Is excel random really random

To understand if Excel’s RAND() or RANDBETWEEN() functions are truly random, it’s essential to grasp the concept of “pseudo-randomness.” Here are the detailed steps to demystify this:

1. Understand Pseudo-Randomness: Excel’s random number generators are not truly random in the physical sense. They are pseudo-random number generators (PRNGs). This means they use a deterministic algorithm that starts with a “seed” value to produce a sequence of numbers that appear random and pass various statistical tests for randomness. Think of it like a highly complex recipe: give it the same initial ingredients (the seed), and it will always produce the exact same “random” sequence. This is why if you open an Excel sheet with RAND() formulas, the numbers will recalculate and change every time you make an edit or press F9. This isn’t true randomness; it’s just a new iteration of the algorithm.

2. How RAND() Works:

   • Function: RAND()
   • Output: Generates a new pseudo-random real number greater than or equal to 0 and less than 1 (i.e., 0 <= n < 1) each time the worksheet is calculated.
   • Key Aspect: This is the foundational PRNG in Excel, upon which RANDBETWEEN() often relies internally. The numbers it generates are designed to be uniformly distributed across its range. If you plot enough RAND() outputs, they should form a relatively flat histogram.

3. How RANDBETWEEN() Works:

   • Function: RANDBETWEEN(bottom, top)
   • Output: Generates a new pseudo-random integer between bottom and top (inclusive) each time the worksheet is calculated.
   • Mechanism: It essentially scales and rounds the output of a RAND() like function to fit within the specified integer range. For example, RANDBETWEEN(1,10) will give you integers from 1 to 10.
   • Consideration: For small ranges and a low number of samples, you might observe what appears to be non-uniformity. This is often due to insufficient sample size rather than a flaw in the algorithm itself. For statistical validity, you need a large sample.

4. Implications of Pseudo-Randomness:

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   • Reproducibility: If you know the algorithm and the initial seed, you can reproduce the sequence of “random” numbers. This is why for cryptographic security, PRNGs are generally not used directly without further enhancements, as their predictability makes them vulnerable. For general simulations and modeling in Excel, however, this characteristic is usually not a concern and often beneficial if you need to rerun a simulation with the same “random” inputs.
   • Statistical Properties: While not truly random, Excel’s PRNGs are designed to exhibit statistical properties of true random numbers, such as uniformity (each number in the range has an equal chance of being selected) and independence (the selection of one number does not influence the selection of the next). They pass most standard statistical tests for randomness for the purposes they are intended.
   • Limitations: For highly sensitive applications like advanced scientific research requiring unpredictable sequences or strong cryptographic keys, dedicated hardware random number generators (HRNGs) or cryptographically secure pseudo-random number generators (CSPRNGs) are used, which often incorporate external entropy sources (e.g., atmospheric noise, hardware timing) to achieve true unpredictability.

5. Testing for Apparent Randomness: You can perform basic statistical tests, like a Chi-Squared test for uniformity, to check if the numbers generated by RANDBETWEEN() (or RAND() transformed to integers) are uniformly distributed. Our tool above demonstrates this. A high p-value suggests the distribution is consistent with uniformity, while a low p-value might indicate a deviation from expected uniform behavior, potentially due to too few samples or a real (though unlikely) issue. Remember, is random really random? No, not truly in the absolute sense, but is excel rand truly random enough for practical purposes? Yes, it largely is. is excel randbetween really random? For most simulation and educational tasks, it’s sufficiently “random.”

The Illusion of Randomness: Deconstructing Excel’s RAND() and RANDBETWEEN()

The question “is Excel random really random” is a fascinating one, sitting at the intersection of practical computing and theoretical statistics. To get straight to the point, no, Excel’s random number generators (RNGs) like RAND() and RANDBETWEEN() are not “truly random” in the pure, unpredictable, quantum-level sense. They are pseudo-random number generators (PRNGs). This distinction is crucial, but for the vast majority of users and applications, Excel’s PRNGs are perfectly adequate and behave as if they were random. Let’s deep-dive into what that means and why it matters.

Understanding Pseudo-Random Number Generators (PRNGs)

A PRNG is an algorithm that produces a sequence of numbers that appears random but is, in fact, entirely determined by an initial value called a “seed.” If you start the algorithm with the same seed, it will generate the exact same sequence of numbers every single time. This deterministic nature is what makes them “pseudo-random.”

• The Seed: Imagine a very long, pre-computed list of numbers that look random. A PRNG is like having a pointer to a specific spot on that list (the seed) and then just reading off numbers sequentially. Each time you ask for a “random” number, it moves the pointer to the next number on the list.
• Determinism vs. True Randomness: True randomness comes from chaotic, unpredictable physical processes, like radioactive decay or atmospheric noise. PRNGs, being algorithms, are entirely predictable if you know their internal state and the algorithm.
• Why Use PRNGs?: Despite not being truly random, PRNGs are widely used in computing for several reasons:
  • Efficiency: They are computationally fast and don’t require special hardware.
  • Reproducibility: For debugging, testing, or scientific simulations, being able to reproduce a specific sequence of “random” numbers is a huge advantage. If a bug appears only with a certain “random” sequence, you can re-run the simulation with that exact sequence to diagnose it.
  • Statistical Quality: Good PRNGs are designed to pass various statistical tests for randomness, meaning the sequences they produce exhibit properties like uniform distribution, independence between numbers, and long periods before repeating.

The Inner Workings of Excel’s RAND() Function

RAND() is the fundamental building block for randomness in Excel. It generates a floating-point number greater than or equal to 0 and less than 1 (i.e., 0 <= n < 1).

• Algorithm Obscurity: Microsoft keeps the exact PRNG algorithm used in Excel proprietary. However, it’s generally understood to be a variation of a commonly accepted algorithm, likely a Mersenne Twister or a similar well-researched algorithm, perhaps with some tweaks. Before Excel 2003, older versions used simpler, less robust PRNGs. Since Excel 2003, the quality of its PRNG significantly improved.
• Volatile Function: RAND() is a “volatile” function. This means it recalculates every time there is any change on the worksheet, or when you press F9 (recalculate) or open the workbook. This constant recalculation gives the impression of continuous, fresh randomness, but it’s just the PRNG moving to the next number in its predetermined sequence.
• Uniform Distribution: The numbers generated by RAND() are designed to be uniformly distributed. This means that, over a large number of samples, every number between 0 and 1 (exclusive of 1) has an approximately equal chance of being generated. If you generate millions of RAND() values and plot them in a histogram, you would expect to see a relatively flat distribution.

Decoding RANDBETWEEN() and Its Statistical Properties

RANDBETWEEN(bottom, top) is a convenience function that generates a pseudo-random integer between a specified bottom and top value (inclusive). It effectively leverages the output of RAND().

• Conversion Process: The formula behind RANDBETWEEN(bottom, top) is conceptually similar to INT((top - bottom + 1) * RAND() + bottom).
  • RAND() gives a number between 0 and <1.
  • Multiplying by (top - bottom + 1) scales this to a range size. For RANDBETWEEN(1,10), this is 10-1+1 = 10. So RAND()*10 gives 0 to <10.
  • Adding bottom shifts the range. RAND()*10 + 1 gives 1 to <11.
  • INT() (or FLOOR()) rounds down to the nearest integer. So INT(1) to INT(10.999...) covers integers from 1 to 10.
• Integer Uniformity: Just like RAND(), RANDBETWEEN() aims for a uniform distribution of integers. Each integer within the specified range (e.g., 1 through 10) should have an equal probability of being selected.
• Sample Size Matters: When testing RANDBETWEEN(), especially with small ranges, you need a sufficiently large number of samples to truly observe uniformity. If you generate only 10 numbers between 1 and 10, it’s highly likely you won’t get exactly one of each number. But if you generate 10,000 numbers, you would expect roughly 1,000 of each integer. This concept is tied to the Law of Large Numbers.

Statistical Tests for “Randomness”

How do we determine if a PRNG is “good enough”? We use statistical tests. These tests don’t prove true randomness (which is impossible for a PRNG), but they assess how well the generated sequence mimics the properties of a truly random one. Random csv file

• Uniformity Test: This checks if numbers are evenly distributed across the range. A common test is the Chi-Squared Goodness-of-Fit Test, which compares observed frequencies of numbers to the expected frequencies in a uniform distribution. Our simulation tool uses a simplified version of this.
• Independence Test: This checks if there’s any pattern or correlation between consecutive numbers. For example, does a high number tend to be followed by another high number? A good PRNG should show no such patterns.
• Frequency Test: Similar to uniformity, ensuring that each digit (0-9) appears roughly the same number of times in a long sequence.
• Runs Test: Checks for sequences of identical outcomes or sequences of increasing/decreasing values.
• Cryptographic Strength: For security applications, PRNGs need to be “cryptographically secure” (CSPRNGs). This means they are designed to be extremely difficult to predict even if parts of their output are known. Excel’s PRNGs are not cryptographically secure and should never be used for generating sensitive data like encryption keys or security tokens.

Practical Implications and Best Practices

Given that Excel’s random functions are pseudo-random, what does this mean for your daily work?

• Simulations: For Monte Carlo simulations, statistical modeling, or creating random samples for data analysis (e.g., drawing a random sample of customers), Excel’s RAND() and RANDBETWEEN() are generally perfectly acceptable.
• Data Masking/Dummy Data: They are excellent for quickly generating dummy data or masking real data for testing purposes.
• Educational Tools: Great for illustrating probability, statistics, and random processes in an educational context.
• When Not to Use:
  • Security/Cryptography: Never use Excel’s random functions for generating passwords, encryption keys, lottery numbers, or any security-sensitive application. For these, you need cryptographically secure sources of randomness.
  • Scientific Research Requiring True Randomness: If your research explicitly requires true, unpredictable randomness (e.g., certain physics experiments), you’ll need specialized hardware or software that taps into entropy sources.
  • High-Volume, High-Performance Needs: For extremely large-scale simulations or performance-critical applications, dedicated statistical software or programming languages with optimized PRNG libraries might be more efficient.

Seed Management and Reproducibility in Excel

One often-overlooked aspect of PRNGs is the seed. In many programming environments, you can explicitly set the seed to reproduce a sequence of random numbers. Excel, however, doesn’t provide a direct, user-friendly way to set the seed for its RAND() function.

• Implicit Seed: When Excel starts or when you perform certain actions, its internal PRNG gets an implicit seed, often derived from the system clock. This is why if you open a workbook at different times, the “random” numbers will change.
• Reproducibility Workaround: If you need reproducibility with Excel’s random numbers, the common approach is to:
  1. Generate all necessary random numbers in a column.
  2. Copy that column.
  3. Paste Special -> Values.
     This “freezes” the current set of pseudo-random numbers, preventing them from recalculating and allowing you to reuse the exact same sequence for analysis or debugging.

Potential Pitfalls and Misconceptions

• Small Sample Bias: The most common misconception when someone asks “is excel randbetween really random” is looking at a handful of generated numbers and seeing apparent clusters or gaps. This is a statistical artifact of small sample sizes. True randomness doesn’t mean perfect evenness in every small subset; it means evenness over an infinite number of trials. Your perceived “lack of randomness” is usually just the natural variance of a truly random process (or a good PRNG mimicking one).
• Modulo Bias: While not typically a major issue with modern PRNGs like those in Excel, a historical problem with some simple PRNGs when converting from a large range to a smaller range (using the modulo operator %) was “modulo bias.” This could slightly favor certain numbers. Modern implementations minimize or eliminate this.
• Correlation Over Time: A weak PRNG might exhibit correlation between numbers generated far apart in its sequence. Good PRNGs have very long “periods” (the length of the sequence before it starts repeating) and are designed to prevent such correlations. Excel’s modern PRNG has a period that is astronomically long, far exceeding any practical use.

The Evolution of Randomness in Computing

The pursuit of better random number generation is an ongoing field in computer science and statistics.

• Early PRNGs: Simple linear congruential generators (LCGs) were common in early computing. They were fast but had relatively short periods and could exhibit noticeable patterns.
• Mersenne Twister: Introduced in 1997, the Mersenne Twister (MT) became a widely adopted standard for non-cryptographic PRNGs. It boasts an incredibly long period (2^19937 – 1) and passes many stringent statistical tests. It’s likely that Excel, MATLAB, Python’s random module, and many other software packages use MT or a similar advanced algorithm.
• Hardware Random Number Generators (HRNGs): These devices tap into physical phenomena (like thermal noise, quantum events, or even mouse movements and keyboard timings) that are genuinely unpredictable. HRNGs are the source of “true randomness” and are crucial for cryptographic applications.
• Cryptographically Secure PRNGs (CSPRNGs): These are PRNGs designed with cryptographic security in mind. They incorporate elements of HRNGs to get an initial seed (entropy) and use algorithms that make it computationally infeasible to predict future outputs, even if previous outputs are known. Operating systems often have built-in CSPRNGs (e.g., /dev/urandom on Linux, CryptGenRandom on Windows).

In conclusion, while “is excel rand truly random” gets a technical “no,” for almost all practical data analysis, simulation, and educational purposes, Excel’s RAND() and RANDBETWEEN() functions provide a sequence of numbers that are statistically indistinguishable from truly random ones and are more than sufficient. Just be mindful of their deterministic nature and avoid them for high-security applications.

FAQ

Is Excel’s RAND function truly random?

No, Excel’s RAND() function is not truly random. It is a pseudo-random number generator (PRNG). This means it uses a deterministic algorithm that produces a sequence of numbers that appear random and pass statistical tests for randomness, but the sequence is entirely predictable if you know the starting “seed” value. Random csv file for testing

Is Excel’s RANDBETWEEN function truly random?

Similarly, RANDBETWEEN() is also a pseudo-random number generator (PRNG). It relies on the same underlying pseudo-random engine as RAND() to produce integers within a specified range. While it generates numbers that are statistically distributed like random numbers, it’s not truly random in the physical sense.

What is the difference between true random and pseudo-random numbers?

True random numbers are generated from unpredictable physical phenomena, like atmospheric noise, radioactive decay, or quantum events. They are inherently non-deterministic. Pseudo-random numbers, on the other hand, are generated by a deterministic algorithm starting from a seed value. While they appear random and pass statistical tests, they are reproducible and predictable if the algorithm and seed are known.

Why do my RAND numbers keep changing in Excel?

Excel’s RAND() and RANDBETWEEN() functions are “volatile” functions. This means they recalculate and generate a new pseudo-random number every time there is any change on the worksheet, or when you press F9 (recalculate), or open the workbook. This constant recalculation is designed to give the impression of fresh randomness.

How can I stop Excel’s random numbers from changing?

To freeze the generated random numbers:

1. Select the cell(s) containing the RAND() or RANDBETWEEN() formulas.
2. Copy the selected cells (Ctrl+C).
3. With the cells still selected, go to Home tab > Paste dropdown > Paste Values (the icon that looks like a clipboard with “123”). This will replace the formulas with their current numeric values, making them static.

Can I set a seed for Excel’s random number generator?

Excel does not provide a direct, user-friendly way to explicitly set a seed for its built-in RAND() or RANDBETWEEN() functions. The internal seed is usually determined by system factors or the application’s state. If you need reproducible random sequences by setting a seed, you would typically use VBA or external programming languages/software. Hex to binary c++

Are Excel’s random numbers good enough for simulations?

Yes, for most general simulations, statistical modeling, Monte Carlo analysis, and educational purposes, Excel’s pseudo-random number generators are generally considered sufficiently robust and statistically sound. They are designed to exhibit properties of uniformity and independence required for such applications.

Should I use Excel’s random numbers for cryptographic purposes?

Absolutely not. Excel’s PRNGs are not cryptographically secure. They are predictable and should never be used for generating sensitive data like passwords, encryption keys, security tokens, or any application where true unpredictability and high security are critical. For such needs, use cryptographically secure pseudo-random number generators (CSPRNGs) or hardware random number generators (HRNGs).

What algorithm does Excel use for its random numbers?

Microsoft keeps the exact PRNG algorithm proprietary. However, it’s widely believed that since Excel 2003, it uses a more advanced and statistically robust algorithm, possibly a variant of the Mersenne Twister, which is a high-quality, non-cryptographic PRNG. Older versions of Excel used simpler algorithms with known limitations.

What is a “volatile” function in Excel?

A volatile function is one that recalculates every time there is a change to any cell in the workbook, or whenever Excel performs a calculation cycle (e.g., pressing F9). RAND() and NOW() are common examples. This can sometimes impact spreadsheet performance if used excessively.

How can I generate a random date in Excel?

You can generate a random date using RANDBETWEEN() combined with date functions:
=RANDBETWEEN(DATE(2023,1,1), DATE(2024,12,31)) will give a random date between January 1, 2023, and December 31, 2024. Remember to format the cell as a date. Hex to binary excel

How can I generate a random number without duplicates in Excel?

Generating truly unique random numbers without duplicates can be complex with RAND() or RANDBETWEEN() directly, as they can produce repeats. For a unique list, you might:

1. Generate a sequence of numbers (e.g., 1 to 100).
2. Assign a RAND() value to each.
3. Sort the entire list based on the RAND() values.
4. Take the top N unique numbers you need.
   Alternatively, use VBA or advanced Excel techniques for more control.

What are the alternatives to Excel’s random number generation?

For more control, better statistical quality, or cryptographic security, alternatives include:

• VBA (Visual Basic for Applications): You can write custom VBA code to implement different PRNGs or control seeding.
• Programming Languages: Python (with random module), R, MATLAB, Java, C++, etc., offer robust PRNGs and CSPRNGs.
• Specialized Statistical Software: SPSS, SAS, Minitab, etc., have highly refined random number capabilities.
• Hardware Random Number Generators (HRNGs): For true randomness required in high-security contexts.

Can I test the “randomness” of Excel’s numbers?

Yes, you can perform statistical tests, such as the Chi-Squared Goodness-of-Fit test, to assess if the generated numbers are uniformly distributed. You can generate a large sample of numbers, count their frequencies in different bins, and compare these observed frequencies to the expected frequencies of a uniform distribution. Our provided tool above demonstrates a basic version of this.

What is the period of Excel’s RAND function?

The “period” of a PRNG is the length of the sequence it generates before it starts repeating. Modern PRNGs, including the one likely used in recent Excel versions (e.g., Mersenne Twister variants), have astronomically long periods (often 2^19937 – 1), meaning you will never practically encounter a repeat of the sequence within typical usage.

Does the system clock influence Excel’s random numbers?

Yes, the system clock is often used, implicitly or explicitly, as a source for seeding PRNGs when an application first starts or when random numbers are requested without an explicit seed. This is why consecutive runs of an Excel file with RAND() functions might yield different results when opened at different times. Hex to binary chart

What if my “random” numbers in Excel seem to have a pattern?

If you observe a pattern in your Excel random numbers, especially with large sample sizes, it’s highly unlikely to be a flaw in Excel’s current PRNG (since Excel 2003). More probable reasons include:

• Small Sample Size: Apparent patterns often disappear with a larger sample.
• Misinterpretation: Human brains are excellent at finding patterns, even in truly random data.
• Incorrect Usage: Mistakes in formula application or calculation settings.

How to generate a random number within a specific decimal range (e.g., 1.5 to 3.2)?

You can use a combination of RAND() and arithmetic:
=RAND() * (max_value - min_value) + min_value
For example, =RAND() * (3.2 - 1.5) + 1.5 will generate a pseudo-random decimal number between 1.5 (inclusive) and 3.2 (exclusive).

Can I use Excel’s random functions for lottery number generation?

It is strongly advised against using Excel’s random functions for generating lottery numbers or any other high-stakes scenarios. While they are statistically good for simulations, their pseudo-random nature means they are predictable if the algorithm and seed are known. Lotteries and gambling require true randomness to ensure fairness and prevent manipulation. Instead, rely on official, regulated lottery systems that use dedicated, certified random number generators.

Does recalculating a spreadsheet with RAND() affect other cells?

Yes, because RAND() is a volatile function, any change in the spreadsheet or a manual recalculation (F9) will cause all cells containing RAND() or RANDBETWEEN() to recalculate, potentially changing numbers in many parts of your workbook. This can impact calculation speed if you have a very large number of such formulas.

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