curve using magma

To calculate the minimum discrimination and the conductor of an elliptical curve using magma for example this elliptic curve, we use this command

E: = EllipticCurve ((0,8,0,48,0));

E;

Elliptical curve defined by y ^ 2 = x ^ 3 + 8 * x ^ 2 + 48 * x on the rational field

F: = MinimalModel (E);

F;

Elliptical curve defined by y ^ 2 = x ^ 3 – x ^ 2 + 2 * x – 2 on the rational field

D: = Discriminant (F);

N: = conductor (E);

My quastion is how to calculate the discriminant and the conductor when the curve has a variable coefficient for example this elliptical curve

$$y ^ 2 = x (x-a) (x-D ^ {p} zeta ^ {k})$$
Or $$a, D$$ are integers and $$zeta ^ {k}$$ is the k-th power of unity

## How to calculate DA and PA website?

How to calculate DA and PA website?

1. ## How to calculate DA and PA website?

How to calculate DA and PA website?

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## st.statistics – How to calculate the mode if all the values ​​are unique values?

(2795.9579999999996, 3447.288, 1068,495, 673.02, 4064,463, 2762,046, 3754,335, 4058,9055000000003, 4544,568, 3438,7275000000004, 1261,605, 904,485, 3646,149 , 981.4350000000001, 1285.14, 4051.5735, 829.125, 2553.48, 1710.09, 2469.0599999999995, 337.125, 3620.2725, 1500.015, 2610.162, 3430.8689999999997, 772.8)

What will be the mode of the above list of values?

Python stats.mode () of the Scipy module giving 337.125 as mode.

Help me in this
Thank you

## shaders – Calculate the exponent in a spotlight equation from the angle of a cone

As I mentioned in the comment, raising a number to an exponent will not make the result null unless it was already zero at the start. (At least not in real numbers of infinite precision. We could try to exploit the floating point precision limits here, but I think it is both more complicated and less efficient than the alternatives we have)

Thus, even if the increase in the exponent makes the shiny part of the cone narrower and narrower, there are still non-zero values ​​well in the dark part. All the way 90 ° from the direction of the light, actually (again, reducing the digital accuracy at the moment).

Since you are rendering in a high dynamic range, it is difficult to choose a cutoff value "dark enough" so that it has no effect on the rendering, even if your exposure is extremely high. . We could become super conservative, but then you treat your cone as wider than necessary most of the time, which reduces the savings you get from slaughter. Or we could try to shift our cutoff based on our exposure settings, but again – too complex, and we can do better!

Since you say you like your distance attenuation function as it is, let's keep that unchanged. We will simply replace this line:

``````lightAmnt *= pow(max(dot(-surfaceToLightVector, lightDir), 0.0f), exponentConstant);
``````

(Note that I changed the name of your variable – the tutorial calls it "light in pixels" but it really points from the surface pixel to the light! So let's name it in a way who is do not back 😉)

First of all, we will note that the inner term is only the cosine of our angle to the axis of light:

``````float cosine = dot(-surfaceToLightVector, lightDir);
``````

In our desired cone corner, which reaches a minimum value that we can calculate on our CPU, and pass as a uniform:

``````float minCosine = Math.Cos(spotlightAngleLimitRadians);
``````

So now we can remap the range of `(minCosine, 1)` in the range (0, 1):

``````float angleFalloff = max((cosine - minCosine), 0.0f) / (1.0f - minCosine);
``````

(If you want, you can pre-calculate the inverse of the denominator and pass it as another uniform so that this division becomes a cheaper pixel multiplication).

You are now guaranteed that the brightness of the projector will reach zero at this limit angle. But you can still use a power function to shape the attenuation curve a bit as you like – here the exponent is arbitrary, we don't count on it to reach a specific angle width, we are just listening to watch this point.

``````lightAmnt *= pow(angleFalloff, exponentConstant);
``````