D12 vs. 2D6: Which Die Roll Reigns Supreme?

The age-old question in tabletop gaming: Is a d12 better than 2d6? The definitive answer, as unsatisfying as it might be, is: it depends. It depends on the desired probability distribution, the modifiers involved, and the specific context of the game. A single d12 offers a flat probability, meaning each number from 1 to 12 has an equal chance of being rolled. 2d6, on the other hand, provides a bell curve distribution, making results around the average (7) more likely than extreme values (2 or 12). Let’s delve deeper into why this difference matters and when each option might be preferable.

Understanding the Probability Distributions

The Flat Distribution of the D12

A single d12 provides a straightforward, uniform probability. Each face (1 through 12) has an equal chance of landing face up, precisely an 8.33% chance. This means you’re just as likely to roll a 1 as you are to roll a 12. This type of distribution favors high-risk, high-reward scenarios where you might be willing to gamble on a potentially low result for the chance of a very high outcome.

The Bell Curve of 2D6

When you roll two six-sided dice and add their results, you create a bell curve probability distribution (also known as a normal distribution). This means the middle values are much more likely than the extreme values. You’re far more likely to roll a 7 (the most probable outcome) than a 2 or a 12.

Here’s a breakdown:

• 2: 1/36 (2.78%)
• 3: 2/36 (5.56%)
• 4: 3/36 (8.33%)
• 5: 4/36 (11.11%)
• 6: 5/36 (13.89%)
• 7: 6/36 (16.67%)
• 8: 5/36 (13.89%)
• 9: 4/36 (11.11%)
• 10: 3/36 (8.33%)
• 11: 2/36 (5.56%)
• 12: 1/36 (2.78%)

This distribution makes 2d6 more reliable for generating consistent, moderate results. It’s ideal when predictability is more important than the possibility of exceptional outcomes.

Comparing Averages and Expected Values

While both a d12 and 2d6 have an average result of 6.5, the way those averages are achieved is dramatically different. A d12 hits every number with equal frequency, while 2d6 clusters around the mean. The effect is that 2d6 gives you a more predictable outcome, while a d12 is very swingy and highly variable.

Impact of Modifiers

Modifiers significantly alter the effectiveness of each die type. The larger the modifier, the less impactful the dice roll itself becomes.

• Small Modifiers (1-3): When modifiers are small, the differences between d12 and 2d6 are less pronounced, especially in the 1-3 range. Personal preference and the desired level of variance are the primary factors in choosing.
• Large Modifiers (4+): With larger modifiers, the impact of the die roll is reduced. The 2d6’s clustered distribution becomes more restrictive, potentially making high target numbers unreachable, especially when negative modifiers are applied. In these cases, the d12 allows a wider range of potential outcomes, even with significant penalties.

Game Design Considerations

Game designers carefully choose between d12 and 2d6 (or other dice combinations) based on the intended feel of the game.

• Risk and Reward: Games aiming for dramatic, unpredictable moments often use d12 (or even larger dice), encouraging players to take risks for potentially huge payoffs.
• Consistency and Reliability: Games emphasizing tactical decision-making and controlled outcomes prefer 2d6 (or similar systems), providing players with a more predictable baseline upon which to build their strategies.
• Complexity: The game Apocalypse World makes heavy use of 2d6 to make outcomes more granular and less black and white. In Apocalypse World you roll 2d6 + a modifier; on a 6 or less, nothing happens, 7-9 something happens, but not what you want; and 10+ something happens that you want to occur. This can introduce a lot more complexity.

Practical Examples in Gaming

• Dungeons & Dragons (D&D): D&D 5e uses a variety of dice, including the d12, to represent different weapon damage values. The greataxe, dealing 1d12 damage, reflects the potential for devastating blows, albeit with less consistent damage than a weapon using 2d6.
• Other RPGs: Many tabletop role-playing games (RPGs) employ 2d6 systems for skill checks and other mechanics, aiming for a balance between player skill and chance.
• Board Games: Board games utilize different dice combinations based on the desired level of randomness and strategic depth. A game aiming for strategic planning might use 2d6 for more predictable movement or resource gathering.

Conclusion

Choosing between a d12 and 2d6 is not about one being “better” than the other; it’s about understanding the mathematical properties of each and selecting the one that best suits the specific needs of your game. By considering the probability distributions, modifiers, and desired gameplay experience, you can make informed decisions that enhance the overall enjoyment and strategic depth of your gaming experience. If you wish to understand the mathematics behind game design in detail, you should check out the Games Learning Society at GamesLearningSociety.org.

Frequently Asked Questions (FAQs)

1. Can I roll a d12 instead of 2d6 in D&D?

Technically, you could, but it would drastically alter the game’s balance. D&D is designed around specific probability curves. Replacing 2d6 with a d12 would make average rolls less frequent and extreme rolls more frequent, significantly impacting combat and skill checks. It’s not recommended without thoroughly understanding the consequences.

2. What’s the difference between a d12 and other dice, like a d20?

The primary difference is the number of sides and the resulting probability distribution. A d20 has 20 sides, each with a 5% chance of being rolled. The larger the number of sides, the more granular the results and the wider the range of possible outcomes. A d20 is generally used for things like hit rolls and skill checks as these are used for binary things such as hit or miss, succeed or fail, and allow for granular percentages to affect the chances.

3. Is 1d10 or 2d4 better for damage rolls?

1d10 has a flat distribution from 1 to 10, while 2d4 creates a bell curve centered around 5. 2d4 is more likely to give you a middling result. 1d10 will give you more variance, and therefore gives you more chance of low rolls and high rolls.

4. Why are there different types of dice in tabletop games?

Different dice types allow game designers to control the level of randomness and granularity in various game mechanics. Some situations call for more predictable outcomes (like 2d6), while others benefit from a wider range of possibilities (like a d20 or a d12).

5. What is a d12 mostly used for?

The d12 is primarily used to determine the damage of certain weapons, spells, or abilities, where a higher potential damage range is desired. It can also be used to select between twelve different outcomes in random events or tables.

6. How does the average damage of a d12 compare to 2d6?

Both have an average result of 6.5. However, the d12 is spread evenly between 1 and 12, and 2d6 is clustered. So 2d6 will have less variance.

7. What is the shape of a d12 called?

A standard d12 is shaped like a rhombic dodecahedron.

8. Are there any games that exclusively use d12s?

While no games exclusively rely on only d12s, some games heavily feature d12-based mechanics due to the wide range of outcomes. Some homebrew games may revolve around this core.

9. How do modifiers affect the choice between a d12 and 2d6?

Large modifiers diminish the influence of the dice roll itself. In cases with significant modifiers, especially penalties, a d12 can provide a wider range of potential outcomes compared to the clustered results of 2d6.

10. Can you “cheat” with weighted dice?

Yes, weighted dice exist and are designed to favor certain numbers. However, using them in organized play or with unsuspecting players is considered cheating.

11. Are some numbers more “lucky” on a d12?

Mathematically, each number on a fair d12 has an equal probability. However, superstition and personal experience can lead some players to believe certain numbers are “luckier” than others.

12. How do you determine percentage chances in D&D?

Percentage chances are typically determined using two ten-sided dice (d10s). One die represents the tens digit, and the other represents the ones digit, creating a range from 1 to 100. This gives each percentage an equal weighting.

13. What happens if I roll a 00 on percentile dice?

Typically, a roll of 00 is treated as 100. Some GMs may rule it as a zero, so always clarify at the start of the game.

14. Where can I learn more about the mathematics behind game design?

Numerous resources are available online and in print, including books, articles, and online courses. Consider exploring websites such as GamesLearningSociety.org and academic papers focusing on game theory and probability.

15. Does using 2d6 make a game less random than using a d12?

Yes, absolutely. The bell curve distribution of 2d6 means that results closer to the average are much more likely, reducing the overall randomness compared to the flat probability of a d12. This is one of the reasons why you only roll 2d6 for damage; imagine how easy it would be to defeat monsters if every monster rolled a 6 or 7 on the hit roll.