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Advantage, Disadvantage and Dice Pools

Rolling more dice can mean several different things. You might keep the best result, add everything, count successful dice or replace a poor roll. These operations change both the result and the chance of success.

Before rolling, ask what the game wants you to do with each die. The word “advantage” alone is not enough: different RPGs reward favourable circumstances in different ways.

More dice do not always mean a larger total

Compare three instructions using six-sided dice:

Instruction Example dice Result
Add two dice. 2 and 5 7
Keep the higher of two dice. 2 and 5 5
Count dice showing 5 or more. 2 and 5 1 success

All three involve two d6, but they answer different questions. Adding dice measures a combined total. Keeping one selects a result. Counting successes measures how many dice qualify.

This distinction is especially important when moving between games. A familiar-looking handful of dice may use a completely different resolution method.

D&D advantage and disadvantage

For ordinary Dungeons & Dragons Fifth Edition advantage, roll two d20 and use the higher. For disadvantage, use the lower. Add the applicable modifier after selecting the die.

Suppose the dice show 7 and 16, with a +5 modifier:

In Custom notation, these are 2d20kh1+5 and 2d20kl1+5. In Math Rock Roller's D&D profile, enter the ordinary 1d20+5 expression and use its advantage or disadvantage setting instead. Do not supply the two-die expression and also enable that setting.

D&D does not normally keep adding d20s for multiple sources of advantage. Its rules also specify how advantage and disadvantage cancel. Determine the applicable mode at the table; the expression is not a substitute for that decision.

Nor does selecting a high die turn every natural 20 into an automatic success. Fifth Edition attack rolls have particular natural-20 and natural-1 rules. Ordinary ability checks and saves are interpreted differently.

Keep highest and keep lowest

Keep notation can select more than one die. kh3 means keep the highest three, not the single highest result multiplied by three.

For 4d6kh3, dice of 1, 3, 4 and 6 leave 3 + 4 + 6 = 13. For 4d6kl3, the same dice leave 1 + 3 + 4 = 8.

Selecting more favourable dice changes the odds without simply adding a fixed number. A +3 modifier always changes a total by three; keeping a better roll sometimes changes it by much more, sometimes by nothing.

Keep-lowest is not universally a penalty. In a game aiming to roll below a target, selecting a lower result may be beneficial. Always establish whether high or low results are desirable.

Drop highest and drop lowest

Drop notation names the dice to exclude. 4d6dh1 drops the highest one; 4d6dl1 drops the lowest one.

With 1, 3, 4 and 6, dropping the highest leaves 8, while dropping the lowest leaves 13. In this example, dropping one lowest is equivalent to keeping three highest.

Dropped dice are excluded, not replaced. This matters when a rule specifically says “reroll”: a replacement creates a new chance, whereas dropping selects from results already rolled.

Success-counting pools

Some games ask how many dice meet a threshold. In Custom notation, 5d10>=8 rolls five d10 and counts results of at least 8.

Faces of 1, 4, 8, 9 and 10 give three successes, not a success result of 32. To record ones as failures too, use 5d10>=8f=1. It reports three successes and one failure separately; it does not automatically cancel a success.

Dedicated profiles can supply different interpretations. Math Rock Roller's classic Vampire profiles apply their supported cancellation and botch rules. Its Shadowrun Sixth World profile counts 5s and 6s on d6 as hits and checks for glitches.

Those games do not share one universal “pool rule”. Pool size, thresholds, special faces and the meaning of failure all depend on the system and edition.

Rerolling replaces a die result

With 4d6r<2, a die showing 1 is rerolled until it no longer matches. A sequence of 1 → 1 → 4 contributes 4, not 6.

With 4d6ro=1, that die receives only one replacement. 1 → 1 contributes 1, because the second result stands. The other three dice remain as rolled unless their own initial results also qualify.

Neither form means “reroll everything and keep whichever complete roll you prefer”. If a game lets you spend a resource for a second attempt, its eligibility, cost and selection rule need separate attention. Pressing Roll again alone does not manage that resource.

Exploding dice add to a chain

An exploding maximum earns another roll that adds to the same die. For 1d6!, a sequence of 6 → 6 → 2 contributes 14. It does not replace the sixes.

Math Rock Roller compares complete explosion-chain totals when applying Custom keep/drop rules. Its thresholds likewise check kept chain totals. A game's instruction to count individual faces within a chain may require a different profile or manual handling.

Savage Worlds uses exploding dice, called Aces, as part of its own rules. Its Wild Die and critical-failure procedures mean a generic mixed-die keep expression is not a complete replacement for the dedicated profile.

Similar names, different operations

Call of Cthulhu Seventh Edition bonus dice are extra tens dice sharing one units die. That is different from rolling two independent d100s and keeping the lower. See the percentile guide for an example.

Pathfinder's natural 1 and 20 can shift a degree of success, while D&D's ordinary attack rules use their own critical and automatic-miss treatment. Math Rock Roller provides separate profiles so these distinctions do not disappear behind one generic d20 roll.

Choose the operation before rolling

Check the dice, selection rule, modifier, target and special results. If a supported game profile matches your rules, use it. Otherwise, use Custom for the dice operation and interpret any remaining rules yourself.

The notation guide provides a compact reference, and the systems page explains profile limits.

Launch Math Rock Roller (opens in a new tab) to compare a plain roll, a keep-highest roll and a success pool.

Rules references

D&D's 2024 Basic Rules, Chaosium's game-system guide, Pathfinder's degrees of success and the Savage Worlds 2020 Test Drive describe the edition-specific examples discussed here.