Theorycraft question double the dice rolled vs double the die roll for critical hit

[jk7275]

In D&D I been in groups that when someone rolled a natural 20 you double whatever the die result is but on occasion I seen groups where you double the amount of dice rolled.

I am curious if anyone done any theory craft on comparing the two ways.

[Altair_the_Vexed]

In D&D I been in groups that when someone rolled a natural 20 you double whatever the die result is but on occasion I seen groups where you double the amount of dice rolled.

I am curious if anyone done any theory craft on comparing the two ways.

When you double your result you will only ever get even numbers, and you will get a flat distribution over time - that is you have an equal chance of getting each number. Example: roll 1d6 x2, and you will get 2, 4, 6, 8, 10, 12 with equal probability.

On the other hand, if you roll 2d6, you get odd and even numbers, and you have more probability of getting the middle numbers in the distribution - there are more ways to get a 7 than there are to get a 2 (two 1s) or a 12 (two 6s).

[Cealocanth]

It shouldn't be hard to analyze how the results differ, but just be aware, I'm by no means an expert on probability.

I'll be using anydice.com to make bell curves.

Alrighty. So let's consider the damage of a 5th level barbarian with a greastword and no rage: 2d6. I picked this class because it's fairly middle of the range, and 2d6 has the most well-known bell curve thanks to non-RPG dice games like craps. The basic damage distribution looks like this, with 7 being the average and most common damage roll.



Assuming you're trying to hit a monster with an AC of 12, this will be your damage output in 87.5% of hits, and 95% of attack rolls, ignoring a miss. A crit is the rest. This is the result the rest of the time assuming you simply double your damage:



And here is the result for 4d6.



So there is a very noticeable difference here. They both have the same average damage, but 4d6 is much more heavily weighted towards the center of the bell curve. Technically they are very similar. In both systems, half the time you roll a crit, you will roll between 12 and 16 damage. Here are the traits that are unique to each system:

2*2d6

• Cannot roll odd numbers
• Result will always be higher than if you had rolled 2d6 alone.
• May feel less rewarding to a player if you're playing on an actual tabletop.
• More predictable amounts of damage.

4d6

• Can roll anywhere from 4 to 24 damage.
• Much more likely to roll damage in the middle of the curve.
• May feel more rewarding because people like to roll handfulls of dice.
• May feel disappointing when you roll a critical hit and deal 4 points of damage.

So they're slightly different, but for the main mechanics of the game they won't make all that much a difference between each other. Unless you run by homebrewed rules, the 4d6 one is actually the mechanic already in place in default 5e. In that way, simply doubling your damage could be considered a nerf or a buff depending on whether you think a small bell curve is a good thing.

[Altair_the_Vexed]

...

So there is a very noticeable difference here. They both have the same average damage, but 4d6 is much more heavily weighted towards the center of the bell curve. Technically they are very similar. In both systems, half the time you roll a crit, you will roll between 12 and 16 damage. Here are the traits that are unique to each system:

2*2d6

• Cannot roll odd numbers
• Result will always be higher than if you had rolled 2d6 alone.
• May feel less rewarding to a player if you're playing on an actual tabletop.
• More predictable amounts of damage.

4d6

• Can roll anywhere from 4 to 24 damage.
• Much more likely to roll damage in the middle of the curve.
• May feel more rewarding because people like to roll handfulls of dice.
• May feel disappointing when you roll a critical hit and deal 4 points of damage.

So they're slightly different, but for the main mechanics of the game they won't make all that much a difference between each other. Unless you run by homebrewed rules, the 4d6 one is actually the mechanic already in place in default 5e. In that way, simply doubling your damage could be considered a nerf or a buff depending on whether you think a small bell curve is a good thing.

Most of what you said there is great and very helpful, but I feel that I have to jump in and dispute your suggestion that the damage is more predictable by doubling the result than by doubling the dice rolled. Sorry

When you roll more dice, you get more average results. That's what the bell curve is showing. The big bulge in the middle of the curve is you getting more results in that average middle area. The more dice you roll, the more likely your result will be in the average middle of the bell curve. So it's more likely you'll get an average result - that seems more predictable to me.

When you simply double the result, you get an equal chance of getting any of the possible results - this seems far less predictable to me.

[Pex]

Of the people I've played with in any D&D system, every time someone wanted to double the roll for a crit it's because they didn't want to roll so many dice since it took too long to roll them and add up the numbers. For everyone else, including me, our way eventually won out because it is a lot of fun to roll lots of dice.

I think it's aesthetics. Spellcasters often get to roll lots of dice. Iconic Fireball is a lot of d6s. Warriors roll one die with the great sword exception. They need a type of magic weapon to get an extra d6. When a crit happens the sensation to have the opportunity to roll more dice is a big deal. It feels like a more powerful hit. In 5E add in rolling more dice for a critical hit on sneak attack, smites, maneuvers, it's a shining moment of glorious power.

[Tinkerer]

My players definitely have tended to prefer the doubling of the rolled value as they would rather have a higher chance of max damage (with the corresponding higher chance of low damage) than have a stronger chance of having a middling value. Doubling the value is much swingier than doubling the dice as pointed out above. But I just let players choose which they are going to use when using a system where that comes into play.

[Jay R]

It depends on the situation. Consider the barbarian described above. If his foe currently has 20 hit points left, doubling the 2d6 will kill him in one shot 1/6 of the time, but rolling 4d6 will kill him in one shot about 5.4% of the time. Similarly, if you need 9 hp or better, you'll get in 83.3% with 2d6 doubles, but 94.6% of the time with 4d6.

So if you need an above average roll, 2d6 doubled is better. If you need a lower roll, then 4d6 is better.

[Telok]

As the numbers of dice increase the x2 dice method will more and more resemble a max damage roll from the normal amount of dice. It's not obvious if you're sticking to two or four dice, but additional dice push thenumbers towards a 'crit = max normal damage roll' paradigm.

As always, fewer dice equals more variance while more dice equals more consistency.

[jk7275]

Oh I forgot to mention one variant when you double the dice you max out half the dice. If a weapon does a d8 instead of rolling 2d8 you roll a d8+8 instead of rolling 4d6 you roll 2d6+12

Has anyone had experience with something like this?

[PhoenixPhyre]

Oh I forgot to mention one variant when you double the dice you max out half the dice. If a weapon does a d8 instead of rolling 2d8 you roll a d8+8 instead of rolling 4d6 you roll 2d6+12

Has anyone had experience with something like this?

I want to say 4e D&D did that, plus some weapons did more on a crit.

[Pex]

I want to say 4e D&D did that, plus some weapons did more on a crit.

I think 4E was automax damage, nothing additional.

[Dimers]

4e: your base damage is maxed including bonuses like Sneak Attack, about 99% of magical weapons add rolled dice, and "high crit" weapons (mostly axes and picks) add another weapon-sized die roll per tier of play.

[Bogwoppit]

Doubling is more random (you aren't changing the probability from the base die roll, just multiplying it), rolling more dice is more average (you're more likely to get the middling results).
The more dice you roll, the more pronounced your bell curve will be - there are way more chances of getting the middle results than there are of getting your outliers.
That means minimum and maximum results are rare, but average results are common.

Whatever works best for you and your group, do that.

[Necroticplague]

In D&D I been in groups that when someone rolled a natural 20 you double whatever the die result is but on occasion I seen groups where you double the amount of dice rolled.

I am curious if anyone done any theory craft on comparing the two ways.

Since everything I'm going to say was already said, I'd just like to note that in 3rd edition, the latter is what one is technically supposed to do.

A critical hit means that you roll your damage more than once, with all your usual bonuses, and add the rolls together.

To the best of my understanding, 5e uses the same rule, though 4e's is the simpler 'max damage', with most enchanted weapons adding some extra dice.

[PhoenixPhyre]

To the best of my understanding, 5e uses the same rule, though 4e's is the simpler 'max damage', with most enchanted weapons adding some extra dice.

The difference with 3e and 5e is in the static modifiers--that quote leads me to believe that the modifiers get doubled in 3e. In 5e, only the dice are rolled twice, the static part doesn't change.

3e: 1d8 + 2 --> 2d8 + 4
5e: 1d8 + 2 --> 2d8 + 2

I could be wrong about 3e though.

[Grod_The_Giant]

The difference with 3e and 5e is in the static modifiers--that quote leads me to believe that the modifiers get doubled in 3e. In 5e, only the dice are rolled twice, the static part doesn't change.

3e: 1d8 + 2 --> 2d8 + 4
5e: 1d8 + 2 --> 2d8 + 2

I could be wrong about 3e though.

This--this cam throw off the math significantly, depending on how your damage bonuses are presented. The 5e Barbarian's +2 rage damage boost contributes less to 5e "roll dice twice" crits than the Ranger's +1d6 hunter's mark.

[Chronos]

In 3.x, any static bonuses (like from strength or a +n weapon) get doubled, but any extra dice (like from a flaming weapon or Sneak Attack) do not. In 5e, it's the reverse: All dice (including Sneak Attack, flaming weapons, etc.) get doubled, but static bonuses do not.

There are also some abilities like the barbarian's Brutal Critical, which add one additional weapon damage die to a crit. Note that this is literally one die, not the weapon's normal damage, so a greataxe gives an extra d12, while a greatsword only gives one extra d6.

[wumpus]

One thing you have to remember is that typically criticals introduce a multiple into the damage rolls that typically are designed around adding additional pluses as you level. Optimizing in such circles tends to focus on doing what ever it takes to grab the multiple (even if it is only *1.1 or so).

Dungeons and Dragons Online often fell into this trap. Originally the kopesh had an advantage with criticals that made up for a lower base damage. As power creep flowed on, kopeshes became literally the only [main hand] weapon anyone would carry and often used in both hands (and basically lasted until two weapon fighting was nerfed into the ground). Thanks to dev turnover they also kept making this mistake: held mobs were instantly hit, suddenly making carrying to picks ideal and the infamously over powered [epic] sword of shadows (all examples are almost certainly long gone, but I'm sure they've had similar failures since).

[Tanarii]

Doubling damage from dice rolled you're more likely to get max damage or close to max. But your also more likely to get the minimum. Crits will be more wild.

Rolling twice the number of dice you're less likely to get min damage or close to min. But you're also less likely to get the minimum maximum. Crits will be more consistent.

Do your players want a better chance of getting a max critical at the cost of a better chance of getting the min, or do they want more consistent criticals? (Conversely, which do they want for Crits against them?)

[Chronos]

Mechanically speaking, the players should prefer the more consistent result in both cases. In most cases, the party is favored to win a fight (since they're expected to win multiple fights per day, repeatedly, enough times in a row to eventually get to high level). More consistency makes the already-likely event even more likely. Less consistency makes the less-likely event more likely.

That said, players and/or characters don't necessarily have that same outlook. A lot of people like taking chances (that's why there's a highly profitable gambling industry, after all). So some will favor the less-consistent outcome even though, in some sense, they "shouldn't".