D20 alternate dice
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Contents |
Introduction
So today, I was thinking about the d20 system and how dice work. If you read Unearthed Arcana (part of the d20-based D&D system), you will find an alternate system where you roll 3d6 instead of a d20. This alternate system is also part of the d20 SRD 3.5
Is it a good idea? Bad? Why would you do this, and why would you not?
The Bell Curve
Unearthed called this the "Bell Curve Variant" because of the statistical properties of a 3d6 roll. If you're not familiar with it, I'll explain. If you are, just skip to the next section.
When you roll one die, all results are equally likely unless the die is weighted in some way. However, when you roll multiple dice at once, you get a result that, more often than not, lies in the center of the distribution. That is, when you roll 3d6 you will get 10 and 11 more often than 9 and 12. This continues all the way out to the edge, at 3 and 18, which combined will make up around 1% of all rolls.
Why is this? Isn't every result equally likely? Well yes, but that's every result not every sum! Remember that when you roll 3d6, you're announcing the result by totaling the dice. If you had a red die, a blue die and a white die, you would not say, "6 red, 3 blue, 2 white." You would say, "11". That means that any of the results that could total up to 11 (there are 27), each of which is equally likely, would be lumped into the same result. So, there are 216 possible results and 27 of them result in 11... that means 11 has 27/216ths of a chance of coming up on any given roll, or 12.5%.
How Does 3d6 Help d20?
So now you want to know how this bell-curve would help your game. The answer is that it will not help... necessarily. The effect is to skew the odds in favor of whoever starts off with the advantage. That is, a creature will not get in a "lucky hit" against a player as often using 3d6 if its attack is too low for the AC of the player, and visa versa.
The reason that you would most want this is if you have a large party. This is because the CR system from D&D is designed around parties of 4. If you have, say, 7 players, then you might want to up the CR of opponents. The problem is that upping the CR increases the lethality of encounters, even though the PCs will win. Treating players as ablative gets you disliked as a DM ;-)
So, in order to have an even encounter for 7 players, what you want to do is use more creatures. This allows for several strategies including attrition damage (you might be able to wade through orcs like butter, but they still do some damage... after 20 fights, that's going to hurt a lot), party-vs-army, etc. However, you also run a risk. Because the d20 system is so volatile, it's easy to a have a few lucky shots in a row ruin your plan for low-damage attrition encounters.
By using a roll that has a bell-curve you avoid this problem for the most part (it's still random chance, but not as random).
How Does This Hurt d20?
The down-side to this is that you cannot roll 1-2 and 19-20. Unearthed has the following table to address the situation for critical hits:
| Old Threat Range | New Threat Range |
|---|---|
| 20 | 16-18 |
| 19-20 | 15-18 |
| 18-20 | 14-18 |
| 17-20 | 14-18 |
| 15-20 | 13-18 |
This table works out well for critical threats, but there's still that matter of range. They made an 18 always hit (which seems sort of wrong), but that does not replace the fact that you can no longer roll a 19 or 20... it just feels wrong.
How do we fix this?!
Superheros to the rescue!
Back in the 1980s
, there was a role playing game called DC Heroes. It was not a great game, but it had some nice features. One of those features was a dice-rolling system in which everything was possible... just not likely. If we map that to the d20 system, you would roll 3d6 as described in Unearthed Arcana, but you would then re-roll and add to the result if you rolled the same number on all three dice.
The distribution of results for this system is surprisingly similar to a straight 3d6, and the only problem is that now, you can't roll a 3. Once again, we have to go back to DC Heroes for a solution: if you ever roll all ones, no matter how many times you've re-rolled, your total result is 3, and you stop rolling.
If you would like to see what the distribution of rolls is like, take a look at the results of almost 6 million trial die rolls, using various methods (this is a logarithmic graph, so shapes are somewhat distorted). Notice that, compared against rolling 4d6 and taking the best 3 (a common stat-rolling technique), the bell-curves are almost identical for 3d6, "3d6+reroll" and "3d6+reroll, 3 ends". The only difference is a slight change in the curve at 18, and a "lumpiness" to the curve as a result of the re-rolls.
Other features of note:
- d20 has the lowest average
- All of the 3d6 methods have nearly identical averages
- Compared to "best 3 of 4d6", even d20 and 3d6 averages are nearly identical
- 18 and 19 are very unlikely results (even more so than 20) when using the re-rolling method... this is an unavoidable consequence of the bell-curve for 3d6.
Conclusion
If you want a system that has less variance and still allows for any possible result, especially for a large party, the 3d6+reroll system works well. However, for normal sized parties, and even for most large parties, a d20 works just fine.
See also
- D20 treasure system - An analysis of the treasure generation system.
About the author
Aaron Sherman has been playing D&D and various other role playing games since the mid-1980s, and has published several online worldbooks for GURPS, Fantasy Hero and other systems.
