There are two mathematically equivalent ways to think about/remember the technique I am presenting here. Since this question seeks to find a method that makes a DM's work easier and it only works if the DM can remember and understand it I will outline both variations.

# [Number of dice] × [Number of sides+1] + Modifier

The expected damage for any single die is (x+1)/2 where x is the number of sides the die has.

Since we are dealing with critical damage here, that number is always doubled so for a single die it simplifies to (x+1)+modifier damage.

For more dice you simply multiply that number before adding the modifier. Thus, the general rule:

$$[Number Of Dice] \times [NumberOfSides +1] + modifier$$

### Examples

5 (1d6+2):

\$1\times7+2=9\$

23 (3d12+4):

\$3\times13+4=43\$

# [Number of dice] + [Maximum possible damage]^{1}

The previous technique took the form:

\$x \times (y+1) + z\$

Where \$x\$ is the number of dice you are rolling, \$y\$ is the number of sides on the die and \$z\$ is the damage modifier.

If you expand that multiplication you get:

\$xy + x + z\$

which we can then rearrange to be:

\$x + xy + z\$

Notice that \$xy + z\$ is actually equivalent to the maximum damage for the attack. For example, the maximum of \$3d6+4\$ is \$3 \times 6+4\$.

Thus, we can simply express the answer as:

$$[NumberOfDice] + [MaxDamage]$$

### Examples

5 (1d6+2):

\$1+(6+2)=1+8=9\$

23 (3d12+4):

\$3+(36+4)=3+40=43\$

^{1 - This is an elaboration and clarification on the idea that EightAndAHalfTails' answer and Glen_B's answer presented. }

# Hex Damage Applies on Each Attack

As you stated in your question, the description from Hex states:

Until the spell ends, you deal an extra 1d6 necrotic damage to the target when you hit it with an attack.

There is no limit to the number of attacks that you can apply this damage to, thus you can apply it to both attacks that you make with Eldritch Blast (or for both melee attacks if you are Pact of the Blade with the Thirsting Blade invocation)

As a reminder, on page 193 the PHB states:

# Making an Attack

Whether you're striking with a melee weapon, firing a weapon at range, or making an attack roll as part of a spell, an attack has a simple structure.

And for further clarification on page 194 it states:

If there's ever any question about whether something you're doing counts as an attack, the rule is simple: if you're making an attack roll, you're making an attack.

As you are making 2 different attack rolls (one for each Eldritch Blast) these are 2 separate attacks and so you are able to add Hex damage to each of the rolls.

### How the Dice Work

So from the examples that you gave in your question, assuming you hit both times:

- If you roll 19 and 19 on your attack rolls, you will deal 1d10 + 1d6 for each hit (EB damage plus Hex damage), for 2d10 + 2d6 total damage
- If you roll 19 and 20 on your attack rolls (in either order), you will deal 1d10 + 1d6 for the normal hit and 2d10 + 2d6 for the critical hit (doubling all damage dice), for 3d10 + 3d6 total damage
- If you roll 20 and 20 on your attack rolls, you will deal 2d10 + 2d6 for each hit (doubling all damage dice), for 4d10 + 4d6 total damage!

Hope that helps!

## Best Answer

From the PHB (p. 196):

The example given answers your first question perfectly.

For the spider, the secondary damage is from poison, so is not inherently part of the attack. This can be seen by the fact that the damage doesn't depend on the attack roll, but a separate saving throw.

Critical hits represent hitting a vulnerable area. With poison, it doesn't really matter

whereyou are hit.