Two ways to turn dice into an outcome
Tabletop games resolve uncertainty in two broad ways. A single die system rolls one die, usually a d20 or d100, adds modifiers, and compares the total to a target. A pool system gathers several dice, and each die is judged on its own: a die that meets a threshold counts as a success, and the number of successes decides the result.
A third family adds several dice into one sum, such as 2d6 plus a bonus. It behaves like a single die system in some ways and like a pool in others, so it is worth keeping separate in your head. This article focuses on the contrast between counting successes and reading one number.
How a pool works
Suppose a game uses six-sided dice and each die showing 5 or 6 is a success. Each die succeeds with probability 1/3, and the dice are independent events that do not affect each other. The number of successes follows the binomial outcomes pattern, with an average of the pool size times 1/3.
| Pool size | Average successes | Chance of at least one success |
|---|---|---|
| 1 | 0.33 | 33.3% |
| 3 | 1.0 | 70.4% (19/27) |
| 6 | 2.0 | 91.2% (665/729) |
The last column comes from the complement: the chance that every die fails is (2/3) raised to the pool size, and subtracting from 1 gives the chance of at least one success. For six dice, (2/3)^6 is 64/729, so the chance is 665/729.
Notice how quickly reliability grows. Going from one die to three more than doubles the chance of any success, while going from three to six adds about 21 points.
How a single die system works
A d20 plus a modifier gives a flat spread: every face is equally likely, so the result is as likely to be 3 as 18. Each +1 changes a target’s success chance by 5 percentage points. The system is easy to learn and the odds are easy to calculate.
The cost is that a single roll has high game variance. A character with a large bonus can still roll a poor number, and a character with a small bonus can roll a great one. That swing is part of the appeal for some tables and a frustration for others.
Spread and predictability
Pools tend to produce more predictable results as they grow. For six dice at a 1/3 success chance, the standard deviation of the success count is the square root of 6 x 1/3 x 2/3, which is about 1.15 on an average of 2. For twelve dice, the average is 4 and the standard deviation is about 1.63. The average doubled, but the spread grew by only about 41%, so the result is relatively steadier.
A single d20 does not behave this way. Adding a bonus moves the whole range but does not narrow it. Summed dice do narrow with more dice, which is why 2d6 clusters around 7 while a d12 does not. The craps odds for each total show the same bell shape from two dice.
Scaling and progression
Pool systems usually scale by adding dice. Each extra die adds roughly the same expected successes, but its effect on any particular threshold is not even. Early dice make a big difference to the chance of at least one success, while later dice mostly raise the expected count.
Single die systems scale by raising the modifier. This shifts a target’s chance by a fixed amount, until the target becomes nearly certain or nearly impossible. Designers often need extra rules to keep high-level characters from auto-succeeding, such as raising target numbers as the game progresses.
Granularity and information
One practical advantage of pools is that the result carries more than pass or fail. Three successes against a target of one can mean a stronger outcome, extra effects or lower cost. A single total can do this too, by comparing how far above the target you rolled, but the margin is spread evenly rather than concentrated around an average.
Pools can also separate different kinds of events. A rule might say that any die showing a 1 causes a complication, regardless of successes. That lets a roll be both a success and a mishap, which a single number cannot express without a separate table.
Speed and table feel
Single die systems resolve quickly: roll, add, compare. Pools take longer to read, since the player must pick out successes from a handful of dice. Many people find that a pool feels more tactile, because investing more dice feels like investing more effort. Others prefer the clean arithmetic of one die.
Choosing between them
Neither is better in general. A rough guide:
- Single die systems favour speed, simple math and dramatic swings.
- Pool systems favour steady scaling, graded outcomes and results that settle around an average.
- Sum-based systems sit in between, with a bell-shaped curve that makes extreme totals rare.
If you are testing a design, a quick simulation or a spreadsheet of each option will show how often players hit a given target. As always, the figures describe long-run behaviour, and any one session can look quite different.