# Dark Peaks: Deep Math

Welcome to Dark Peaks: Deep Math, where we go into the nitty-gritty details of the mathematics behind some of the Dark Peaks mechanics. Before reading this, check out our review on Dark Peaks: Deep Maw! We go into how some of these mechanics function in our original review.

## Definitions

**Level Dice**: also called LD are which dice the players will use during their expedition. The deeper they go into the Maw, the more dangerous it is, which increases the Level Dice. Increasing the LD, changes the difficulties of the rolls, and requires characters to become more powerful before they proceed. The Level Dice levels are d4, d6, d8, d10, and d12.

**Skill Check**: When you roll a skill check, you roll the LD, and add your stat. Pretty straight forward. This can also me modified with Risk Dice (See Below)

**Difficulty**: Having multiple Dice Levels means that there are multiple difficulty scales.

**Stat Boundaries**: Each of the primary stats must have a minimum of 1. Once two of these stats (or 3 weapon stats) meet or exceed the maximum value of the LD, you can no longer gain experience in adventures with that LD.

**Risk Dice**: These are dice that can be added to the roll. This die will be the same as the LD. However, if the Risk Dice is below a certain value, you automatically fail, regardless of the total value of the check.

## Regular Skill Checks

Based on the Stat boundaries we set up, here are the rules we created:

- 1 is the absolute minimum
- 1 less than the maximum Level Die is a High value for stats
- Low and medium values will be marked ⅓ and ⅔ of the way between the High and Minimum values.

We get some interesting values based on this.The following image shows the chances of success based on the Level Die, and the stat value. When a cell is highlighted in green, then it’s automatically a success. There is no point in rolling. When a cell is in red, the roll is impossible without using a Risk Die.

And… Wow. That’s a lot of green. Here we can glean quite a bit. Let’s take a specific look at the first table (D4 Difficulty) The base value that each character starts out with in stats is 2. This means by default, every character can pass an easy d4 LD check, without ever rolling. OK, so these values can be reduced through something like injury, but even at that, an easy check has a 75% chance of success. While this does even out with the D12 further on, the odds of automatic success are too great. There is little incentive to ever use Risk Dice, unless you have a really low stat.

Looking down to the d6 LD makes this even more problematic. Especially when you consider the advancement rules. A value of 3 will *still* automatically succeed on any checks that aren’t Hard or more difficult. If the players so chose, at the d4 LD adventure they could do the following, within the rules.

- Advance 2 of their weapons skills to a value of 5+
- Advance 1 Stat to 5+
- Raise all remaining stats & skills to 3

Or alternatively something like

- Raise 1 Stat to 12
- Raise all stats & skills to 3

Then, when they’re ready to move on, advance a weapon skill, or stat to the LD value of 4, and in this case, every single one of their skills and weapons would be able to pass any check with a difficulty of less than 5. Which in this case would be Easy and Medium. The 5 chosen skills that they brought to 5 would only be in danger when the difficulty is “Almost Impossible”.

## Our Thoughts

To me, this brings 3 thoughts to mind:

- The difficulty span does not extend far enough for almost impossible
- The difficulties are not balanced between successes and failures between tables
- Additional restrictions must be put in place for capping experience.

For the first two, it’s really just a shift in the numbers. By expanding from the 4 difficulties of “Easy, Medium, Hard, and Almost Impossible” into 6 difficulties, you get to see how well balanced this game is. A simple change in scope resolves a lot of the issues when you take a look at the gradient.

I would recommend these difficulties. However, with this, you would have to make the assumption that everything that’s done in the D12 LD is remarkably harder than the d4 LD. For example, swinging across a chasm at d4 LD may have a difficulty of 7 (almost impossible). When you get to the d12 LD, this would be a simple task that you’ve done many times before. Now the chasm’s at d12 depths, I would have to assume would be like the grand canyon.

What this does is balance the tables symmetrically, with similar odds at all levels. Medium stays medium difficult and hard stays hard. One thing to note is that I’ve added a level before “Almost Impossible” called “Insane”. Really, Insane has similar odds to the original Almost Impossible, but once you consider the use of Risk Dice, “Almost Impossible” seems fairly likely. Once Risk Dice are used, a new level of success must be considered.

However, I did add another option below Easy, called Dead Simple. Anything with an average level of stat or higher has 0 chance of failure. It comes into play only for incredibly low stats. While not generally useful, not including it just felt incomplete to me somehow.

### Level Up Houserule

For the third thought, I still think there are easy ways to game the system. I can already hear at least someone saying “Those aren’t the types of people to play with”. But you know what? Who are we to tell them that optimizing is wrong? I’ve played and GM’d both highly optimized games, as well as the opposite. And you know what? They were both fun.

I have no problem with optimization, but if you can see a clear loophole, you gotta stick your finger in the dam. Luckily, it’s a pretty easy fix on this one. These are the house rule restrictions I would use.

- If all 4 Stats are greater than or equal to ½ LD +1, you no longer gain experience from that LD.
- If any 2 Stats meet the LD value, you no longer gain experience from that LD.
- If any Stat is higher than the LD value, you no longer gain experience from that LD.
- Any weapons skills may not exceed your highest Stat.

## Risk Dice

When you use Risk Dice, you have a chance to increase your result by a LOT! However, you always have a chance for automatic failure. As you adventure deeper, these become even more Dangerous. Let’s take a look at the breakdown:

It’s… beautiful. It’s elegant. I love it and nothing should change! Next section!

## Risk Dice & Skill Checks

OK, now it gets more complicated. For this section, I’m only going to be using the Modified challenge system we created. The original one aligns very closely with “If it didn’t automatically fail, then it succeeded”. I’m interested to see how far this will extend to the Modified Challenge Ratings.

To calculate these odds, we had to create a matrix of results for each of the LD, factoring in the automatic failures. We used tables similar to this one for the calculations:

From the section above, including Risk Dice *always* has a chance of automatic failure, so any of the items highlighted in yellow show the maximum amount of success

And it turned out magnificently! The mathematical odds are exactly what I want from an RPG. I know before we talked about the Roll4 Nat 20 on skill checks houserule. The tldr; exploding d20’s adds so much more to the game. It’s similar to how Deep Maw uses risk dice, and has always worked well with my groups. And Dark Peaks proves this mathematically with their inclusion of Risk Dice.

Even with a minimum stat, almost impossible becomes merely “Very unlikely”. With the higher your stat, the greater the likelihood. Certain things can also be gleaned from the information above.

Firstly, If the challenge rating is not at minimum a “Medium” level, then never roll a Risk Dice (unless you have an abysmal rating in the stat). Mathematically it’s not work the chance of catastrophic failure.

Where this gets me more enthused is with the “Hard” or “Insane” difficulty checks. For the average skill, your odds only go up ever so slightly with an average stat on a hard check, and your odds with a high stat still go *down*. Yet, when you get to insane, high stats will go up marginally. Taking in the average stat, this makes risk dice a high-risk, high-reward outcome incredibly balanced.

Honestly, this is the single best mechanic in the game.

### Advantage, Disadvantage & Fate Dice

As a quick overview of these mechanics, Fate Dice are a collection of dice that are shared with the group. They are rolled at the beginning of the session, and at any time, a player can switch out their dice roll with the value of a Fate Dice, though it can not modify a Risk die. This is a great way to counteract the swinging difficulty of rolls, without drastically modifying the mathematics.

Advantage & Disadvantage can be a bit problematic. When you have disadvantage on a roll, you use ½ your stat or skill value rounded down. Honestly, I think this works fine. But for Advantage, you double your skill value. For lower skills, this isn’t a problem, but when it gets closer to the higher end, you would be able to succeed on a nearly impossible roll 100% of the time. Here the problem comes in with the bounds of the numbers. This would be our house rule on that.

### Advantage Houserule

If a character has an advantage, their base skill is increased by ½ it’s value for the purpose of the skill check, rounding down. If they have a disadvantage, their base skill level is halved for the purpose of the skill check, rounding down.

## Combat Caveats

Okay, up until now I only talked about skill checks alone, but the final item we have to take a look at is the elephant in the room. Armor. This is the rules as written:

“Any dice roll which is equal to or below a character’s armour value is ignored. This means that certain to hit rolls will miss even if they are equal to or greater than the challenge rating of the enemy creatures.”

This, of course, plays all sorts of havoc on the math that was done above for the chances of success. It should be noted that this rule only affects regular dice, not risk dice. But it’s a very similar mechanic to Risk Dice in nature. The math involved is fairly simple when looking only at the dice roll, based directly on the LD being used.

It does, however, bring up an interesting challenge. Technically, players and creatures can have armor high enough that they are literally invincible to attacks. If an enemy has an armor of 5 on LD of 4, you literally can not roll a result that would hit.

While I feel like the system implies that this should never be the case, an explicit rule to avoid this would help for new Games Masters. To avoid this, we recommend this houserule

### Armor Houserule

Any dice roll which is equal to or below a character’s armour value is ignored. This means that certain to hit rolls will miss even if they are equal to or greater than the challenge rating of the enemy creatures. When adventuring on any level, the armor may not exceed ⅔ of the LD, rounded up.

## Dark Peaks: Deep Math

Dark Peaks: Deep Maw is a wonderful setting with a spectacular system built around it. Reading through it prompted me to really dive into interesting mathematics. While I think there was some room for improvement through our houserules, they are, in essence, incredibly minor changes.

*Dark Peaks* is available from Drive Thru RPG for $19.99

As the person who devised the maths, it’s really good to see a breakdown of it all from an outside perspective! It’s not perfect, but hey, only Dolly Parton is perfect 😉 Thank you very much for writing this article!

(Co-devised, I should say. Don’t want to nick credit.)

I’m glad you liked it! After spending a few hours playing around with the math, I thought to myself “Why aren’t we sharing this?”. Dark Peaks has a unique roll system with great balance, the world must know about this!