PIN: Is there a mathematician in the house?

Mr_McGee

Hello... I was issued with a PIN where 3 digits were the same. It was easy to remember but I didn't think it was secure so I changed it. Should I have been worried?

never-in-doubt

no - no reason to be worried! I got one sent with 2922 and another with 4404 and all was fine!

Random number generator eat your heart out!

p00hsticks

If you think about it there are only 10,000 different combinations of PINs available to allocate (from 0000 to 9999) . If the banks started removing those that consist of four digits the same (of which there are ten) and those that contain three digits the same (of which there are 90) and those which consist of consecutive digits such as 1234, then there is more chance that people are going to end up with the same PINs as each other !

Each combination is as likely to be randomly selected as the next, but if you're not happy with it then do as you have done and change it to something different.

I'd guess that if most people were asked to list four digits at random they'd pick four different numbers - it's just the way the human mind works. So going by that hypothesis, if you're worried about someone guessing your pin you are probably safer with a pin in which at least one digit is repeated....

CannyJock

Mr_McGee wrote: »

Hello... I was issued with a PIN where 3 digits were the same. It was easy to remember but I didn't think it was secure so I changed it. Should I have been worried?

There's a 1 in 10,000 chance of guessing a 4 digit number regardless if the digits are the same or not

So what's the 4 different digits you set it to? 1234?

Mr_McGee

Thanks NID & p00hsticks.

BTW is there anything MSEs don't know something about?!!:D I am a first time poster but a long time lurker so thank you and all the regulars for your contributions.

Mr_McGee

CannyJock wrote: »

There's a 1 in 10,000 chance of guessing a 4 digit number regardless if the digits are the same or not

Thanks CJ... what is the probability of guessing right if you assume 3 digits are the same?

NickX

Mr_McGee wrote: »

Thanks CJ... what is the probability of guessing right if you assume 3 digits are the same?

On the assumpton that 3 of the digits are the same, the probabilty of guessing correctly is 1 in 400.

CannyJock

Mr_McGee wrote: »

Thanks CJ... what is the probability of guessing right if you assume 3 digits are the same?

Well, you've got 111, 222, 333, 444, 555, 666, 777, 888, 999, 000, so that's 10 sets of digits.

Your fourth digit is 1 of 10 from the set 1234567890 so that's 100 basic combinations. But the fourth digit can be in 1 of 4 positions so 0111, 1011, 1101, 1110 giving you a total of 400.

If you want to exclude the sets where all 4 digits are the same, then your 4th digit can only be 1 of 9 values, so that's 90 basic combinations and a total of 360.

That's how I'm reading it - but need more coffee so could be talking nonsense

EDIT: Looks right, Nick's got the same number

Mr_McGee

Thanks for that Nick & CJ. Perhaps it is just psychological after all... it's the first time I have ever changed my PIN!

chattychappy

Just looking at the maths, I would say no. If you had 4 digits the same, then maybe a small worry. Someone finding the card might well guess a sequence had been used (this is the best they could do) - so might try repeated sequences. As there are only 10 combinations, the chances of guessing first time is 1/10, guessing second time is 1/9, guessing third time is 1/8. So the chances of guessing before blocking = 1 - (9/10 x 8/9 x 7/8) = 3/10, or 30%.

I suppose some combinations are more likely - eg 0000 or 9999.

So you see, even with 4 digits the same things are not too bad.

For 3 digits the same (and 4th one different), the maths is more complicated:

Number of digits that could make up the repeated digit = 10
Number of digits that could make up the "other" digit = 9
Number of positions the "other" digit could appear in = 4

Therefore the number of combinations with 3 digits the same = 10 x 9 x 4 = 360.

Even if you told someone that you had 3 digits the same, the chances of them guessing first time are 1/360. The chances of them blocking the card with 3 unsuccessful attempts = 359/360 x 358/359 x 357/358 = 357/360 = 99.2%

So there is a less than 1% chance that even if you told someone you had 3 digits the same, they would guess the number before blocking the card.

I think the biggest risk is non-mathematical. It maybe easier for someone to see and remember what you type onto a pad if there are repeated digits. And again, some combinations are probably riskier than others - eg 0001...

chattychappy

CannyJock wrote: »

EDIT: Looks right, Nick's got the same number

Me too, working independently....