Why did my 5% option not appear in 20 draws?

Because that happens about 36% of the time. A 5% chance means each draw independently has a one-in-twenty chance, not that the twentieth draw is owed. Over 20 draws the probability of never seeing it is 0.95 to the twentieth power, which is more than a third.

Do the weights have to be whole numbers?

No. Fractional weights work exactly, which is why the draw uses a cumulative sum rather than the common trick of repeating each option in a list — that trick only handles whole numbers and falls apart at any scale.

How is this different from the weighted picker?

That one draws a single result to make a decision with. This draws hundreds to show you the distribution and how far a real run strays from the weights. Different questions: one is 'what shall I do', the other is 'is this fair'.

Weighted Draw Simulator

A 5% drop rate over forty attempts feels like it ought to come up twice. It comes up twice about a quarter of the time — the rest of the time it is once, or none, or four. That gap between what a weight promises and what a run of draws delivers is where almost every argument about rigged loot, unlucky streaks and broken generators comes from. This draws from your weights and puts the observed counts next to the expected ones, so the difference is visible rather than felt.

Options and weights

One per line, weight last: 'common 70'. No number means a weight of 1.

How many draws

Each draw is independent — weights do not run out.

Seed (optional)

A word repeats the same sequence.

The draws will appear here.

What this generator does

Runs a weighted draw many times and reports the distribution against theory. The weighted picker already here draws one result for a decision; this draws hundreds and shows the shape they make. That comparison is the whole content — a page that only drew would tell you nothing about whether the draw was fair.

How to use this tool

List the options, one per line, with a weight after each.
Set how many draws to make.
Press Draw.
Compare the Got column against Expected — and draw more to watch the gap close.

Understanding the controls

Options and weights: One per line with the weight last, so 'common 70' is seventy times more likely than an option weighted 1. Weights need not sum to 100 or be whole numbers; they are relative.
How many draws: Each draw is independent — the weights never run out and a rare result can appear twice in a row. Raising this is what makes the observed counts close in on the expected ones.
Seed: A word reproduces the same sequence exactly, which is what you want when demonstrating a specific run to somebody else.

Worked examples

70/25/5, forty draws: Expected 28 / 10 / 2. A run giving 31 / 7 / 2 is entirely ordinary.
The same, twenty thousand draws: Within a fraction of a percent of the weights every time.
A weight of zero: Never drawn — the option is listed and stays at nothing.
What is never claimed: That a gap between expected and observed means the draw is broken.

Common use cases

Checking whether a loot table or drop rate behaves as intended
Showing a class why a small percentage still misses often over few trials
Testing a weighted picker before relying on it
Deciding how many trials a rare outcome needs to show up reliably
Settling an argument about whether a run of bad luck is unusual

How this generator works

Weights are summed and each draw picks a point in that total, walking the cumulative sum to find which option owns it. That handles fractional weights exactly, unlike the common shortcut of repeating each option in a list. The expected count is simply the option's share of total weight multiplied by the number of draws — an exact figure, not a simulation — which is what makes the side-by-side comparison meaningful.

Randomness and fairness

Draws use the browser's cryptographic random number generator, over a fine grid so fractional weights are honoured exactly. Give a seed and it switches to a documented generator that is deterministic, not cryptographic — it is for repeatability, not security. The expected counts are arithmetic and involve no randomness at all.

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

Assumptions this tool makes

Draws are independent and the weights stay fixed throughout the run.

Limitations and good to know

Every draw is independent, so this does not model anything with a pity timer, a guarantee after N failures, or a pool that empties.
It shows one run at a time. The distribution of many runs is a different question, which the coin run calculator answers exactly.
Weights are relative and unitless; the tool cannot tell you whether the weights themselves are the right ones.

Common mistakes

Reading a gap between expected and observed as a fault: That gap is what randomness looks like at small numbers, and it is the reason this page shows both columns. Increase the draws and watch it shrink — if it does, the weights are working.
Assuming weights must add up to 100: They are relative. 70/25/5 and 14/5/1 give identical odds, and the page shows the share each weight actually represents.
Expecting a rare option every 1-in-N draws: A 1-in-20 chance does not arrive on the twentieth attempt. Over twenty draws it fails to appear at all about a third of the time, which is the single most common source of 'this is rigged'.

Practical tips

Run 40 draws five times before changing a weight. The variation between those runs is the noise you are trying to see past.
To find out how many draws a rare option reliably needs, raise the count until it stops missing.

Privacy and your data

Your options and weights never leave your browser. Nothing is uploaded, nothing is stored, and nothing is written into the page address. Analytics records that the tool ran and how many draws were made, never the options.

Frequently asked questions

Why did my 5% option not appear in 20 draws?: Because that happens about 36% of the time. A 5% chance means each draw independently has a one-in-twenty chance, not that the twentieth draw is owed. Over 20 draws the probability of never seeing it is 0.95 to the twentieth power, which is more than a third.
Do the weights have to be whole numbers?: No. Fractional weights work exactly, which is why the draw uses a cumulative sum rather than the common trick of repeating each option in a list — that trick only handles whole numbers and falls apart at any scale.
How is this different from the weighted picker?: That one draws a single result to make a decision with. This draws hundreds to show you the distribution and how far a real run strays from the weights. Different questions: one is 'what shall I do', the other is 'is this fair'.