Whats the right id lenght for 0,00000001% chance of collision?

[User124125]

Hi there,

in the description its stated that :

"by default, you'd need to generate roughly 4,000,000,000,000,000,000 ids ... to reach 50% chance of collision"

I feel like 50% chance of collision is quite scary. So the big number 4,000,000,000,000,000,000 doesnt realy persuade me.

Im more interested in a close to 0% chance of collision...

How do I find out which length is the right for me if I want 0,00000001% chance of collision ?

Or do I just set it to maxLength 98 and hope for the best?

Sry If this is too nooby of a question. Maybe the docs could get a different formular other than sqrt(36^(n-1)*26) So people can calculate how to be more collision safe in their projects.

[JoltCode]

Hi there,

in the description its stated that :

"by default, you'd need to generate roughly 4,000,000,000,000,000,000 ids ... to reach 50% chance of collision"

I feel like 50% chance of collision is quite scary. So the big number 4,000,000,000,000,000,000 doesnt realy persuade me.

Im more interested in a close to 0% chance of collision...

How do I find out which length is the right for me if I want 0,00000001% chance of collision ?

Or do I just set it to maxLength 98 and hope for the best?

Sry If this is too nooby of a question. Maybe the docs could get a different formular other than sqrt(36^(n-1)*26) So people can calculate how to be more collision safe in their projects.

Just to be clear, you'll only reach this 50% chance of collision at 4,000,000,000,000,000,000 - the chance of collision increases as you decrease entropy, or, by generating more ids. And to put in perspective how ridiculously large this number is, the population of earth in 2024 is roughly 8 billion. Every single human would need therefore need around 500 million ids each (810^9 500,000,000) = 4,000,000,000,000,000,000 (or 4*10^18) to reach 50% chance of collision. So you probably don't need more than this.

Still concerned? You can always increase the entropy as you suggested, but beware, that will come at a performance cost.

[ericelliott]

The chance of collision depends very much on how many IDs you want to generate, so instead of answering your question directly, I'll tell you how many IDs you can generate by default with less than 10^-10 chance of collision: ~57 trillion. Or roughly 7,000 IDs for every human in the world.

[User124125]

The chance of collision depends very much on how many IDs you want to generate, so instead of answering your question directly, I'll tell you how many IDs you can generate by default with less than 10^-10 chance of collision: ~57 trillion. Or roughly 7,000 IDs for every human in the world.

First thank you for the answers and the project !

Lets say I wanted to use the ids for something like wikipedia , 7000 ids for every human in the world seems reachable over a span of 40 years uptime or so .... articles on articles will be added to the system and at some point it will just secretly fail ...

thats why i was asking for a formular, so one could calculate for their own project and determine the point of failure roughly and can act beforehand.

You said your calculation uses the default length ... would you be willing to share the formula so one would be able to calculate with variable id length ?

[ericelliott]

First, even if you were the most popular site in the world, YouTube, you'd get roughly 262 million posts per year x 40 years = ~10.5 billion posts x 2.5 average interactions per post - and even after 40 years, there's still an infinitesimally small chance of a single collision using default values.

Here's the formula - this is the birthday paradox square root approximation adapted to the structure of CUID2 values:

• n: The number of IDs you can generate before reaching the specified probability of collision.
• 36^(l-1):
  • 36: Represents the number of possible alphanumeric characters (0-9, a-z) that can be used for each subsequent character in the ID.
  • (l-1): Represents the total number of characters in the ID minus one (the first character is always a letter).
• 26: Represents the 26 possible lowercase letters for the first character in the ID.
• log(1/(1-p)):
  • p: The probability of collision.
  • log: The natural logarithm, used here to scale the collision probability.
• 1/(1-p):
  • 1-p: This is the probability that no collision occurs.
  • 1/(1-p): Invert to get the likelihood of collision.