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Is there a difference between the results of Math.floor(Math.random() * x) + 1 and Math.ceil(Math.random() * x)?

Ben Craven
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  • If `Math.random() * x` is a integer they will have different values. However, the chance of that is small. – mousetail Jun 10 '22 at 13:48
  • Are you asking if there is any difference in the spread/likelihood of the random numbers this produces? – DBS Jun 10 '22 at 13:49
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    The difference is the first can never return `0` and the second can. – Etheryte Jun 10 '22 at 13:49
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    Math.random gives a number between 0 included and 1 excluded. Multiplying it by x gives a number between 0 included and x excluded. Therefore doing Math.floor + 1 or Math.ceil on that number gives the same result ( Random integer between 1 included and X included ) – Xavier B. Jun 10 '22 at 13:50
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    Does this answer your question? [Better algorithm generating random numbers in JS](https://stackoverflow.com/questions/55172070/better-algorithm-generating-random-numbers-in-js) – FZs Jun 10 '22 at 13:56
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    @XavierB. incorrect - `Math.floor(0 + 1) == 1`, but `Math.ceil(0) == 0` – Alnitak Jun 10 '22 at 14:19

2 Answers2

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Math.random() produces floating point values in the interval [0, 1) (from zero inclusive to one exclusive). This means that there is a slight difference between the two approaches:

Math.ceil(Math.random() * x) will produce integers in the interval [0, x] (from zero inclusive to x inclusive). This is because Math.ceil(0) will return a zero. Although the chance of getting that is extremely small.

function minRandom() { return 0; }
function maxRandom() { return 0.9999999; }

const x = 10;
console.log("min:", Math.ceil(minRandom() * x));
console.log("max:", Math.ceil(maxRandom() * x));

Math.floor(Math.random() * x) + 1 will produce integers in the interval [1, x] (from one inclusive to x inclusive). This is because Math.floor(Math.random() * x) itself produces integers in the interval [0, x-1] (zero inclusive to x-1 inclusive).

function minRandom() { return 0; }
function maxRandom() { return 0.9999999; }

const x = 10;
console.log("min:", Math.floor(minRandom() * x) + 1);
console.log("max:", Math.floor(maxRandom() * x) + 1);
VLAZ
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Yes, there's a difference.

There is a chance, albeit a very very small one, that the second version could unexpectedly return zero.

This happens if Math.random() itself returns exactly 0.0, which it legally can.

Alnitak
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  • I'm not really sure it's unexpected. Well, unless you never wanted a zero. But it's a totally valid output. – VLAZ Jun 10 '22 at 13:58
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    @VLAZ kinda - it's certainly valid, but it might surprise some people (including some of the other commentators here). – Alnitak Jun 10 '22 at 13:58
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    ¯\\_(ツ)_/¯ Any output can be a surprise if you don't know how something works. – VLAZ Jun 10 '22 at 14:02