# Benfords Law Lottery Numbers

### Benford’s Law and The Lottery! Lottery Post

Benford’s Law and The LotteryBenford's law, also called the first-digit law, states that in lists of numbers from many real-life sources of data, the …

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### Benford's law Wikipedia

1. A set of numbers is said to satisfy Benford's law if the leading digit d (d ∈ {1, ..., 9}) occurs with probability 1. P ( d ) = log 10 ⁡ ( d + 1 ) − log 10 ⁡ ( d ) = log 10 ⁡ ( d + 1 d ) = log 10 ⁡ ( 1 + 1 d ) {\displaystyle P(d)=\log _{10}(d+1)-\log _{10}(d)=\log _{10}\left({\frac {d+1}{d}}\right)=\log _{10}\left(1+{\frac {1}{d}}\right)} The leading digits in such a set thus have the following distribution: The quantity P ( d ) {\displaystyle P(d)} is proportional to the space between d and d + 1 on a logarithmic scale. Therefore, this is the distribution expected if the logarithms of the numbers (but not the numbers themselves) are uniformly and randomly distributed. For example, a number x, constrained to lie between 1 and 10, starts with the digit 1 if 1 ≤ x < 2, and starts with the digit 9 if 9 ≤ x < 10. Therefore, x starts with the digit 1 if log 1 ≤ log x < log 2, or starts with 9 if log 9 ≤ log x < log 10. The interval [log 1, log 2] is much wider than the interval [log 9, l...

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### (PDF) Benford’s Law and Number Selection in FixedOdds

Benford’s Law and Number Selection in Fixed-Odds Numbers Game. There are many ways in whic h number lottery games can be organized. In a parimutuel.

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### Benford's Law: Theory and Applications Chapter 1

guess each number occurs one-ninth of the time and not one-tenth of the time, as 0 is the leading digit for only one number, namely 0). The content of Benford’s Law is that this is frequently not so; speciﬁcally, in many situations we expect the leading digit to be dwith probability approximately log10 d+1 d, which means the

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Benford’s Law. Take a collection of seemingly random numbers, for instance the gross domestic product of 212 countries, and then examine the leading digit. For instance, for the number $435 million (the 2015 GDP of Tonga) the leading digit is 4. The leading digits will of course be from 1-9, since 0 cannot be a leading digit. Posted in: Law Commons ### Does Benford's Law apply to lotto results? Quora Answer (1 of 3): Reading up on this and my experience with with writing code for my lottery program I would say no.. it speaks more of coincidences of a wide scale than actual facts on one event.. Keep in mind that when the numbers are drawn that is what i … Posted in: Law Commons ### Fraud detection using Benford’s Law (Python Code) by The frequency of occurrence of leading digits according to Benford’s law. Newcomb noticed that the pages in the front, used for numbers beginning with the lowest digits, were more worn than those in the back’s and that’s why the leading digits were much more likely to be small than large. Then, in 1938, physicist Frank Benford rediscovered the theorem of … Posted in: Law Commons ### Lottery algorithm based on Benford's Law that will make mikestratton / lottery.php. Created 6 years ago. Star 1. Fork 1. Star. Lottery algorithm based on Benford's Law that will make your rich! Raw. lottery.php. Posted in: Law Commons ### Understanding and Applying Benfords Law ISACA Understanding and Applying Benford’s Law. Date Published: 1 May 2011. There are many tools the IT auditor has to apply to various procedures in an IT audit. Almost all computer-assisted audit tools (CAATs) 1 have a command for Benford’s Law. 2 This article will attempt to describe what Benford’s Law is, when it could apply and what Posted in: Law Commons ### Benford's Law *Predicts* Random Numbers! YouTube Benford's Law shows up all over the place, and most people have no clue.Source: Probability Laws Get You Free Drinks!https://youtu.be/78BdGh0vvi4Scam School Posted in: Law Commons ### Benford's law presentation .pdf BENFORD\u2019S LAW What Qº Which one doesn’t follow ()Benford’s Law%& a³ Population b³ Lottery jackpot prizes c³)*Company stock market values d³.Gas prices e³ Population density Q Who is ()Benford’s Law named after%& a³ Tommy ()Benford b³ Mark ()Benford c³ -Franklin ()Benford d³ … Posted in: Pdf Law ### Effective Use of Benford's Law vided demonstrating where Benford’s law proved successful in identifying fraud in a popula-tion of accounting data. INTRODUCTION In the past half-century, more than 150 articles have been published about Benford’s law, a quirky law based on the number of times a particular digit occurs in a particular position in numbers (Nigrini 1999). Posted in: Law Commons ### Benford's Law Calculator ezcalc.me Benford’s Law. Established empirically, the Benford’s law, also called the Newcomb–Benford law, the law of anomalous numbers, or the first-digit law, claims that many, but not all, data sets with a natural origin, including the results from mathematical operations, might produce relative frequencies for the first digit where the occurrence of the smaller numbers is higher than that … Posted in: Law Commons ### statistics Benford's law with random integers Benford's law does apply to random integers, but only as the upper and lower bounds go to infinity. The limit lim N → ∞ P N 1 ( 1) (the proportion of integers from 1 to N which have a leading digit of 1, as N goes to infinity) diverges, and equals 1/9 at every 10 n, n ≥ 2, which explains my result. If I set the upper bound on the random Posted in: Law Commons ### Following Benford's Law, or Looking Out for No 1 BenfordS Law 1990 census 6.7% 5.8% 7.9% 30 . 20. o 17.6% 12.5% much dirtier and more worn Than —0 + Aid). Thisformuia predicts the frequencies of numbers found in other pages. (A logarithm is an exponent. Any many categories of statistics. FIRST SIGNIFICANT DIGIT Dow Illustrates Benford's Law TO illustrate Benford's Law, Dr. Mark J. Nigrini Posted in: Form Law ### Find Financial Fraud with Benford's Law Invest Excel There’s a certain logic to Benford’s Law. A number that begins with 1 needs to increase by 100% to become a 2. A number that begins with 5 needs to increase by 20% to become a 6. A number that begins with 9 needs to increase by 11% to become a 0. That is, an increasing number spends more time with 1 as the leading digit than 2, more time Posted in: Law Commons ### Benford's Law — Indicator by GrantPeace — TradingView About. As seen in "Digits", the fourth episode of the Netflix series Connected, Benford's Law is applicable to almost every data set that is said to be randomly occurring such as the global financial markets. The law is most frequently used for surveillance and detection of fraud, money laundering, and manipulation of data. Posted in: Law Commons ### What is Benford’s Law and why is it important for data Posted in: Law Commons ### Benford's Law and Photography Nouspique The counterintuitive idea behind Benford’s Law is that if you take a given data set of numbers (e.g. all the street addresses in a city), the lowest first digit (1) occurs more frequently than any other, the 2nd lowest (2) occurs more frequently than any other except 1, and so on …. We tend to think the distribution of first digits in any Posted in: Law Commons ### Benford’s Law Made Easy Fraud Magazine Using Benford’s Law, the method involves finding a pattern in the frequency of digits in a list of figures, beginning from the far-left digit in a figure. As he wrote in the article, digital frequencies refer to the proportion of numbers that have a 1, 2, ¦ 9 as a first digit, and the proportion of numbers that have a 0, 1, ¦ 9 as a second Posted in: Law Commons ### Does Benford's law apply to prime numbers? 1. The answer to our question clearly depends on where the prime numbers come from. It is very difficult to quantify the instructions "pick a random integer" or "pick a random prime" in a way in which satisfies the most basic laws of probability. To see what we mean let A and B be subsets of the positive integers N. If P(A) is the probability that the "random" integer we pick is in the set A, then we would need that Now if each integer is equally likely, we then have so P( {1} ) < 1/n for every integer n. The probability of picking any one integer (hence any set of integers), would have to be zero! So when we say "pick a random integer" we can not pick from the whole set of positive integers with each integer being equally likely. (See [Raimi1969] and [Raimi1976] for a deeper discussion of these issues and Benford's law.) Posted in: Law Commons ### Using Spreadsheets and Benfords Law to Test Accounting Data 1. Take the case of someone who wants to evaluate corporate purchase invoices—a popular target of corporate abuse. Although the amount of information contained in each invoice is likely to be considerable, this example will focus only on the purchase amounts. The goal of applying Benford’s Law here is to know how “natural” such transactions are. Step 1: Select the Sample Data The first task is to obtain sample test data and store them in an Excel spreadsheet—the more observations included, the better. Using the data for a complete year is best, but if the number of items is large, smaller samples are permissible. For statistical reasons, however, there should be at least 100 observations. Step 2: Parse the Lead Digit As noted previously, Benford’s Law focuses on the lead digit in sets of naturally occurring numbers. The actual magnitude of the data (i.e., whether an amount is$10, $100 or$1,000) is unimportant. In a spreadsheet, one can select or “parse” the lead digit for each dollar...

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### Benford's law Rosetta Code

Benford's law, also called the first-digit law, refers to the frequency distribution of digits in many (but not all) real-life sources of data.. In this distribution, the number 1 occurs as the first digit about 30% of the time, while larger numbers occur in that position less frequently: 9 as the first digit less than 5% of the time.

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### Benford’s Law & Cryptocurrency Trading Data BitMEX Blog

Benford’s Law & Cryptocurrency Trading Data. BitMEX Research. 21 Nov 2019. Abstract: In this report we examine Benford’s law, a mathematical rule which describes the frequency of the leading digit in various real world sequences of numbers. We look at various datasets from the cryptocurrency ecosystem, such as coin prices and trading volume

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### Benford’s Law: Textbook Exercises and MultipleChoice

Benford’s Law describes the finding that the distribution of leading (or leftmost) digits of innumerable datasets follows a well-defined logarithmic trend, rather than an intuitive uniformity. In practice this means that the most common leading digit is 1, with an expected frequency of 30.1%, and the least common is 9, with an expected frequency of 4.6%.

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### Benford's Law for Phone Numbers Statalist

Benford's Law for Phone Numbers. 28 Sep 2018, 23:51. I understand that Benford's law aren't used for "non-natural" numbers such as telephone numbers because they communicate systematic information. However in a number such as this. 888-999-4346.

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### Benford's law CivFanatics Forums

This means that if, for instance, you decided to pick up all the numbers in the front page of various newspapers, thus ending with random numbers from random sets (lottery numbers, temperatures, casualties, etc.), then on average 30.1% of these numbers would start with a 1, 17.6% would start with a 2, and so on

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### Using Excel and Benford’s Law to detect fraud Journal of

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### Benford's Law EDN

Dow Illustrates Benford's Law. To illustrate Benford's Law, Dr. Mark J. Nigrini offered this example: “If we think of the Dow Jones stock average as 1,000, our first digit would be 1. “To get to a Dow Jones average with a first digit of 2, the average must increase to 2,000, and getting from 1,000 to 2,000 is a 100 percent increase.

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### Benford's Law calculator fx Solver

Benford's Law, also called the First-Digit Law, refers to the frequency distribution of digits in many (but not all) real-life sources of data. In this distribution, 1 occurs as the leading digit about 30% of the time, while larger digits occur in that position less frequently: 9 as the first digit less than 5% of the time. Benford's Law also concerns the expected distribution for digits

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### IDEA Tech Tip: Using Benford's Law CaseWare IDEA

Benford’s Law is always a popular topic in the audit and forensic accounting world. This rule, which predicts how often you should expect to see numbers 1 through 9 as the leading digits in accounts payable, deposits, disbursements and other select large data sets, can be an invaluable tool to detect potential fraud.

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### The Benford’s Law Hustle™ NoahSD's Awesome Poker Blog

1. Do a quick experiment for me: Open a random article in Wikipedia by clicking here. (I didn’t doctor that link or anything, but if you don’t trust me, feel free to navigate to Wikipedia the old-fashioned way. The random article link can be found on the left of any article’s page.) Find the first number in the article and remember its first digit. (If there isn’t a number, go to another random article.) Repeat this three times. The vast majority of you will have been a one or a two. Only about one in six of you will have seen an eight or a nine. Weird, huh? However, there’s also a pretty good chance that you noticed a gimmick when you did that, and you might think you figured this out. If you didn’t, check out the Wikipedia page for the Nobel Prize in Physics. The first number in that article is 1895, which does indeed start with a one, but, it’s a year. Wikipedia probably references a lot more years after the year 1000 than before the year 1000, so of course years appearing on Wikipe...

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### Detecting numeric irregularities with Benford’s Law – The

A team of German economists applied a Benford’s law analysis to the accounting statistics reported by European Union member and candidate nations during the years leading up to the 2010 EU sovereign debt crisis. They found that the numbers released by Greece showed the highest degree of deviation from the expected Benford’s law distribution.

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### An Introduction to Benford's Law Chapter 1

agrees with Benford’s law” [98]; and Z. Shengmin and W. Wenchao found that “Benford’s law reasonably holds for the two main Chinese stock indices” [148]. In the ﬁeld of biology, E. Costas et al. observed that in a certain cyanobacterium, “the distribution of the number of cells per colony satisﬁes Benford’s law” [39,

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### (PDF) Benford’s Law and Naturally Occurring Prices in

Benford’s Law suggests that the first digits of numerical data are heavily skewed towards low numbers. Data that fail to conform to Benford’s Law when conformity is …

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### Numbers follow a surprising law of digits, and scientists

On the other hand, data sets that are arbitrary and contain restrictions usually don’t follow Benford’s law. For example, lottery numbers, telephone numbers, gas prices, dates, and the weights

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### Understanding Benford’s Law Live Trading News

Distributions that would not be expected to obey Benford’s law. Where numbers are assigned sequentially: e.g. check numbers, invoice numbers; Where numbers are influenced by human thought: e.g. prices set by psychological thresholds ($1.99) Accounts with a large number of firm-specific numbers: e.g. accounts set up to record$100 refunds

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### Benford's Law Fraud Detection Software Cyber Security

Benford’s law, also known as the ‘Law of First Digits’ expects the count of the 1st digit in a number to occur a known set amount of times in a set of data. The basic principal being within any natural dataset the 1st digit of a number will start with 1 more times than a …

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### Benford’s Law and Temperature Fraud Musings from the Chiefio

The idea depends on Benford’s Law which states that the frequency of the first digit of many data sets will have a log distribution so that more will be a 1 and decreasing down to very few being a 9. There are limits to Benford’s Law. One being that the data are more likely to obey it when they span a few orders of magnitude.

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### Do Random Number Generators Follow Benford's Law

The random number generator did not generate truly random numbers. In Benford's Law, the range is 35.3%, but for the generators data, it only was 5.8%. Also, in Benford's Law, the likelihood of a certain first digit occurring decreases chronologically. However, in these findings, there was no logical order in the likelihood of the digits.

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### Detecting Manipulations in Data with Benford's Law – A C#

1. If you have ever taken a statistics class, at some point you undoubtedly had a homework assignment to flip a coin a few hundred times and record the results for a class experiment the next day. Think back—were you tempted perhaps to take a short cut and just scribble some results down ("H/T/H/T/H/T") without actually flipping that annoying coin? Well, of course—it's only natural for students to take shortcuts when they think they can get away with it. Besides, you know the expected result, right? There are bound to be equal numbers of heads and tails… Maybe you even thought you'd be clever and mix the results around a little so they look believable. Well… what if we told you that using just the results and a mathematical phenomenon known as Benford's Law, we could pick out the cheaters from a room full of bored statistics students? Read on, and we'll show how this rare bit of magic can be not only surprising, but surprisingly useful as well. In fact, we'll give you a C# class and sa...

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### The Benford’s Law Purpose Driven Math

The Benford’s describes the first digits amazingly accurately on many natural data sets. The most striking thing about the law is the lopsided frequencies in favor of the lower digits, with 1 showing up around 30% of the times and with the …

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### Proof of Benford's Law Physics Forums

May 4, 2020. May 4, 2020. #1. etotheipi. The significant digits of numbers in sets of numerical data supposedly follows "Benford's Law", which asserts that the probability that the first digit in a given data point is is about . An upshot is that we expect ~30% of significant digits to be . The proof is outlined here and I can follow their

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### Benford’s Law Blog Bellew

Benford’s law, also called the Newcomb–Benford law, the law of anomalous numbers, or the first-digit law, is an observation about the frequency distribution of leading digits in many real-life sets of numerical data. The law states that in many naturally occurring collections of numbers, the leading significant digit is likely to be small.

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### Benford's Law – DIY Big Data

In this post, I discuss how to use Benford’s Law to identify non-human actors in user interaction logs. Application of Benford’s Law Benford’s Law is an observation that a collection of numbers that measure naturally occurring events of items tend to have a logarithm frequency distribution for the first digit of these numbers.

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### Need suggestions about using Benford's Law : sportsbook

Need suggestions about using Benford's Law. I have designed and using a betting prediction model based on Benford's law. Initially I didn't think much of it. Recent numbers started showing mysterious patterns. Everyday one of my picks run to 10 odds (Twice to 20+) and win from there. And there is always an 3-5 odd winner everyday as well.

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### Amazon.com: An Introduction to Benford's Law

ISBN-10 ‏ : ‎ 0691163065. ISBN-13 ‏ : ‎ 978-0691163062. Item Weight ‏ : ‎ 1.5 pounds. Dimensions ‏ : ‎ 6.4 x 0.8 x 9.3 inches. Best Sellers Rank: #715,065 in Books ( See Top 100 in Books ) #980 in Statistics (Books) #1,576 in Probability & Statistics (Books) Customer Reviews: 4.9 out of 5 stars.

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### Does Benford's law apply to lottery games?

With that in mind, Benford’s Law DOES apply to lottery games and here is how we can observe it: First, you must disregard the actual numbers on the balls, at least to the extent that the frequency of the actual numbers are not what you are tracking. In Pick 3, we don’t expect the digit 1 to be drawn more often than the digit 8.

### What is Benford's law in math?

“Benford's law, also called the first-digit law, states that in lists of numbers from many real-life sources of data, the leading digit is 1 almost one-third of the time, and larger numbers occur as the leading digit with less and less frequency as they grow in magnitude, to the point that 9 is...

### How do you use Benford's law to spot Fraud?

WHEN TO USE BENFORD'S LAW TO SPOT FRAUD. Briefly explained, Benford's Law maintains that the numeral 1 will be the leading digit in a genuine data set of numbers 30.1% of the time; the numeral 2 will be the leading digit 17.6% of the time; and each subsequent numeral, 3 through 9, will be the leading digit with decreasing frequency.

### How do you apply Benford's law to frequency distribution?

To apply Benford’s Law, therefore, an accountant must count the number of times a 1 appears as the lead digit in the data values, the number of times a 2 appears, etc., and then examine the resulting frequency distribution. The distribution is “natural” if it follows Benford’s distribution, and suspect otherwise.