Dice and Math!

Aug 1, 2021

The main reason we switched from the classic polyhedrons to our new dice for Aspect Prime was that it allowed us to easily do in real-time what otherwise would have required a spreadsheet. The dice automatically do the math so the Players and Guide can create dynamic abilities in real-time. Today we'll discuss how that is possible.

Don't panic! We'll put the super mathy stuff in these italic blocks, feel free to skip those bits, they are just the math proofs.

For those who are not familiar with the Aspect Prime dice, first we will describe how they work. Feel free to skip ahead to the Why Aspect Prime Dice section if you are already familiar with how the dice system works.

There are four kinds of dice in Aspect Prime. The 6-sided blue Add (or A) dice, The 8-sided purple Balanced (or B) dice, the 10-sided red Critical or Crit (or C) dice, and the pictogram Oracle die.

The A, B, and C dice are the combat dice and the ones both players and the Guide use. The Oracle die… we will discuss in another post.

### Dice Pools and Notation

Skills are used to determine results of character action. Every skill, whether Death, Charm, Transform, or Entertain, each has its own dice pool.

Dice are notated in Aspect Prime materials with just their letters: A, B, and C. So a dice pool of AABC is two Add dice (the blue 6 sided), one Balanced die (the purple 8 sided), and one Crit die (the red 10 sided).

### Modifying Your Dice Pools

A key part of what makes Aspect Prime so fluid is the ability to quickly modify your dice pools in meaningful ways. You might be making your pool stronger because you spent an Arcane Component, you got some assistance from an ally, or you’re calling in some Divine Favor.

You might be weakening a pool because a foe has moved further out of range, you were Nullified, or you just want to target a larger area.

In any case, you have choices as to how you make these changes.

Upgrading Dice: +A -> B -> C

For each upgrade, you can choose one of these three options:

• +A add another Add die to the pool
• A -> B convert an Add die to a Balanced die
• B -> C convert a Balanced die to a Crit die

Downgrading Dice: -A <- B <- C

For each downgrade, you can choose one of these three options:

• B <- C convert a Crit die to a Balanced die
• A <- B convert a Balanced die to an Add die
• -A discard an Add die from the pool

Don’t have enough dice to downgrade? No worries, you will always roll at least one Add die, even if your total downgrades and upgrades leave you with 0 or fewer dice.

### Success, Edge, and Crits

Aspect Prime Dice have three kinds of symbols: Success, Edge, and Crits.

Success are the slashes. The more success you roll, the greater your chance of succeeding.

Edge is the dots. They improve your general situation without specifically contributing to the success of this roll.

Crits are the C shapes. These can be spent for powerful boons. Each of the combat roles has a Crit use unique to that role. You can also gain more ways to use them through talents.

Now that you have a general understanding of the dice system, let us answer:

### Why Aspect Prime Dice?

We've been talking about these dice for more than a year now, but we never talked in depth about WHY. What is it about these dice? And what do we mean about improving the math? Here are some reasons:

• Rolling multiple dice is just more fun
• Counting is faster than adding
• Single roll resolution and work delegation
• We can scale rolls in both quantity and quality
• Upgrading a die vs adding a die is similar in value
• Lots of little reasons

We'll address each of these in order in more detail. Let's start with:

### Rolling multiple dice is just fun!

Grabbing a handful of dice and rolling them FEELS just so satisfying. The clatter as they all hit the table is lovely. Rolling stats, a fireball, or sneak attack in D&D is always fun. But adding 15d8 together after rolling them can be tedious. Which brings us to:

### Counting is faster than adding!

With Aspect Prime dice, you're just counting and reporting the numbers. 4 Success, 2 Edge. No adding of multiple 2 digit numbers, no summing piles of 1 digit numbers. Just counting.

This makes it a lot easier for players of all ages and skill levels not only to play but to also run the game. We've had 7 year olds running adventures with Aspect Prime with ease. And speaking of making the game smoother, the Aspect Prime dice allow for:

### Single roll resolution and work delegation

By only requiring a single roll for any action, we speed up the action. Roll, count, here is the total. Did it succeed? Yes? Did I meet the Edge target? Yeah? Here's what I'm going to use that Edge for...

While we do have to subtract the target's defense when dealing damage, that's math delegated to the target, not the active participant.

The Player tells the Guide "Neera hits the two nearest goblins with her Flame Whip for a 7,2". The Guide says if it hits and then subtracts each goblins' defense to figure out how much damage it took. Meanwhile, the action keeps going.

There are multiple people at the table! Being able to delegate out bits of the work of playing helps streamlines the game nicely.

### We can scale in both quality and quantity.

In order to expose the ability for players to modify powers on the fly, we needed a smooth upgrading and downgrading system for the combat rolls. We wanted to be able to both scale accuracy and potential impact.

With a two-roll system you could get this by scaling the to-hit roll as well as the damage roll separately (which is what we did with Aspect in 2011). However, we wanted a single roll. The Aspect Prime Combat Dice do this neatly with upgrading by quantity or quality.

When upgrading your dice pool you can either add A dice or upgrade dice to B or Cs. Adding A dice increases your quantity, upgrading dice increases the quality. A dice give you more Edge per upgrade, while the Bs and Cs give you more Success per upgrade.

So when your ally passes two upgrades to you or you get Savvy upgrades against a foe you've pinned up against the balcony, you can choose whether or not you want to use that advantage to get risky and wild with more A dice or refined and accurate with a higher quality roll.

And we can do this because:

### Upgrading a die vs Adding a die is similar in value

There are advantages and disadvantages to both and so they are somewhat equal in value. Let's take a closer look at how the dice compare:

Upgrading a die (A to B to C) is going to give you more accuracy AND give you more average success.

The A dice have a 66% chance to roll no success. Going from an A die to a B die is going from a 66% chance to miss to a 25% chance to get no success. Going from a B to C is going from 25% to a 10% chance. For reference, 3 A dice have a 29.6% chance to miss.
Going from an A die to a B gives on average .625 more success. Adding an A die is on average 0.5 success, so upgrading is just more success. Going from a B to C adds another .575 success AND a 10% chance for a Crit.

Adding an A die is going to give you more Edge AND give you a higher max potential roll.

The A dice add an average of 0.833 Edge. Upgrading from an A to B only increases by another 0.167 Edge. Going from a B to C you actually lose an average of 0.2 Edge, so have even less average Edge than with just an A die. The max Edge rolled on an A or B die is 3. This goes down to 2 on a C die.
Adding an A die gives you a potential of 2 more Success. Going from an A to a B doesn't increase that max, but does mean you could potentially roll 2 Success AND 2 Edge on a single roll (12.5% of the time), though two A dice could potentially roll a 2,3 which is slightly better (but only 5.56% of the time). Going from a B to a C gives you the potential of rolling 3 Success or 3 Success and a Crit.
So three A dice COULD roll 6 Success, it just is not as likely. One C die has a 20% to roll a 3S or 3S+Crit. Three A dice have a 28.95% chance to roll a 3S or greater, and probably with some bonus Edge. However, a C die has only 10% chance to roll ZERO Successes, while three As will roll Zero Success 29.6% of the time.

Different dice are worth different average amounts of Success. In all it looks like this:

• A dice are worth 0.500 Success total, so 0.500 per upgrade.
• B dice are worth 1.125 Success total, so 0.563 per upgrade.
• C dice are worth 1.700 Success total, so 0.567 per upgrade.

We value Successes at 1 and Edge at 0.5 when we do the balancing, so if you compare the total average value of each die including both Success AND Edge, they look like this:

• A dice are worth 0.917 total, so 0.917 per upgrade.
• B dice are worth 1.625 total, so 0.813 per upgrade.
• C dice are worth 2.300 total, so 0.767 per upgrade.

People generally prefer upgrades even though they are on average lower in value. That's because upgrades give consistency and more Success. Success means winning now, and Edge means delayed Success through upgrades, stalling enemies, lowering enemy defenses, and reducing incoming damage.

Players can choose if they want consistent results or high risk and reward.

### Lots of Little Reasons

There are numerous other little perks to using these dice, some of which were intentional, some were not.

The upgrading and downgrading mechanic is fun

Grabbing dice and then swapping them around to get the right set for your roll is interesting and fun. You get to make quick decisions that will impact your roll. When downgrading, do you toss an A die to keep as much quality as possible, or risk going with more lower quality dice?

We can easily take into account three factors

In Aspect Prime, we build your die pools with three factors. Your base stats (Dexterity, Genius, Appeal, etc), the associated Skill Ranks (representing training you've undergone), and your Gear. Any one of these can give you more dice, but having all three is what gets you the more refined C dice.

Honestly we could do a whole blog post on the Three Factors and how they impact dice, defenses, etc.

These dice stop faster than d12s and d20s

Yeah this one we sorta noticed after we started using them. It is pretty handy in minimizing how many dice end up on the floor during a game.

These dice scale right at high level

So because the C dice are so consistent, adding more of them doesn't make higher levels more swingy. You will be getting a lot more Crits, but that is intended (and one of the reasons we switched to d10s for Crit dice rather than the d6s we used at first).

The scaling of stats follows the scaling of average die rolls. For example, the Save roll vs the Save target for (non-Controller) Heroes at the same grade is always between a 41.88% and 47.08% success rate.

Easy to learn

The Aspect Dice are a nice balance of simple and deep.

• Players only have to learn about 3 die types.
• There's only one rolling mechanic.
• There are potentially deep decisions, but it is hard to choose wrong.

### In Closing

We started Aspect Prime with some specific goals.

• Nothing was sacred. We certainly tried to do this with pre-existing dice, but once we tried these, it was clear nothing else came close.
• Intuitive to play. Once you play a session, upgrading and downgrading is quick and easy.
• Unlimited possibilities. This mechanic allows us to do things on the fly with no math that we could only do with algebra before.
• Balance. We fine-tuned the character progression and the dice so they work together.
• Fun! With fluid and interesting conflict resolution we get out of the way to let you tell your stories.

Aspect Prime dice do all the math so you don't have to. So grab a fistful and get playing!

BONUS MATH!
You really waded through all of that?
Just for you as a bonus, I'm going to paste in the math analysis comparing each die to each other die. The two upper charts compare the dice based on how much Edge or Success they generate, the last chart compares them all on total value (valuing Edge at 0.5, Success at 1, and Crit at 2).
I spent a lot of time fiddling with the numbers on this chart to get them right, so now you can see the final data.

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