Random Number Between 1 and 20
Twenty outcomes, each with an exact 5 percent chance. That is the cleanest number on this site, and it is why the twenty-sided die became the standard roll in tabletop games.
1 to 20 1
20 possible values, each equally likely. Tick nothing and repeats can happen; that is what random means.
Exactly 5 percent per number
Twenty equally likely outcomes gives every value a flat 5 percent chance. That is what makes the range so useful: a target number reads straight off as a percentage. Needing 15 or higher means six winning values out of twenty, which is 30 percent, and you can do that arithmetic in your head at the table.
How often the top number turns up
- A single 20 is 5 percent, or 1 in 20.
- Across 20 draws, the chance of at least one 20 is 64.15 percent. So more than a third of 20-draw stretches contain none at all, which is normal rather than unlucky.
- Two 20s back to back is 0.25 percent, or 1 in 400.
- Seeing every value from 1 to 20 at least once takes about 72 draws on average.
The gambler’s mistake
After a long dry spell people start saying a 20 is overdue. It is not. Each draw is drawn from the same twenty numbers with no memory of the last one, so the chance is 5 percent whether the previous draw was a 1, a 20, or the eleventh 3 in a row. Streaks in a twenty-wide range look dramatic and mean nothing.
Uses
Checks and saves in tabletop games, picking one of twenty questions, assigning twenty desks, choosing a page number. For the die itself use roll a d20, and for a different range set your own bounds on the random number generator. If you want half of twenty, 1 to 10 works the same way at 10 percent per value.