Bell Curve Rolls

( ⇪ Adventuring Variants )

In a nutshell: Average rolls become more likely, fringe rolls become less likely.

Here’s perhaps the most fundamental variant to the d20 rules: Don’t use a d20! Instead, roll 3d6 whenever you would roll a d20, applying bonuses and penalties normally. The possible results when rolling 3d6 (or any other multiple dice) form a bell curve — that is, a range of odds that favors average results much more than extreme results.

Rules For Rolling

This system requires several changes to how rolls are made.

Automatic Successes and Failures

Automatic successes (for attack rolls and saves) happen on a natural 18, and automatic failures on a natural 3. Neither occurs as often as in standard d20 (less than 1/2% of the time as opposed to 5% of the time).

Taking 20 and Taking 10

You can’t take 20 using the bell curve variant. Instead, you have two new options: You can take 16, which makes the task take ten times as long, or you can take 18, which makes the task take one hundred times as long. As with the rules for taking 20, you can only take 16 or 18 when you have plenty of time, when you aren’t distracted, and when the task carries no consequences for failure. For a check that normally requires a standard action, taking 16 uses up 1 minute and taking 18 uses up 10 minutes.

The rules for taking 10 remain unchanged.

Threat Range

Because it’s no longer possible to roll a natural 19 or 20, the threat ranges of weapons change in the bell curve variant.

For easy reading, threat ranges are now expressed with numeric threat “types” that are indicative of how many dice roll results cause a critical threat. The threat types are 13, 24, 35, 45, and 66. The first digit represents the number of dice roll results for the old d20 threat range system, and the second digit represents the number of dice roll results for the new 3d6 threat range system.

Table: Threat Ranges
Type d20 (%) 3d6 (%)
13 20 (5%) 16-18 (4.63%)
24 19-20 (10%) 15-18 (9.26%)
35 18-20 (15%) 14-18 (16.2%)
45 17-20 (20%) 14-18 (16.2%)
66 15-20 (30%) 13-18 (25.93%)

When applying effects which double a threat range, the new threat range type can be found by doubling the old threat type’s first digit and then using that new first digit’s associated second digit. For example, if a Type- 1 3 weapon has its threat range doubled, it becomes a Type- 2 4 weapon. Similarly, if a Type- 3 5 weapon has its threat range doubled, it becomes a Type- 6 6 weapon.

With the bell curve variant, the narrowest threat range becomes slightly more narrow (4.6% rather than 5%), and the new 14-18 range (16%) falls between the old 18-20 and 17-20 ranges. But because the Improved Critical feat and the keen edge spell double threat ranges, characters still improve their weapons in every case, despite the flat spot on the table.

Monster CRs

Any time creatures are encountered in groups of four or more, reduce their CR by 1. For example, a single troll is CR 5, and two trolls are CR 5 each (and thus a CR 7 encounter), but four trolls become only CR 4 each (a CR 8 encounter). Monsters with fractional CRs move down to the next lowest fraction when encountered in groups of four or more; the goblin (ordinarily CR 1/2) becomes CR 1/3, for example.

The original text of this variant was talking about ELs, and this setting uses CR budgeting, but the reasoning holds true anyway. If you’re putting four or more of a creature in an encounter, it’s very likely because the written CR is already lower than the party’s ECL, and therefore the creature already has relatively weak AC and other stats. Weaker stats are easier to beat in a bell curve system than in a d20 system. For example, a troll at CR 5 has an AC of 16. Four trolls after reducing CR becomes a CR 8 encounter, which is a reasonable challenge for a party at ECL 7. An unoptimized Fighter in an ECL 7 party has an attack bonus of roughly +9, giving them a 90%+ chance of hitting a troll on a bell curve (as compared to 70% chance on a d20). Even if we assume someone even less optimized like a +7, that’s still a 74%+ chance to hit! You’ve got to have at least four of them in there just to make it a real challenge.

Luck Domain and Feats

The granted power of the Luck domain changes, because simple rerolls aren’t as useful in the bell curve variant as they are in the standard rules. When electing to reroll a result, a cleric with access to the Luck domain rolls a 4d6 for the reroll (instead of a 3d6), dropping the lowest die. For example, if you rolled 2, 5, 6 and 6, you would drop the 2 for a total of 17. The same change applies to all of the Luck feats which allow rerolls.

The Luck domain’s spells change as well, with auspicious odds replacing protection from energy at 3rd level and mass auspicious odds replacing break enchantment at 5th level.

Bell Curve Rolls

Hyperion Voyages Ternal Ternal