Random Number 1-20 (d20 Roller)

Every step is worth five percent

The neat thing about a range of twenty is how easy it is to think about. Each number is exactly 5%. That makes 1 to 20 the friendliest range for anyone who wants to turn “how likely is this?” into a number they can actually reason with.

Tabletop role-players exploit this constantly, whether they realise it or not. When a game master says “roll a d20 and get 11 or higher,” that’s 10 numbers out of 20, a coin flip. Need 15 or higher? Six numbers, 30%. A +2 bonus on that roll shifts it to 40%. You can do the whole thing in your head once you see that every point is a twentieth.

You need to roll	Numbers that succeed	Chance
5 or higher	16	80%
10 or higher	11	55%
11 or higher	10	50%
15 or higher	6	30%
18 or higher	3	15%
20 exactly	1	5%

That’s also why the 5% critical hit feels the way it does. You’ll see one about once every twenty rolls, which over a long session works out to a handful of big moments for the whole table. If you want advantage, disadvantage and modifiers handled for you, the d20 dice roller does all of that. This page gives you the bare number.

Twenty questions and the power of halving

The other famous twenty is the parlour game. One person thinks of something, and everyone else gets twenty yes-or-no questions to work out what it is. It’s older than radio (it was a popular radio quiz in the 1940s) and it hides a startling bit of maths.

Each perfect yes-or-no question cuts the possibilities in half. Twenty halvings in a row can separate 2 to the power of 20 different things, which is 1,048,576. In theory, a perfect questioner could pin down any one of a million objects. In practice humans ask sloppy questions (“is it big?”), so the real number is far smaller, but it explains why good players feel almost psychic.

A classroom twist we like: the teacher generates a number from 1 to 20 and the class has to find it with as few yes-or-no questions as possible. The best possible strategy needs at most five questions, since four halvings only cover 16 numbers. Kids who discover “is it more than 10?” on their own feel brilliant.

Number lines and counting games

For younger learners, 1 to 20 is the range where counting stops being trivial. Teen numbers are notoriously awkward in English because they’re said “backwards” (fourteen puts the four first, unlike twenty-four), and lots of kids write 41 when they mean 14. Random practice helps.

• Jump the number line. Put a 0 to 20 number line on the floor with tape. Generate a number and a child jumps to it. Generate again and they say how many jumps forward or back to reach the new one.
• Before and after. Generate a number; the class calls out the numbers either side.
• Teen number spelling. Generate a number between 11 and 19 (re-generate if you get something outside that) and the class writes it in words.

Probabilities for 1 to 20

Probability facts for random numbers from 1 to 20

Fact	Value
Possible results	20 (1 to 20, inclusive)
Chance of any one number	1 in 20 = 5%
Even numbers / odd numbers	10 even (50%) · 10 odd (50%)
Prime numbers in range	8 (40% chance of a prime)
Same number twice in 2 picks (repeats on)	1 in 20 = 5%
A chosen number appears at least once in 10 picks	40.1%
Picks until a repeat is more likely than not	6 picks
Average (expected) result	10.5
Average picks to hit one specific number	20

Twenty-item lists

Twenty is a convenient size for lists: spelling words for the week, chores in a big house, challenges in a team-building session, or a “20 before 20” bucket list for a teenager. Number the list and let the generator pick.

Some ideas we’ve found useful:

1. Spelling tests. Generate the order of the twenty words, so students can’t memorise the sequence from the sheet.
2. Group challenges. A list of twenty quick challenges for a staff away-day, picked one at a time.
3. Gym finishers. Twenty bodyweight finishers on a laminated card, one picked at random after each session.
4. Debate warm-ups. Twenty silly motions, one per lesson. The debate topic picker has plenty of real ones if you need more.

Avoiding the same item twice

With twenty options and repeats on, you’ll see a repeat sooner than you expect. By the sixth pick, it’s already more likely than not that something has come up twice. Tick No repeats if each item should only be used once until the list resets.

The odds of extremes

People sometimes ask whether 1 and 20 come up less often, because on a cheap plastic d20 they can feel rare. On this generator they don’t: each end of the range has the same 5% as everything in the middle. Cheap physical d20s, on the other hand, are often slightly lopsided from the moulding process, and tabletop players have run thousands of test rolls to check their dice by floating them in salt water to find the heavy side. A digital roll avoids the whole debate.

For a bigger pool, the 1 to 25 page suits full classes, and the main number generator accepts any custom range.

Twenty-sided history

The icosahedron, a solid with twenty triangular faces, is one of the five Platonic solids described by ancient Greek mathematicians. Twenty-sided dice are far older than role-playing games: archaeologists have found icosahedral dice from Roman-era Egypt, some marked with Greek letters. They mostly sat in museums until 1974, when Dungeons & Dragons put the shape back on kitchen tables.

Teachers also use twenty for quick “show me” warm-ups: generate a number and the class shows it on mini whiteboards as a tally, a ten frame plus extras, or a sum of two smaller numbers.

Finally, a tip for game masters improvising on the fly: keep a list of twenty random encounters or plot twists in your notes and generate from 1 to 20 when the players wander somewhere unexpected.