# Does Benford’s Law apply to the lottery?

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## Does Benford’s Law apply to lottery numbers?

Data produced by chance processes on the integers such as lotteries will not follow Benford’s Law because each of the nine digits will be equally represented—but lottery jackpot prizes do obey the Law (Fewster, 2009).

## What does Benford’s Law not apply to?

The law usually doesn’t apply to data sets that have a stated minimum and maximum, like interest rates or hourly wages. If numbers are assigned, rather than naturally occurring, they will also not follow the law. Examples of assigned numbers include: zip codes, telephone numbers and Social Security numbers.

## Can you apply Benford’s Law to anything?

As can be seen, Benford’s Law should be applied only to large data sets. For IT auditors, that would be data such as files with hundreds of transactions (e.g., invoices to customers, disbursements, payments received, inventory items).

## Is Benford’s Law ever wrong?

You would be wrong. The answer is: significantly more. That means that in those sets of naturally-occurring numbers, the probability that a number will start with 1 is just over 30%, while the probability that it will start with 9 is just under 5%. … Probability of a digit starting a number according to Benford’s law.

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## How do you test for Benford law?

Testing Lead Digits Using Benford’s Law

1. Step 1: Select the Sample Data. …
2. Step 2: Parse the Lead Digit. …
3. Step 3: Create a Frequency Distribution. …
4. Step 4: Compute the Expected Distribution. …
5. Step 5: Plot the Results. …
6. Step 6: Perform a Chi-square Test. …
7. Step 7: Reach a Conclusion; Are the Data “Natural?”

## What is the reason for Benford’s Law?

Since the 1990s, a phenomenon known as Benford’s law has been held aloft as a guard against fraud – as a way to check whether data sets are free from interference. Benford’s law tells us something about the frequency of leading digits in natural data sets – that is, how many numbers beginning with 1s, 2s, 3s, etc.

## How does the IRS use Benford’s law?

The agency’s arsenal also includes a mathematical truth known as Benford’s law. Armed with this law, the IRS can sniff out falsified returns just by looking at the first digit of numbers on taxpayers’ forms. … In the number set 0 to 199, over half of the numbers start with 1, and less than 6 percent start with 2 to 9.

## Does Benford’s law apply to the second digit?

Most subjects exhibit fabrication patterns that conform to Benford’s law for the first digit, but not for the second or higher-order digits.

## How reliable is Benford’s Law?

Unfortunately, my analysis shows that Benford’s Law is an unreliable tool. And, as one applies more sophisticated methods of estimation, the results become increasingly inconsistent. Worse still, when compared with observational data, the application of Benford’s Law frequently predicts fraud where none has occurred.

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