Revisiting 2d10, doubles, extra dice, and degrees of success

In my first post on this topic, I talked about 2d10 as a variant for Dungeons and Dragons, and focused on the ways it interacted with its existing systems. Because of that, I limited how far I used things such as degrees of success. Now that I'm considering, because of the OGL mess, how I would build a system around 2d10, I'm rethinking how I did things in that post, and the subsequent Weal and Woe pools.

Math First

First, let's take a step back and consider how much effect do you get from rolling an extra die (3d10), and then selecting the best or worst two. Let's revisit this table from my Abilities and Skills post:

Odds of rolling different targets with 2d10 at different levels of ability.

As you can see, even with no training a character would usually pass a test with a target number of 10, a character with either a maximum ability modifier or skill training and specialization (which will give a similar result as those with decent Skill Training and a decent ability score) have a good chance of succeeding on a Medium test, and those with all three have a good chance of meeting a target number of 20 at low levels (but those with only one or two of Skill Training, Specialization, or maximum ability modifier become more likely to reach it at higher levels).

Target numbers of 25 or above are basically there to give those who have mastered a skill something more challenging at higher levels. A target of 30 is almost impossible--it should only be attempted at high levels, and adventures shouldn't hinge on successfully making that check. In some ways, 25 and 30 are more useful to show the odds of the most capable character getting one or two extra successes versus DC 20.

So that's what it looks like if you're only rolling two dice. What if you're rolling three and taking the two best. Then, your odds of success look something like this:

Odds of rolling different targets with 3d10 keeping the two best at different levels of ability.

This makes the higher targets of 25 or 30 look more achievable, as low odds basically double (high odds only change incrementally).

What if you're stuck with the two worst?  That looks something like this:

Odds of rolling different targets with 3d10 keeping the two worst at different levels of ability.

Now really high rolls look practically impossible. Most of the odds that were less than 50% before are effectively cut in half. This suggests that target numbers of 25 and even 30 at high levels are something you should only throw at your players when they attempt something ill-considered and you expect them to fail--but you want to give them a chance to do something epic if they succeed.

Weal and Woe, Mostly Woe

So we want the probability shifting that comes from throwing an extra die, but we probably want to call it something different from Weal and Woe, which is what I was using earlier. I suggest that when a player rolls an extra die, you call it a Fortune die, and when the GM rolls the extra die, you call it a Doom die. This applies no matter what circumstance grants it (spells, favorable or unfavorable circumstances, aid from another party member). The reason for this is that I want to keep my Weal and Woe Fortune and Doom Pools as an optional element, and if we have a mechanic called Fortune dice, we can easily add the idea of a Fortune Pool, as the resource from which those Fortune dice come.

We can also give each player character a fortune point, similar to D&D's inspiration. They can gain a Fortune Point whenever they roll doubles, and spend them to roll a Fortune die. Note that unlike the Advantage/Disadvantage, spending a die for Fortune has no effect on whether the DM rolls a Doom die. You merely have to declare you're doing so before the DM discards a die, and then you each roll, and remove a die in the order you roll.

Degrees and Doubles

In my first post introducing the 2d10 mechanic to D&D, I included two mechanics that interacted with one another, doubles and degrees of success. I stipulated that degrees of success only applied to ability checks, while doubles applied to all rolls that would use a d20 in D&D (including attacks and saves), and had to explain how to handle doubles in each situation.

That said, if I'm creating my own system more or less from scratch, I don't have to adapt it to how D&D handles different types of d20 rolls. That allows me to smooth things out more and make it more consistent. So let's adjust things this way: all rolls have degrees of success and failure. This includes attack rolls, saving throws, and ability checks (though since they're all the same, we no longer need to divide them up this way).

So an attack roll can have one, two, three, or more degrees of success, while a saving throw can have one, two, or three degrees of failure.

That also lets us approach high doubles and low doubles differently. A high double increases your degree of success by one, while a low double decreases your degree of success by one. However, universally, degrees of success and failure are every 5 points above or below the target number. Therefore, it may be easier to treat a high double as adding five to your roll, and a low double of subtracting five from your roll. This results in moving you up and down the success ladder the same, and may be easier to remember. (And it's definitely useful for doing opposed rolls, where a double could change who wins.)

We can also use the skill descriptions to describe what various degrees of success mean for different skills, and spell descriptions for what degrees of failure mean for saving throws (it might be useful to take a look at Mutants & Masterminds, which does this already for a lot of its abilities, with certain conditions being stronger versions of other conditions, so that when you fail against an attack that applies a condition, the degree of failure determines which condition applies).

One thing to think about more in-depth is the concept of zero degrees of success, or a Near Miss. In many contexts, this is simply a failure with no additional consequences. You failed to pick the lock, you missed the enemy, etc. But I'd like to encourage GM's to allow it to be a success with consequences, or at a price. This is especially the case for high, almost impossible to achieve target numbers (anything higher than 20 for most parties). If it's very hard for your PCs to reach the target number, there's still a decent chance of almost making it. In that case, it may be worthwhile to let them have it, but at a price.

So here are some ways GMs can use a Near Miss:

• A failure with no additional consequence. You don't convince the king, but you don't offend him either. You don't find the evidence you were looking for, but you can keep looking. You miss the enemy, but assuming he doesn't kill you in the meantime, you can try again next round.
• A partial success. You try to grab the gold, but only get a few coins. You try to catch the falling potions, but only rescue one. In these cases you did part of what you were trying to do, but not all.
• A success, but it takes ten times as long. This is particularly useful in a situation where the character can simply try again. It's less interesting to have the player roll multiple attempts than it is for the GM to just declare that they succeed, but it takes a while. Especially when the GM uses this to increase tension. What would have taken a round on a success instead takes a minute. What would have taken a minute takes ten minutes. What would have taken an hour takes all day. GMs should always present it as a choice: "After a minute of poking at the lock, it's clear this is going to take a while. Are you going to keep at it, knowing that a patrol may come by at any minute?" Then the GM uses a random roll to determine whether the patrol arrives, using their favorite method to determine if a random encounter happens.
• A success with a consequence. You succeed, but something bad happens as well. You get the lock open, but made enough noise to attract a guard in the meantime. You convinced the king that there's a problem, but his solution is not one you like. You avoid the pit trap, but now your party is separated by it with no way to reconnect. In general, you don't want the consequence to be worse than what would have happened with a degree of failure. GMs don't usually need to give the players a choice to use this option.
• A success at a price. You succeed, if you're willing to pay the price. That price may be gold to pay the guard, or a level of Stress, or a valuable item falling from your pack to the jagged rocks below the cliff you're climbing. In this case, the GM should present this as a choice.

Stress

Many games have different pools for different types of injury. Consider for example the Warhammer Age of Sigmar RPG Soulbound. This has Toughness (an HP pool which you recover after every battle), and Wounds (more significant injuries that take time to recover from). D&D doesn't exactly do this, but the exhaustion mechanic (and especially the one introduced in One D&D) gives us an ability to give players conditions that affect their performance and that take time to recover from. Many tables use the exhaustion mechanic to introduce penalties when players lose all their HP and go down and need to be healed to get back on their feet. With the 5e version, that is very punishing.

But I do think I want something along these lines. Let's call it Stress for now. You receive a level of Stress whenever you go down to 0 HP in combat. It can also be the price you pay to turn a Near Miss to a success, or if you fail an important roll (say you're traveling in a hostile environment and fail your Survival check), or it could represent an injury you receive from a trap. For each level of Stress, you subtract 1 from all your rolls, and when you exceed the maximum, you're down for good. This can mean dead, or just collapsed, unable to get up again.

In One D&D the maximum number of exhaustion levels one can reach is equal to 10; after that you die. I think I'd make that something dependent on the character stats. For example, you can make the maximum equal to the character's Fortitude + Will ability modifiers, but you would need a minimum value for players who decide to dump both Fortitude and Will. I would say if you have 0 in an ability score, you can use 1 instead. (So if you have Fortitude of 3 and Will of 0, you'd have 4 Stress Levels.)

Recharging

D&D 4th edition had at-will, encounter, and daily abilities, and encounter abilities would recharge after each battle. As a whole, people didn't like it. But recently, I've played a number of video games with a similar mechanic, such as Chained Echoes and Pillars of Eternity 2. I like how you can go from battle to battle, and only worry about retreating when you gain wounds which you don't recover from quickly. From tabletop games, I'm inspired by the Soulbound Toughness and Wound mechanics mentioned above, and by the spell point mechanic used in Aetaltis, a D&D 5e campaign. In Aetaltis, spell points recharge, and you regain a number of them every hour.

A Stress, wounds, or whatever I decide to call it gives me a more durable mechanic for injury, that comes with a built-in penalty to rolls. So on top of that, I can have a hit point pool that recharges rapidly after a battle. For spell points, I can have those recharge at a rate dependent on Will and class every hour. This will require a smaller maximum number of spell points compared to spell slots. In general, it'll probably be more spells at low levels, and fewer at high levels, with spell points allowing a few high level spells to be cast or a number of low level spells.

I'll talk about my ideas for magic in a later post.

Abilities and Skills

Here, I'm considering how best to design a non-OGL role-playing game. See my other 2d10 posts.

Abilities

Dungeons and Dragons famously has six ability scores: Strength, Dexterity, Constitution, Intelligence, Wisdom, and Charisma. Each ability has a value of between 3 and 18 for humans (originally the result of rolling three six sided dice), and gives a modifier of one for every two points above 10, and a modifier of negative one for every two points below 10.

While this is traditional, it's also old fashioned. If I were to redesign it, I would make the following changes: there is no difference between the ability score and the modifier. Instead, your score is your modifier, and your ability scores go from 0 to 5 (alternatively going below 0 for non-humanoid monsters).

But let's simplify it from six abilities to four. We need a good mix of physical and mental, and of abilities that represent strength and dexterity. So we have an ability for physical strength: Fortitude. And an ability for physical dexterity: Agility. But we also need an ability for mental dexterity: Mind. And finally one for mental strength: Will.

So we have our four abilities. Fortitude is a mixture of Strength and Constitution from D&D. It represents physical toughness and endurance, as well as physical fitness and muscle strength. Agility is most like Dexterity from D&D. It represents flexibility, accuracy, and muscle memory. Meanwhile, Mind is a good match for D&D's intelligence, and maybe the part of Wisdom that relates to noticing things and paying attention. It represents mental adaptability, quickness of thought, reasoning, and recollection. Finally, Will matches for both Charisma and the part of Wisdom that represents willpower. It's force of personality and stubbornness.

When creating your character, players start with 6 points to distribute among their four abilities, and can't put more than 3 in any one. So you could do 3-3-0-0, 3-2-1-0, or 3-1-1-1, and still put a three in your primary stat.

The problem with D&D is that the abilities are not created equal. Almost everyone needs Dexterity (for their armor class), and Constitution for the hit points. But not many characters need Intelligence. Usually you can get by with one specialist for that. And Strength can be dumped by a surprising number of builds, including combat builds relying on Dexterity. For that matter, only one skill depends on Strength. (And none depend on Constitution, but you still need the HP.) But a total of five skills depend on Wisdom.

I'd like to try to balance things out a bit better, with four skills for each ability, for a total of 16. I'd also like to have a few specializations available for each skills, which grant a bonus similar to expertise, but which can be tailored to fit the campaign.

Design Thoughts

Aside from the abilities, I'll need to consider the secondary stats, such as defense and hit points, and how those are derived. Here's my initial thinking:

• Chance to hit depends on Agility, whether done with a bow or a sword or a spear
• Damage depends on Fortitude, whether done with a bow or a sword or a spear
• There may be some exceptions, with significant downsides. A dagger may depend on Agility for both damage and hit chance, but it doesn't do much damage. A firearm or crossbow may not depend on Fortitude for damage, but they have long reload times.
• I base this at least partially on the fact that firing a bow requires a good bit of strength, which isn't reflected in D&D.
• Defense (AC) depends on a combination of Mind and Agility (probably the maximum for most people, but some unarmored fighting styles may let you add these).
• Health (HP) depends on a combination of Fortitude and Will. I'll probably sum these, as I favor a fairly high starting HP.
• Spells can target any of these defenses.
• Spellcasting can depend on Mind, Will, or both. I think it will probably be both for the pure spellcasters (Mind gives accuracy, Will gives damage), but may work differently for half-casters and others who have more stats they need to raise.
• Many D&D skills can be combined. Lore will cover many kinds of knowledge. Investigation, Insight, and Perception may be covered by one Mind skill. Persuasion and Intimidation can be one Influence skill, and Performance and Deception may fall under the same skill. Specialization can give bonuses to certain sub-skills.
• Rather than expertise, we may have the concept of specialization. That grants a +3 to a skill in a specific situation. When the Performance skill is used for a musical instrument, you may have a specialization.  Or a con artist may have specialization to his Performance in weaving a convincing lie. I'm thinking that each background may grant a specialization, as well as a skill.
• I plan to apply degrees of success to everything, including attacks and spells. Getting a higher degree of success does more damage, or has a stronger effect for a spell.
• For weapons, there will be no dice rolls for damage. Instead you add a fixed number between 0 and 5 representing the weapon damage to your Fortitude, and multiply that times your degrees of success to determine how much damage you do.
• I haven't decided whether spells should have the caster roll, or the target roll, or both depending on the spell. When the caster rolls, the more degrees of success, the better for the caster; when the target rolls, the more degrees of failure, the worse for the target.

Skills

So let's summarize the skills I have in mind:

• Fortitude Skills
• Athletics - Running, jumping, swimming, climbing, all the things athletes do.
• Labor - Farming, mining, digging pits, anything requiring long hours of backbreaking labor. From clearing collapsed tunnels to building a fortified camp, you'd be surprised how often this comes up in adventuring. And when you're not adventuring, there's always a need for strong backs.
• Survival - Weathering harsh conditions, trekking long distances, and rousing from little sleep to do it again the next day. Includes finding shelter and water as you travel.
• Steering - Sailing a ship, driving a vehicle, or riding a horse all require physical work to steer the vehicle or animal where you want to go.
• Agility Skills
• Finesse - From pick-pocketing to swapping the Gem of Doom for a fake while no one's looking, anything that requires fast hands falls under Finesse.
• Stealth - Moving quietly, keeping to shadows, and slipping through crowds unseen. All of these fall under stealth.
• Acrobatics - From balancing on a wire, to tumbling, to parkour, sometimes quick reflexes save the day.
• Crafting - Making potions, magic items, armor, weapons, food, baskets. They all require careful handling and exacting detail.
• Mind Skills
• Mechanics - Locks, traps, the strange gnomish contraption that looks like it's about to explode. Understanding how things work often allows you to take it apart, and maybe even put it back together.
• Observation - Noticing that you're being watched, spotting the secret door, hearing the beating heart under the floorboards, reading the expression of people and the tells of animals, all this falls under observation.
• Lore - You read. Therefore you know stuff. Maybe even a lot of stuff.
• Arcana - You're sensitive to the flow of magic, able to understand its currents and figure out what it does.
• Will Skills
• Concentration - Remaining focused despite distractions, and people trying to stab you--and sometimes succeeding.
• Influence - Someone said the core of diplomacy is to talk softly and carry a big stick. Whether it's threats or promises, you're good at getting what you want. Applies even when dealing with animals and others who don't share your language.
• Performance - Dancing, singing, playing an instrument, impersonating someone, or weaving a convincing lie. It's all about rejecting another person's reality and replacing it with your own. And if you're convincing enough, you can bring them along for the ride.
• Profession - One might think that having a professional job like scribing or shopkeeping would require one to have a sharp mind. One would be wrong. The primary requirement of such a job is to be able to keep focused, remain polite, and endure the petty slights of customers, bosses, and colleagues, day in and day out.

Specializations

In addition to skills, players also have specializations. Specializations come from both the class, and from the background. For example, a bard could have a Music specialization in Performance, or someone with the farmer background could have a Farming specialization in Labor. Specializations cover specialized use of skills, and provide a flat +3 on top of the skill bonus. The specialization itself describes what conditions that additional bonus applies in, but ultimately it's up to the DM whether you can use your specialization bonus.

Most of these specializations are described in the backgrounds and class features which grant them, but the DM may allow additional ones. Here are some possibilities to give some ideas:

• Athletics
• Swimming
• Climbing
• Running
• Jumping
• Labor
• Farming
• Mining
• Building
• Digging
• Survival
• Arctic
• Desert
• Mountains
• Forests
• Plains
• Cities
• Steering
• Sailing
• Rowing
• Riding
• Piloting
• Finesse
• Pickpocketing
• Legerdemain
• Stealth
• Nature
• Darkness
• Crowds
• Acrobatics
• Balance
• Stunts
• Traversal
• Crafting
• Alchemy
• Smithing
• Cooking
• Mechanics
• Locks
• Traps
• Steampunk
• Vehicles
• Observation
• Empathy
• Animal empathy
• Tracking
• Secrets
• Alertness
• Lore
• Medicine
• Religion
• History
• Nature
• Military
• Arcana
• Spirits
• Magic Items
• Curses
• Blessings
• Concentration
• Spellcasting
• Influence
• Animal Handling
• Oratory
• Intimidation
• Performance
• Dancing
• Music
• Acting
• Deception
• Profession
• Scribing
• Shopkeeping
• Innkeeping
• Trading

The Math

The fifth edition of D&D uses something called bounded accuracy. This limits how high rolls can get by keeping limits on the modifier, since the ability modifier maxes out at 5, and the proficiency modifier maxes out at 6, for a total of +11. Sort of. Then there's expertise, that doubles your proficiency modifier, spells like Bless and Guidance, that add 1d4, and Bardic inspiration, that adds d12. There's also the rogue's Reliable Talent, that causes any roll on the die below 10 to count as a 10. This means, at a minimum, a 10th level rogue with Reliable Talent and Expertise and Guidance and Bardic Inspiration, gets a total 25. On average, they would get about 35. That's a bit outside of bounded accuracy.

How would I control this? For one, I wouldn't grant expertise. I'll instead use specialization that will grant a flat +3 that doesn't scale with level. Second, abilities that would normally grant an extra die will instead grant an extra d10 roll that can replace one of the d10 rolls. (From the Weal pool, if we're using that. I'll probably make the pools an optional variant. If you're not using the pools, this is only limited by the class feature.) So while those will increase the average, they won't increase the maximum.

Otherwise, I'll scale similarly to how 5th edition does. Characters will receive bonuses to their abilities from their ancestry, background, and culture, but the maximum at 1st level for any ability will be 4. Until 10th level, the maximum will be 5, and until 20th, it will be 6. At 20th level, the maximum will increase to 7.

For the bonus from the skill, I think it will work similarly to proficiency bonuses in 5e, scaling with level. At first I was going to use the same scaling as D&D, 1 + level/4 rounded up. However, since I'm starting with a slightly higher ability modifiers, which increase to 7 rather than being limited to 5, and since my average rolls are higher by half (and my ~65% probability is about two points higher), maybe I'll just do level/4 rounded up. So skills will max out at 5, while ability modifier maxes out at 7.

Now, let's do some math, to determine what is Hard, Medium, and Easy for different characters. As a starting point, I consider something where someone has a 75% chance of success to be Easy, where someone has a 50% chance of success to be Medium, and where someone has a 25% chance to be Hard. Now with 2d10, we won't match exactly those numbers, but let's try to get relatively close. Players have a 55% chance to roll an 11 or higher, so we'll define that as our Medium. They have a 79% chance to roll an 8 or higher, but a 2% chance to roll a double 4 or double 5, which would effectively make those values below 8. So an 8 or higher will represent 77% chance of success. Meanwhile, a 2d10 has a a 21% chance of rolling a 15 or higher, +2% for the chance to roll a double 6 or double 7. So a 15 is a hard 2d10 roll, with a 23% chance of success.

So Easy, Medium, and Hard will represent a 77%, 55%, and 23% chance of success. Now let's define our characters:

• Novice: +0 to the roll. No matter the level, no character's trained in everything, and most character's will have one dump stat that remains at 0. When that character is first to make this roll, that's what he does it with.
• Average: +skill bonus to the roll. An Average character may have the skill, but doesn't necessarily have the ability score bonus.
• Gifted: +max ability modifier to the roll. A Gifted character has a maxed out ability modifier, but no training in the skill. Often, he'll be the best choice to make the roll.
• Skilled: +skill bonus + specialization bonus to the roll. Everyone has some specializations, but that doesn't mean that they're naturally talented with the ability. This assumes no bonus from the modifier, but Skilled can also represent someone with skill training and a decent modifier without specialization.
• Adept: +skill bonus + max ability modifier. Some things you're just good at. The Adept has both the max ability modifier and the skill bonus, but doesn't have specialization. You won't always have an adept for every skill, but you'll count yourself lucky when you do.
• Master: +skill bonus + specialization + max ability modifier. Then again, some people have it all. This is the best a character can get without relying on the fortune of Weal dice.

So first, let's consider what sort of rolls are Easy, Medium, and Hard for each character ability level. I selected levels 1, 5, 10, 15, and 20, since that covers are the skill bonuses and ability score maximums.

This gives us some idea of how easy it is to accomplish something. Even at level 1, what's Hard for the Novice character is Easy for the Master, and Medium for the Adept. A target number of 30, however, never ceases to be Hard, even for the Master. Such a task shouldn't be attempted without, at least, some favorable circumstances to help. And a 25 doesn't become Medium for the Master until level 20, and is still hard for the Adept.

In general, I think what's Medium for the Average character should be Easy for the Adept and should be Easy for the Master to achieve with an extra degree of success, and what's Hard for the Average character should be Medium for the Adept and should be Easy for the Master. I think this achieves that.

Where do attack rolls fit on this? Somewhere between Adept (characters are always skilled with their weapons, and usually max their attack roll as much as possible), and Master (as higher level characters tend to pick up magic weapons, that can give them a bonus close to the specialization bonus). Still, it's best not to design with Masters in mind, either for skill rolls or for enemies.

That does bring us to our design space for challenges. In general, I believe that an Easy target number should be Medium for the Novice character and Easy for the Average character, while a Medium target number is Hard for the Novice character and Medium for the Gifted character and Easy for the Expert, while a Hard target number is Hard for the Skilled and Medium for the Master.

Note that the standard 10/15/20 fits this fairly well for that level of difficulty. You can continue using that all the way up to high levels without leaving anyone behind, though it will start to become trivial to the Master, and pretty easy for the Adept. One way to handle that is to add higher levels of difficulty. Here's what I propose:

• Target of 10: Easy Difficulty. Anyone can do it, and most people have a decent chance.
• Target of 15: Medium Difficulty. It takes some luck for the novice to achieve, but every party should have someone with a decent chance of accomplishing it.
• Target of 20: Hard Difficulty. A novice can pull it off. Barely. Most parties will have difficulty accomplishing it.
• Target of 25: Expert Difficulty. If you have an Adept in your party, you might be able to pull it off, but it won't be easy.
• Target of 30: Specialist Difficulty. Only the very best in the world can pull it off, and even they fail more often than they succeed.

Note that something that is Hard difficulty is Expert difficulty to achieve with an extra degree of success, and Specialist difficulty to achieve with two degrees of success. Setting the target of 30 means that your party probably won't manage it. But setting it to Hard, means they have a small chance of getting three degrees of success. Here are the probabilities for each of the character ability levels to accomplish these difficulties at levels 1, 5, 10, 15, and 20.

Sometimes, though, you want to know what will actually be hard for your party. For that, I suggest balancing around Easy for Average, Medium for Gifted, and Hard for Skilled. I personally find this useful for skill challenges, so I know what my players are generally able to handle.

• Levels 1-4: 9 (Easy)/15 (Medium)/19 (Hard)
• Levels 5-8: 10 (Easy)/16 (Medium)/20 (Hard)
• Levels 9-12: 11 (Easy)/16 (Medium)/21 (Hard)
• Levels 13-16: 12 (Easy)/17 (Medium)/22 (Hard)
• Levels 17-20: 13 (Easy)/18 (Medium)/23 (Hard) 

This results in the following for the percentage odds of success (including the possibility of doubles, assuming I calculated them correctly):

Easy tasks remain Easy for the Average character (though they eventually approach Hard for the Novice character), Medium tasks fairly Hard for the Average character, and Medium to Easy for the Adept, and Hard tasks are Hard to Medium for the Adept, and approximately Medium to Easy for the Master.

Update (1/19/2023): Figuring out the math is of course an iterative process. I've created a new version based on two different assumptions: one where a Gifted (max ability, no skill) and Skilled (skill and specialization, no ability modifier) represent a more likely highest ability in the party, and one where the standard 10/15/20/25/30 are used throughout the game. 

Dungeons and Dragons with 2d10

If you've played Dungeons and Dragons, then you know that the basic dice mechanic is a d20. You roll a d20, add a modifier, and compare that result to a  Difficulty Class, or DC, for a skill, or the Armor Class (AC)  of an enemy, to determine whether you succeed or fail.

There are three types of d20 rolls in D&D: attack rolls (attacking an enemy with a weapon, your bare hands, or certain spells), saving throws (to prevent spells and other bad effects from happening to you), and ability checks (everything else where you want to accomplish something and there's a chance of failure). Rolling a natural 1 (a 1 shows on the die) or a natural 20 (a 20 shows on the die) has a special effect only for attack rolls: natural 1 always misses, and natural 20 always hits and does extra damage. There are a few other places it matters (halfling luck allows you to reroll any natural 1), but many D&D tables houserule additional effects of a natural 1 and natural 20.

The d20 gives a nice, flat probability distribution. You're as likely to roll a 1 as a 20 as a 10. For that reason, it's exceptionally swingy. In many situations, this doesn't matter. If a lock has a  DC of 13 and a rogue has +5 with his thieving tools, he has a 65% chance of succeeding. If he rolls a 1 or a 20, he usually doesn't succeed or fail more.

Where that swinginess can produce weird results is with opposed rolls. Let's say your skinny rogue is wrestling  with an ogre. The rogue has a -1 on his grappling check, while the ogre gets +4. You would think that the rogue wouldn't have a chance. But because of D&D's famous swinginess, he gets a 26% chance of outwrestling the ogre. That's a lot considering there's a +5 difference.

Many games reduce the swinginess by using dice pools. For example, the Powered by the Apocalypse game engine uses a 2d6 dice pool. GURPS and AGE use a 3d6. 3d6 gives a nice bell curve with results from 3 to 18, centered on 10.5. The problem is that with a standard deviation of 2.96, 67% of the rolls will end up between 8 and 13. The chance of rolling an 18 or a 3 is only 0.5%. In short, it's too narrow a distribution. If you wanted to use 3d6, you'd have to adjust all the bonuses and DCs to make it work.

However, a much more reasonable result can be achieved with a 2d10 roll. For comparison:

Probability distribution curves for 1d20, 3d6, and 2d10. Courtesy of AnyDice.

While the 2d10 has a sharp peak at 11 (slightly off from the 10.5 average of the d20 and the 3d6), it's not as sharp as the 3d6. This means it's more likely to roll higher or lower.

The best way to see this is not a probability distribution chart, but looking for the chance to roll at least a number, as shown below.

Probability of rolling at least # for 1d20, 3d6, and 2d10. Courtesy of AnyDice.

In D&D, a difficult check is one where you need at least a 15 to succeed. Players are usually cautious about attempting rolls that require a higher roll than that. With a d20, the odds of succeeding against a 15 is 30%, while with 3d6, it's less than 10%. With a 2d10, the odds are 21%, which I consider a decent compromise.

Now, let's consider the odds of rolling an 8 or higher. This is generally the to-hit number needed to hit an enemy with average AC for the players' level. Under 1d20, the odds of hitting are 65%. With 2d10, it's 79%, and with 3d6 it's 84%. Here we see that 2d10 and 3d6 are much closer to each other than to d20, but a higher average to-hit chance for players is actually an argument for this system--very little is as disappointing as missing in combat.

So let's see how we would do this conversion.

Simple Conversion

Considering all this, how do we implement a 2d10 system in D&D? Simple, any time you roll a 1d20, you substitute a 2d10 instead. If you are doing something that gives you a reroll or extra roll (advantage, disadvantage, luck), you roll 2d10 twice, and take the one (higher or lower) that fits the requirement.

But what about natural 1s and natural 20s? You can't roll a natural 1 anymore, and you roll a natural 20 only 1% of the time. It would be disappointing for critical hits to happen so seldom.

For this we introduce the idea of doubles. If you roll the same number on both d10s, and they are five or less, this is a low double. Count that as critical miss for an attack roll. If you roll the same number on both d10s and they are six or more, that is a high double, count that as a critical hit for attack rolls. Importantly, a natural 1 and natural 20 are not an automatic failure or success except for attack rolls in combat. 

We can also use low doubles for abilities that let you re-roll when you roll a natural 1 (for example, halfling luck). Instead substitute low double for natural 1 in that rule. But a low double isn't a 1. If you roll two fives, that's a 10, and it's more of a gamble to reroll that than to reroll an actual 1 any place but for attack rolls, where two fives are an automatic failure.

In addition to this simple conversion, there are some optional rules you can add.

Optional rule 1: Doubles and Degrees of Success

Many DMs allow for degrees of success and failure for ability checks. If your result (roll + modifier) is 5 more than the DC, you are more successful than if you just met the DC, and if your result is below 5 less than the DC, you fail more. A table of degrees of success would look like this.

Roll range	Degrees of Success
DC+10 <= result	3 degrees of success
DC+5 <= result < DC+10	2 degrees of success
DC <= result < DC+5	1 degree of success
DC-5 <= result < DC	0 degrees of success
DC-10 <= result < DC-5	1 degree of failure
result < DC-10	2 degrees of failure

What degrees of success or failure means depends on the DM and the context of the roll. Here are some possibilities:

• For any sort of knowledge or information check (Arcana, Nature, Survival, Perception, History, Religion, Investigation), the higher your degree of success, the more information you obtain. However, more degrees of failure might actually make it harder for others, as you trample over important clues or confuse your party members with your misinformation.
• With three degrees of success, you don't just climb a wall, you clamber up it at full speed and give anyone following advantage on their climbs.
• With two degrees of success, you climb up at half speed as usual, but those who follow you have advantage on their climb checks.
• One degree of success is just success. 
• Zero degrees of success is a failure, but it's a near miss. The DM can allow you to try again without penalty, or even allow you to succeed for a price: it takes longer, or you alert a guard, or you gain a level of exhaustion, or you convince the guard to let you through but you need to bribe him.
• With one degree of failure, you not just fail, you lose ground, so if you can try again at all, it's going to be harder. You fell if you were trying to climb a wall, or you insulted the person you were trying to persuade.
• With two degrees of failure, the task just became impossible, and you're going to have to try another way. You jammed the lock and can't pick it now, or the pipe you were trying to climb collapsed.

Importantly, not all ability checks need to have degrees of success or failure. Some can be a simple pass/fail, no extra benefits or consequences for more or less degrees of success. But degrees of success or failure give us options, many of which DMs already use a lot of the time. 

With a 2d10 system, degrees of success become more significant, as you're less likely to roll really low or really high, so more degrees is more extraordinary. Importantly, with degrees of success, we can apply high and low doubles to ability checks without turning a double into an automatic success or failure. With this option, a high double increases the degree of success by one, while a low double decreases the degree of success by one. This is equivalent to adding five for a high double and subtracting five for a low double.

We can even circle back to attack rolls, and apply degrees of success to them. In this case, a result  5 higher or lower than the AC does not grant an extra degree of success or failure, but rolling a high or low double does. A critical hit requires two degrees of success--you need to roll a high double, but you also need your roll plus modifier to be above or equal to the AC. A high double plus modifier that's below the AC hits, but doesn't critical. Likewise, a low double can turn a hit into a miss. As an option, you can also use 1 degree of failure (a low double plus modifier that is also below the AC) as a fumble. Note that there are generally no fumble rules in fifth edition D&D, so use that with caution. (If I used it, I'd grant an opportunity attack to enemies when a character fumbles.)

Finally, we can apply this to saves as well. A high double automatically saves, a low double automatically fails. If we really want to, we can turn a low double that is also below the DC into a critical failure (take double damage from the spell or effect) and a high double that is also above the DC into a critical success (take no damage if you would have taken half), but again, use with caution. The  rogue's or monk's Evasion ability with this particular variant is equivalent to one extra degree of success for Dexterity saves. 

When we allow high double and low double to both be meaningful, keeping the higher roll or the lower roll with advantage or disadvantage can become confused. For the sake of simplicity, the higher degree of success is the roll to keep with advantage, or discard with disadvantage. In most cases, a high double beats a higher roll beats a lower roll beats a low double. But there are exceptions: a double 5 is better than a 1 and a 2 for ability checks, but not for attack rolls and saves, where a double 5 automatically fails but a 3 plus a high modifier might succeed.

Optional rule 2: Extra Dice

In the simple conversion, we attempted to keep advantage and disadvantage the same--just roll 2d10 again. Let's revisit that. What if, instead of rolling 2d10 twice, we rolled 3d10 and picked the two dice we wanted for advantage, or discarded the highest die roll for disadvantage?

Probability of rolling at least a value for advantage and disadvantage variants, ignoring doubles. Courtesy of AnyDice.

You'll notice right away that for the probability to roll at least a value, the difference between 3d10 pick the highest or lowest differs very little from the best of two 2d10 rolls. The difference between those advantage calculations and the regular d20 advantage is also pretty small. There is a marked difference between disadvantage with 2d10 and disadvantage with d20, though, for complex mathematical reasons that I won't go into because I haven't figured them out yet.

What's the reason we might want to use an extra d10 instead of more 2d10 rolls? For one, it makes advantage and disadvantage easier--always choose the high double, never choose the low double with advantage. For example, if you rolled two 5s and a 1, a 1 and a 5 is always better than a low double 5, no matter the type of roll (6 > 10-5). For disadvantage, it's the inverse, though I find it simpler to discard the highest and not worry about doubles--players are less likely to feel cheated if that happens to remove a low double or result in a high double. 

It also makes double and triple advantage or disadvantage easier to adjudicate--just add more d10s. For the most part, double and triple advantage don't exist in Fifth edition, but there are exceptions, such as the Elven Accuracy feat and the Lucky feat. For Elven Accuracy, roll 4d10 (advantage + 1d10) and choose two d10s. For every luck point spent on a roll, you can add another d10, but you always choose two d10s.

But what if you have disadvantage and use a luck point? Lucky doesn't have to cancel disadvantage in this case. Instead you roll 3d10 for disadvantage, then 1d10 for the luck point, remove the highest d10, and pick two of the remaining d10s. This way lucky no longer converts disadvantage into super advantage, but it can still help to mitigate it.

Finally, if more than one person can reasonably use the Help action to help another in a roll, then you can add a d10 for each person helping.

However, for features like halfling luck or a Divination Wizard's Portent, where you replace a roll rather than take the highest or lowest roll, you roll a fresh 2d10 instead of adding a d10. (RAW, you don't keep any advantage or disadvantage that the roll would have.)

Optional rule 3: Inspiration

Finally, what about Inspiration? Here, I favor borrowing from the most recent One D&D playtest (these are playtest rules for the next version of D&D). In this version, you can spend Inspiration to grant yourself advantage after rolling. If you rolled with disadvantage initially, you don't just cancel the disadvantage--you convert it to advantage. This works whether you roll 2d10 twice (pick the best rather than the worst) or 3d10 (don't discard the highest before picking two dice). Otherwise, you roll an extra d10 or roll 2d10 again. But you can't use inspiration if you already have advantage.

The thing I would change is that instead of gaining inspiration when you roll a 1, you gain inspiration after the final result of your roll is a double--either high or low. (I say "after the final result" to make it clear that you can't use the inspiration you gain on the same roll that grants it to you.) It represents both determination to do better after stumbling, and riding the high of success. (This also means that a feature like halfling luck doesn't make it almost impossible to gain inspiration from die rolls.)

Summary

If you apply all these optional rules, the end result would look something like this:

• High double: Both d10s have the same value of 6 or higher.
• Low double: Both d10s have the same value of 5 or lower.
• Ability Check: roll 2d10 + modifier (high double adds 5, low double subtracts 5)
• Ability Check Degrees of Success/Failure: For every 5 above or below the DC, you get an additional degree of success or failure, respectively. What this means depends on context.
• Saving Throw: roll 2d10 + modifier (high double always succeeds, low double always fails)
• Attack roll: roll 2d10 + modifier (high double always hits, crits if would hit anyway, low double always misses)
• Advantage: roll 3d10, pick two (it's always advantageous to pick high doubles and avoid low doubles, otherwise pick the highest two d10s)
• Disadvantage: roll 3d10, drop the highest.
• Inspiration: Gained when roll any double final result. Can be spent after roll to turn into advantage (even if initially rolled with disadvantage), roll an extra d10 if necessary
• Luck point: Roll an extra d10, pick two d10s. (If initially rolled with disadvantage, still remove the highest roll before picking two.)

My group has decided to playtest these rules. We're playing the Icewind Dale: Rime of the Frostmaiden module, so I'm interested in seeing what effect this has when no changes are made to the module to adjust for this.