Everyday randomness
Why random numbers repeat
You ask for a number. You get 7. You ask again… another 7. By the third one, you’re giving the screen a suspicious look. Fair enough. Let’s see what’s going on.
Skip to the experimentImagine you’re choosing a number between 1 and 10. You’re happy with anything. You just weren’t expecting to meet the same number quite so often.
After a few sevens, it’s easy to start rooting for the others. What about 3? Has the generator forgotten 9 exists?
Try picturing a bag with ten numbered slips inside. You pull out the 7, show it to everyone, then put it back. Give the bag a shake. Nothing in there has changed: ten slips, one of them a 7.
You remember the last pick. The bag doesn’t.
Maybe a familiar feeling.
Now try both versions of the bag: one where you put each slip back, and one where you leave it out.
Will the 7 come back?
Try a handful of picks. One bag lets numbers come back. The other keeps them out.
Put it back
Repeats allowedAll the numbers get another chance.
Keep it out
No repeatsOnce picked, that number sits this one out.
Give it a go. We’ll draw from both bags.
The amber cards are numbers you’ve already met in that handful. We draw from each bag separately.
Same bag. A different little ritual.
On the “Put it back” side, a number can come back straight away. On the “Keep it out” side, it has had its turn. Once you’ve taken all ten slips out, there’s nothing left to pick.
Try dealing a few times. Some batches from the first bag will look nicely mixed; others will have a number that seems to love the spotlight. Neither result changes the rule. Every new draw still gives each slip the same chance.
That’s all independent picks means here: the last pick doesn’t change the chances of the next one.
Here’s the part that catches people out.
Pick ten times from 1–10, putting the number back each time. Getting all ten different numbers would actually be the unusual result. The chance of a repeat somewhere in those ten picks is about 99.96%.
Give yourself more room—say, numbers from 1–100—and the chance of a repeat in ten picks drops to about 37.2%. Still enough that you shouldn’t be shocked when one turns up.
There’s a small distinction hiding in there. “Will the next number be another 7?” is one chance in ten in our original bag. “Will any number turn up more than once over ten picks?” gives a repeat lots more opportunities to happen.
Show me how you got those percentages
For ten different picks from 1–10, the second pick must avoid one number, the third must avoid two, and so on.
Chance of no repeats:
1 × 9/10 × 8/10 × … × 1/10
Subtract that result from 1 for the chance of at least one repeat. Use 100 instead of 10 for the wider bag. These are calculated chances, not totals collected from readers.
Sometimes you really do want the 7 to sit down.
If you’re picking three different winners, or giving everyone in a class a turn, a repeat is a nuisance. You want to leave each picked slip out of the bag. There’s nothing less random about that; you’ve just chosen a different rule.
Use unique numbers for different numbered picks, or shuffle a list to put everyone in an order. For a fresh chance on every tap, the regular generator is doing the right thing when it lets numbers return.
And if 7 comes up again? You’re allowed to give it a look. Just don’t take it personally.
A small note about the experiment
One short run can’t tell you whether a generator is working properly. This demo uses Web Crypto for its random choices. The first side makes fresh picks; the second shuffles the available numbers and takes them once each. Both sets stay in your browser.
Let everyone have a turn.
Pick numbers without repeats, for the times when one 7 is plenty.
Pick unique numbers