Why is the average higher than just rolling fewer dice?

Because the dice that get discarded are the low ones. Rolling 4d6 and keeping the best 3 averages 12.24, well above the 10.5 you would get from three plain dice — dropping the lowest of a group systematically removes the smaller results.

Keep-Highest Dice Roller

Rolls a set of dice and keeps only the highest of them, summing just the kept results — useful for ability-score generation, advantage-style rolls, or any 'roll extra and keep the best' house rule.

Sides per die

Number of dice

Keep highest

Seed (optional)

Replays the same rolls. Deterministic, not cryptographic.

Your roll will appear here, with the odds of getting it.

✓ The probabilities add up to one — 126 distinct sorted rolls, weighted by how many ways each can come up
✓ Dropping the lowest pulls the average up — 12.24 against the 10.5 that 3 plain dice would average — which is why treating this as 3 dice is wrong
✓ The range is what the kept dice can reach — 3 to 18, from all ones to all 6s on the kept dice, and those are the first and last totals any roll gave
✓ Every possible roll is counted exactly once — 1,296 ordered outcomes counted, which is exactly 6^4, gathered into 126 sorted ones
✓ Each total's chance is the share of rolls that make it — counted again a face at a time, without listing a roll: all 16 chances, the average, the spread and the most likely total agree

What this generator does

Rolls several dice, keeps the best of them, and shows what was discarded as well as what counted — then gives the exact odds of the kept total. Rolling four and keeping three averages 12.24 rather than the 10.5 three plain dice would give, and this says so beside every roll rather than leaving you to guess.

How to use this tool

Set the dice sides, count, and how many to keep.
Press roll to see every result and which were kept.

Understanding the controls

Sides per die: The size of each die. Every die in the roll is the same size; the odds are worked out exactly for whatever you choose.
Number of dice: How many are rolled before the best are taken. Rolling more shifts the kept result upwards — with two dice the average of the highest is noticeably above the average of one.
Keep highest: How many of the rolled dice are counted. Four dice keeping three is the classic ability-score roll; two keeping one is a straightforward advantage roll.
Seed: Empty for ordinary random rolls. Type anything to replay the same sequence, which is how a table can roll the same characters twice. Deterministic, not cryptographic.

Worked examples

4d6 drop lowest, the classic ability score: Roll 4 six-sided dice, keep the best 3. The kept total averages 12.24 rather than the 10.5 that three plain dice would average — the discarded die is doing real work.
Advantage on a single d20: Roll 2 dice, keep the highest 1. This is the 'roll twice, take the better' mechanic some games call advantage.

Common use cases

Ability-score generation
Advantage-style rolls
Board games with 'best of' dice rules

How this generator works

The dice are rolled, sorted, and the best few summed. What the page adds is the exact distribution of that sum, which is not something you can read off a table of single dice: every sorted combination of faces is enumerated once and weighted by its multinomial coefficient — how many orderings produce it — so the probability of each kept total is exact with no sampling error. The weights are then checked to sum to the full number of ordered outcomes, which is what proves nothing was double-counted or missed. The session panel keeps the last hundred rolls and compares their average against the exact expected value.

Randomness and fairness

Each die is rolled independently from your browser's cryptographic random source, so every face is equally likely before anything is dropped. The kept total is not uniform, and that is the point: dropping the lowest die pulls the whole distribution upwards and narrows it. The odds shown are exact rather than sampled — every sorted combination of faces is enumerated once and weighted by how many ways it can be rolled, and the weights are checked to add up to the entire sample space. Give a seed and the dice come from a deterministic generator instead, replaying the same rolls for the same seed — deterministic, not cryptographic.

For how randomness is produced across the whole site, see how Generate Random works.

Limitations and good to know

The exact odds are enumerated rather than approximated, so very large numbers of large dice are refused instead of being estimated.
The running tally of kept totals is held in the page only, so closing the tab ends the session and the comparison against the expected average starts again from zero.
Dropping dice changes the shape of the distribution, not just its average — a kept total is more tightly clustered than the same number of plain dice.
Ties are irrelevant here: identical faces are interchangeable, so which physical die was kept makes no difference to the total.

Frequently asked questions

Why is the average higher than just rolling fewer dice?: Because the dice that get discarded are the low ones. Rolling 4d6 and keeping the best 3 averages 12.24, well above the 10.5 you would get from three plain dice — dropping the lowest of a group systematically removes the smaller results.