## This is a perfectly valid use of Divine Smite and a smite spell

We can see in the description for Divine Smite that the attack must be a melee weapon attack:

Starting at 2nd level, when you hit a creature with a melee weapon attack, you can expend one spell slot to deal radiant damage to the target, in addition to the weapon’s damage. [...]

We don't have any additional restrictions on the use of Divine Smite, other than that we must have a spell slot to expend.

The various Smite spells available at time of writing (Banishing, Blinding, Branding, Searing, Staggering, Thunderous, Wrathful) all begin with a variant of the following:

The [next] time you hit [a creature] with a melee weapon attack...

There is not a restriction saying you cannot combine these two effects. So, given they meet all requirements (a melee weapon attack and a spell slot to expend), a paladin could indeed use both a smite spell and the Divine Smite feature on a single attack.

We can also look in the Sage Advice Compendium for further clarification:

**Can my paladin use a smite spell along with Divine Smite? As in, I cast wrathful smite, hit, then use Divine Smite on the same attack?**

Yes, you can use Divine Smite on the same weapon attack that benefits from a smite spell, such as wrathful smite—as long as the attack you make after casting the smite spell is a melee weapon attack. Divine Smite doesn’t work with any other kind of attack.

While this is certainly powerful, it is also resource-intensive. A low-level paladin choosing to do this might struggle to perform during the rest of the adventuring day.

# 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

Given the example of (2d6)×2 (henceforth referred to as 'Doubled Damage') vs (4d6) (referred to as 'Doubled Dice'):

When you double the damage rolled instead of doubling the dice rolled, you create a more evenly distributed curve. Using either method, you have the best odds of rolling the average damage for the dice you are using but in the doubled damage you are far more likely (16.7%) to roll the average than when rolling double the dice (11.3%).

You can also see in the below diagram that when you double the damage rather than the number of dice rolled, you have a much higher chance of rolling the maximum or minimum damage possible (2.78%) compared to almost no chance at all (0.08%) on doubled dice. Doubling the damage rolled also has the effect of eliminating all possible odd-number results.

The standard deviation from the mean in a doubled damage scenario is 4.83, whereas when you double the dice rolled the std dev is only 3.42 points from the mean. To put this into perspective, it means that when you double the rolled damage you are more likely to land in the range of 14 ± 4.83, whereas when you roll the doubled dice, you are more likely to land in a tighter range of 14 ± 3.42.

What does this mean? The larger the standard deviation, the more distributed your data are. A bigger std dev (relative to the range of the sample) means that your data are more distributed across your sample, while a smaller std dev means you will see a steeper curve, with results more closely grouped in the middle of the data spectrum.

The end result: damage results are more varied by doubling the damage rolled with increased odds of rolling either min or max damage when compared to doubling the number of dice.You can reproduce the following table on anydice.com by inputting:and selecting the default Table view, Normal data options.The differences become more apparent when we graph the numbers together along a curve. Note that there are no yellow nodes on odd numbers — this is because you cannot have an odd-numbered result when doubling the damage (any number multiplied by two results in an even number).

The chart below can be reproduced by using the two anydice functions above and selecting the graph view, normal data options.In this chart, the yellow nodes represent the possible outcomes of Doubled Damage, while the black nodes represent the standard method of Doubled Dice. When compared this way we can see that the odds for rolling any even number increase greatly, and that overall the damage output of Doubled Damage is more evenly distributed (it deviates more from the mean, creating a nice even pyramid-shaped distribution) than that of Doubled Dice (which has a much more normalized bell curve).

One more graph to really send the point home. In this example, we are comparing a simple 1d6 damage critical:

Anydice.com code for this table:From this table, it becomes apparent that your damage result varies greatly when doubling the damage (though the actual number of possible results is cut in half). For each possible result, we have the same odds, as expected — a 1d6 has the same 16.667% chance of turning up any given number, and that doesn't change when we double the results of the 1d6 roll.

On the other hand, it is apparent that rolling Doubled Dice results in a much smaller standard deviation from the mean result of 2d6.

An interesting side note: the distribution for 2d6 is in fact the same as rolling 2d6 and doubling the result — 2d6 has 11 possible outcomes, which is the same number as the possible outcomes of (2d6)×2.