Oh no! Here come the statisticians

What are the odds of hundreds of replies to a simple question?

  • alert
  • submit to reddit

Secure remote control for conventional and virtual desktops

[Lucy wrote about a man who claimed to have random pressed buttons on a remote control and suddenly been able to order pizzas and limos on someone else's credit card. Hmmm. Anyway, she asked what the odds were that you could randomly get a credit card number and expiry date right. All those budding mathematicians out there saw your chance]

Digital shopping fraud was a fluke, claims crook

With reference to your story about the alleged on-line credit card fraud, you asked for any calculations of the probability of the random number entry resulting in one correct sequence.

Assuming that all the numbers in a credit card sequence after the 4 digit card type id at the start are equi-probable, just working on the card number and ignoring the expriry date results in a probability of 0.1^12, or one in a billion.

Some of the assumptions may be wrong, but he would have had to enter 12 numbers in a row with a probability of getting each one correct as one in ten.

If you include the first 4 digits and the date, then the likelihood of success drops by a tenth for each number.

Not exactly a watertight defence.

Ed Doxat

Assuming a 10 digit credit card, and a 4 digit date (mmyy), the odds are:

10^10 * 12 * 4 (assuming that the cracker will only use the next 4 years as a credit-card expiration).

What this gives us is: 480,000,000,000 to one.

Approximately, of course.


Assuming a credit card number has the form: xxxx-xxx-xxx-xxx, this gives 10^13 possible credit card numbers; the expiry date has the form: MM / YY

Assuming a card is valid for ~5 years, and given there are 12 months / year, this gives at maximum 60 possible expiry dates; therefore the odds of getting the right combination of credit card number and expiry date, purely by luck, are in the region of 1 in 60 * 10^13, or, if you like, 1 in 600,000,000,000,000.

To put it another way, you're over a million times more likely to win the lottery...

James Nichols

Just a first approximation, but assuming there are about 200 million Visa users in the world:

200E+6 / (10^15) (12) (6)

^15 digits ^12 months ^six years of dates

= 2.78E-9 or about 1 in 360 million

Looks like our friend should have put his money into the lotto, he'd have better odds.

Larry Bernstone

1 in 100,000,000,000,000,000,000

Useless statistic: at a rate of one attempt every thirty seconds, it would take on average 47,564,687,975,646 years to come up with the first valid combination.

Andy Crawford

Assuming a 16 digit credit card number, and one of the next 48 months as a possible expiration date, and one valid credit card number for each man, woman and child on earth (6 billion), the odds are 80 million to one that you would get make a valid, random entry on the first try.

Joe Fitzgerald

Basically to guess a number between 0 and 9 you have a one in ten chance, to guess two numbers correctly you have a one in hundred chance (1/10 * 1/10). So the chance of getting all 16 numbers correct is about 1 in 10000000000000000. It is about a 1 in 1000 odds to get the corresponding expiry date so in total the odds of this rather sad man doing what he said is:

1 in 1000000000000000000

This will probably be proved wrong by someone with more maths sense than me, but what the hey, it looks OK...

Johnny Malcolm

[That's enough. Sorry to all those that didn't make it. This was a completely random selection]

Beginner's guide to SSL certificates

More from The Register

next story
Holy vintage vehicles! Earliest known official Batmobile goes on sale
Riddle me this: are you prepared to pay US$180k?
'Open source just means big companies can steal your code.' O RLY?
Plus: Flame of the Week returns, for one night only!
Bible THUMP: Good Book beats Darwin to most influential tome title
Folio Society crowns fittest of surviving volumes
Microsoft to bring back beloved 1990s super-hit BATTLETOADS!?*
* Or maybe not. It is just a trademark filing, after all
U wot? Silicon Roundabout set to become Silicon U-BEND
Crap-spouting London upstarts to get permanent road closure
Hey, you, PHONE-FACE! Kickstarter in-car mobe mount will EMBED your phone into your MUG
Stick it on the steering wheel and wait for the airbag to fire
NEWSFLASH: It's time to ditch dullard Facebook chums
Everything hot in tech, courtesy of avian anchor Regina Eggbert
Fire fighters call for no-drone zone around bushfires
UAVs can take down water-spaffing 'copters, so firies want them to butt out
prev story


Why cloud backup?
Combining the latest advancements in disk-based backup with secure, integrated, cloud technologies offer organizations fast and assured recovery of their critical enterprise data.
A strategic approach to identity relationship management
ForgeRock commissioned Forrester to evaluate companies’ IAM practices and requirements when it comes to customer-facing scenarios versus employee-facing ones.
Reg Reader Research: SaaS based Email and Office Productivity Tools
Read this Reg reader report which provides advice and guidance for SMBs towards the use of SaaS based email and Office productivity tools.
Choosing a cloud hosting partner with confidence
Download Choosing a Cloud Hosting Provider with Confidence to learn more about cloud computing - the new opportunities and new security challenges.
New hybrid storage solutions
Tackling data challenges through emerging hybrid storage solutions that enable optimum database performance whilst managing costs and increasingly large data stores.