Random number generator

Fair numbers: why the method matters

Computers make random numbers as long strings of bits, and those have to be turned into your range. The easy way, taking the remainder after dividing, is subtly unfair. Take a random byte (0 to 255) and use its remainder after dividing by 100 to pick 1 to 100: 256 is two hundreds and 56 more, so the numbers 1 to 56 come up three ways each and 57 to 100 only two. The low numbers would be 50% more likely.

Octoolo avoids this: it draws from your computer's cryptographic random source, throws away the few values that would cause the imbalance and draws again. Every number in the range has exactly the same chance, which the result line says: “Each of the 100 possible numbers had a 1 in 100 chance”. Ranges can hold up to 9,007,199,254,740,992 values (2⁵³), from negative numbers to very large ones.

No repeats, sorting, and lottery numbers

With No repeats on, the numbers are drawn the way balls leave a lottery machine: each one can come out only once. Asking for more numbers than the range holds, such as 60 from 1 to 49, gives a message instead of a list. With it off, each number is drawn independently and the same one can appear twice, like rolling a die again.

Sort from low to high only changes the order shown; the numbers drawn are the same. The quick ranges include two lottery shapes:

• 6 from 1 to 49, used by many national lotteries: one of 13,983,816 possible sets.
• 5 from 1 to 69, Powerball's white balls. Draw the Powerball itself separately with From 1 To 26. The odds of matching all six are 1 in 292,201,338.

Random numbers do not make a lottery ticket more likely to win; every set has the same chance. They do avoid the birthdays and patterns many people pick, so a win would be shared less often.

Decimals, and other uses

With Decimals, the numbers are drawn on a grid of the places you choose: with 2 places from 0 to 1, each of 0.00, 0.01 and so on up to 1.00 is equally likely. Up to 10 decimal places are allowed, as long as the range does not get too large to count.

• Picking a winner: number the entries and draw one. For names, the wheel of names shows the draw.
• Sampling: draw 50 rows from 1 to 2,000 without repeats, sorted, and copy them as lines into a spreadsheet.
• Teaching: draw 1,000 numbers from 1 to 6 with repeats to see how close each count comes to a sixth.

Every new draw is made the moment you change a setting, and Earlier under a single number keeps the last few, so a classroom can see what came before.