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View Full Version : Dice, probability and you: A few thoughts on luck and effectiveness



Chaos Jackal
2020-07-08, 12:58 PM
Let me preface with this. This isn’t an article detailing calculations and probabilities. It is simply a collection of thoughts, ideas and experiences.

I see a lot of guides out there who often fail to address probabilities, many misconceptions about high odds and what they can ultimately do, as well as a severe lack of how the dice can affect the social interaction side of the game, and these are the things I hope to expand more upon.

Before I delve any deeper, I have to mention two things. One, these are just opinions. Hopefully still helpful. Two, while nowhere near a munchkin, I’m a player who likes to optimize. This goes for both combat and roleplaying. I don’t just cherry pick my caster spells or use a maul over a greataxe. I also pay attention to small details in narrative or an environment, and I try to analyze situations thoroughly. As you’ll read below, if I’m a perceptive rogue I’d rather play perceptively instead of waiting to be asked to roll Perception.

We all know D&D is a game of luck. We’re simulating battles and interactions through dice rolls, relying on probability and averages to produce a result that will keep the game interesting while giving the encounters some credibility. But probability is a fickle mistress. A bunch of goblins or crossing a river can prove way more of a hassle than one would expect while the BBEG ends up dead in a round and a half due to a paladin rolling two Smite crits. And between these extremes lie a multitude of unexpected circumstances, from rogues failing Stealth checks to barbarians making Intelligence saves. They can spice up fights and provide entertainment, or they can frustrate someone to no end as the d20, the greatest force in the game after the DM, refuses to acknowledge it’s not a d6. The only thing that plays no part in an average is the impossible. The improbable is very much there, and it can often mean the difference between victory and defeat.

With dice rolls being so crucial, character optimization is naturally tailored around reducing the impact of luck. Stats, proficiency modifiers, damage dice, they are the tools the game gives to enhance the aforementioned encounter credibility. +7 rather than +5 on an attack roll won’t save from the natural 1, but it will save from the natural 10. Proficiency in Deception doesn’t convince the shopkeeper a piece of wood is in fact a bar of gold, but it might pass that aquamarine for a sapphire. Shifting the odds in your favor is the primary way to reduce the impact luck can have in your gameplay. But there’s more to D&D than a good roll, and players often seem to forget or ignore that. The very nature of someone’s gameplay can change the number of situations where a dice roll is required. We’re all quick to blame the dice and our bad luck when things go south, and many times we don’t realize how easily that bad luck could have been avoided by simply neutralizing the need for luck, whether it’s combat or social interaction.

Let’s start with combat. This part is primarily about spellcasters, but general guidelines apply to all classes. The heart and soul of D&D, combat is usually the most exciting moment of a session, and the thing that every player who cares even a little about optimization primarily prepares for. But as we well know, there’s much more to a fight than waving sticks. There’s positioning, choice of targets, potential obstacles in the battlefield, magic and things like grappling someone or who the DM decides to attack, all ever-present factors to take into account. And this is the part where risk and reward come into play.

A martial’s risks and the rewards associated with them will usually relate to their choice of target and their position in the field. Focusing on one enemy is usually the preferred choice of action, but what if the majority of enemies present aren’t very threatening? Taking on a few of them at once just with the intent to stall while the rest of the group focuses on the one or two actually dangerous is definitely the preferred course of action, rather than having a bunch of random monsters run around and attack targets with little in the way of AC and HP. Conversely, if the DM doesn’t really have a plan of attack for his monsters, instead having them randomly attack without taking into account proximity of an enemy or the danger they pose, or, worse, if the DM goes full metagaming mode and has a pack of wolves rush the wizard before he even gets a cast off despite half of them provoking AoOs then it’s obvious that stalling tactics are pointless. Generally, the way the DM plays out the encounters is gonna be very important for a martial, particularly someone who wants to try and do the job of a traditional "tank". With taunt-like effects being few and far between, understanding whether or not the DM will decide to hit such a character with a bunch of monsters or whether he’ll chase down the disengaging rogue greatly changes the course of your actions (especially considering that a lot of times what people see as a tank isn't actually doing the role all that well by default).

Let’s look at that rogue for a second. Standing by the side of his sword and board fighter, he attacks and hits the angry monster, getting Sneak Attack damage in. Then, he opts to make an offhand attack as a bonus action instead of using his Cunning Action to disengage. On the monster’s round the monster, which has multiattack, goes for a bite at the fighter while swiping with its tail and claws at the rogue. The rogue has a decent AC between his studded leather and 20 Dex, but the monster rolls a 12 and a 20 with a +5 modifier, hitting on the first attack and critting on the second. The rogue takes a ton of damage, and on the next turn, after he finally disengages, another, smaller monster, with one attack and a +3 attack modifier, takes the AoO from the party’s cleric that it currently fought and goes in for the kill on what it perceives as a weakened target. The attack hits and the rogue falls unconscious.

Now, the rogue can, and likely will, claim that his luck was terrible. After all, he had three attacks hit him, with the first two having a 45% chance to hit and the third having only a 35% chance. While the rogue is certainly down on his luck, his course of action played a big part in his fall. He basically traded in his safety for the chance to do weapon damage one more time. If he hadn’t hit with his first attack and thus hadn’t yet dealt Sneak Attack damage, then the option of attacking instead of disengaging would have had way more merit, given the brunt of a rogue’s damage is Sneak Attack. However, our rogue had already dealt the brunt of his damage, and yet opted to stay in melee as a d8 HD character instead of fighting cautiously, leading to the series of events described above. Probability definitely favored the rogue here, thus making the risk relatively small. However, the reward was even smaller. Without the Dual Wielder feat, the average damage a rogue can do with an offhand is 3.5, assuming he uses a shortsword. The reward is small enough to not outweigh the also small risk. Yes, that attack has a 45% chance to hit, but not being within melee range of a monster already engaged in combat is usually a 0% chance. The rolls theoretically favor the rogue, but there can also be no rolls at all. Why cause luck to play an even bigger role than it already does?

Spellcasters, with their typically wider array of tools, have more to think about. For a spellcaster, positioning and choice of target is also important, but their means of attacking are just as important. A spellcaster doesn’t have the option of attacking with a longsword rather than a maul or going rapier rather than two shortswords… he has way more than that. Shoot a beam? Buff an ally? Make a wall? Paralyze an opponent? Each of these options has the potential to affect the battlefield a lot more than a sword swing. But each of these options also comes with its own risks and rewards. A spellcaster’s spell selection is risk and reward on its own. Spellcasters have a variety of effects. Even in the relatively tamer environment of 5e a spellcaster with enough creativity can wreak havoc with something like Minor Illusion. But as the saying goes, with great power comes great responsibility and a great many ways to mess things up.

Many of a spellcaster’s seemingly most powerful effects allow for one or more saving throws. The potential of a spell can be devastating; however, there exists a possibility of its potential being 0. Hold Person seems very powerful at first glance. But let’s look at it more carefully. For one, it can only be used on humanoids, greatly reducing the number of potential targets right from the start. Then, it requires a Wisdom save. While Wisdom isn’t something that usually comes in spades, it tends to be at least average, or something an enemy might have proficiency in. And to make matters worse, even if the enemy fails the save, it gets another one on its turn. Depending on the initiative order, this can be mildly annoying or very frustrating. So now think of Hold Person again. It has a chance to completely waste your action, alongside a spell slot which, unlike sword swings, is something finite. Then, if it doesn’t do that, it now has a chance to basically have you and the target both waste your actions, as the target uses up his turn to shake off the paralysis. And only after that is it actually the powerful effect it’s supposed to be. You can cast it as a higher level spell later on to target additional enemies, but why cast Hold Person on two opponents when you can cast Hypnotic Pattern on five, for the same spell slot and allowing only one saving throw? Hold Person’s reward is good, but its risk is just too high. Unless the target’s Wisdom is truly pathetic, the odds might be in your favor, but that’s not enough.

Now let’s look at the all-time classic, Fireball. Fireball is a blast spell, so its impact is limited solely to the damage it can do. Fireball deals an average of 28 damage in a decently large area, starting at level 5. By comparison, at level 5, a greatsword martial with the relevant fighting style and max Strength can pull an average of 26.66 damage if their attacks hit, either on one target or divided between two. Of course, Fireball gets a Dexterity saving throw, but even then it does damage, even if it’s halved. Fireball can always have an impact, however small. This usually makes it better than a spell like Hold Person, not necessarily because the effect is stronger but because it’s more reliable. You might not have the impact that you want, but you’ll have an impact. You don’t waste a turn. And there’s many fights where you can’t afford to waste a turn. An enemy might have better Dex than Wis, but depending on how dangerous the fight is and the number of opponents it will often still be better than the chance-to-do-nothing Hold Person.

This goes on for every spell in the game. If it doesn’t involve a saving throw or an attack roll, and has a half-decent effect, it’s usually good. Sleep is arguably the most powerful low level control and among the best spells you can have in half of tier 1. While DM-dependent, illusions can be devastating. Wall of Force is basically broken in every edition. Synaptic Static, while seemingly having low damage, always has an impact, just like Cone of Cold, while simultaneously having a better chance to hit fully (Int is quite the uncommon save) and a nice debuff to go with it if it does. On the other hand, so-called staples like Scorching Ray, the Hold line, or Disintegrate, just won’t cut it. Yes, they can be powerful if they hit, but if they don’t, they waste your turn. 10d6+40 is great, but your save DC can only get so high, and the risk of doing nothing against the enemies you’ll face when Disintegrate becomes available… yeah. Levelling up usually just makes this worse. Save DCs increase, but so do monster saving throws and number of save proficiencies, not to mention Legendary Resistance. In addition, on higher levels fights are often decided within two turns. Spending one of these two turns doing nothing can weigh heavily against you.

Of course, there are things like Banishment, or the aforementioned Hypnotic Pattern, where the reward is powerful enough for you to take the risk. Banishment is often an “I win” button which targets Charisma and gives no repeated saves, with an extra niche against outsiders, while Hypnotic Pattern can simply end a fight with many small mooks more effectively than a Fireball, albeit not as flashily. But usually you can stack the odds however much you want, and indeed, there might be do-or-die situations that call for a save-or-suck spell, but ultimately you’ll find yourself in these situations much less if you don’t depend on save-or-suck spells in the first place. If you opened with a 4th-level Hold Person which was resisted by two of your enemies, including the most powerful one, followed with a Cone of Cold that was again resisted by two enemies, and then tried and failed to Disintegrate the strongest among them, then you might or might not be unlucky depending on their stats and proficiencies, but it doesn’t change the fact that trapping two of them under a Wall of Force and using a defensive spell to avoid getting hit and lose concentration on your Wall was probably a better idea. Blame your bad luck if you must, but think if there was another option first.

Doing your best to avoid adding any more luck in the equation is just as important in social interactions. This, unfortunately, is very DM-dependent; there are DMs who will ask you to roll for nearly everything, DMs that hardly take your actions right before the roll into account, or DMs that do both. But if your DM isn’t roll-happy, and if your actions right before can influence the roll instead of all DCs being determined by a chart, then do your utmost to reduce rolls. Don’t stare blankly at the DM and ask them if you know what’s going on. Don’t ask to roll Insight or Perception on your own. Think on a situation. Voice your thoughts on an issue, be it the secret lore behind an ancient order, or the true intentions of the ambassador. Mention how you carefully keep an eye on that line of bushes, or how your character has encountered a similar phenomenon like the one you’re dealing with in the past.

You’ll still roll, have no doubt about that. You can’t escape the dice forever, so tailoring your character to face the situations they might encounter is still important. But quite often, you can turn a situation on its head by just being a good roleplayer. If you say that you’re watching the path carefully or that you suddenly turn to look behind you rather than waiting for the DM to ask you to roll Perception, you might avoid that roll entirely, or you might end up rolling 10 and still succeed despite your lack of Wisdom and proficiency. If you make a funny or convincing argument while haggling you might avoid the Persuasion roll, instead of just saying “I’ll try to haggle down the price”. Roleplaying in social situations is just as important as weapons and spells in combat. A truly strong character depends on it as well, unless you’re playing a hack-and-slash campaign or adventure. You might not enjoy roleplaying, but it’s not irrelevant to character strength. Not only are you more fun at a table, you’ll also play effectively.

It might sound absolute, or extreme, but remember. The dice are always your enemies. They’re a means for your opponents to escape your attacks and tricks. Plan for them accordingly. Make the best of the situations that ask for that roll. But don’t ask to roll even more.

tKUUNK
2020-07-08, 09:30 PM
Yeah this is good perspective, thanks for taking the time to write it up.

I agree, with the understanding that there's a time and a place to toss those dice and tempt fate.

In your rogue example, if the rogue's bonus action attack has a solid chance to take the big monster out of the fight, maybe it's worth rolling the dice instead of using cunning action to disengage. With an eye on the initiative order to help guide that decision.

And if you're trying to prevent guards from calling for help, you might want to risk a Hold Person instead of casting hypnotic pattern or fireball- things that can draw attention just by being cast. (Although, as you said, why not choose Sleep, if it's on your spell list, or better yet find a less risky way to get the same result...yep!)

Nice post.