One for the mathematicians

[DaveO1959]

I saw this in the Accuraterip documentation:

"For example 100 people rip Madonnas latest CD, of those 100 twenty have errors, the other 80 all have identical rips. If you were to rip your Madonna CD there are 2 possibilities, AccurateRip would report that 80 other people agree with your rip (confidence of 80), or that 80 disagree if your had errors. What are the odds of 80 people agreeing with your rip, but they really had a bad rip (ie those 80 people had bad rips which happened to give the same check code)? the odds are 4 billion x 4 billion (repeated 80 times), an astronomical number. If more than 3 people agree with your rip, it is 100% certainty it is accurate."

Can anyone explain the math behind that 4 billion x 4 billion x 80 number?

[Michael Sargent]

Re: One for the mathematicians

I'll take a shot at it...

4 billion is (about) the total number of values that can be represented with an unsigned 32-bit number. So, if you calculate the AccurateRip "signature" of a track as a 32-bit number, then there is only one correct value, and about 4 billion incorrect values. So the odds of two people getting the same AccurateRip signature for bad rips are one-in-four-billion (your odds of getting the value) times one-in-for-billion (the odds of someone else getting the same value). For each additional user, the odds are one-in-four-billion less (so we multiply).

The odds should be read as 1/4B x 1/4B x 1/4B x ... 77 more times ... x 1/4B (not 1/4B x 1/4B x 80).

Now can I have breakfast? :-)

[DaveO1959]

Re: One for the mathematicians

I'll take a shot at it...

4 billion is (about) the total number of values that can be represented with an unsigned 32-bit number. So, if you calculate the AccurateRip "signature" of a track as a 32-bit number, then there is only one correct value, and about 4 billion incorrect values. So the odds of two people getting the same AccurateRip signature for bad rips are one-in-four-billion (your odds of getting the value) times one-in-for-billion (the odds of someone else getting the same value). For each additional user, the odds are one-in-four-billion less (so we multiply).

The odds should be read as 1/4B x 1/4B x 1/4B x ... 77 more times ... x 1/4B (not 1/4B x 1/4B x 80).



Now can I have breakfast? :-)

Have some toast