Can a deterministic program generate useful random-looking samples?

Yes. Pseudorandom generators do this for simulation and statistical computing, subject to their properties and intended use.

Does a fixed seed guarantee identical results everywhere?

No. Generator choice, software behavior, call order, and other pipeline factors also matter.

Are three heads followed by tails more likely than another head?

Not for independent fair flips; each next outcome still has probability one half.

AI Glossary / Graphs and symbolic AI / Intermediate

Randomness

Definition

Randomness refers to variation described through uncertain outcomes and probability rules rather than a fixed predictable outcome in the relevant model. In computing, pseudorandom generators produce deterministic sequences designed to behave suitably like random draws for particular purposes. Randomness does not mean that every outcome is equally likely or that useful statistical regularities are absent.

What it means

A single outcome may be unpredictable while repeated outcomes have a stable distribution. A fair coin model assigns probability one half to each side, but it does not require a short sequence to alternate or contain exactly equal counts. Runs and clusters can occur naturally.
In AI, randomness can enter through sampled data, initialization, shuffled training examples, exploration, or generated outputs. These sources can affect results differently. A changing result does not by itself prove that a system is intelligently exploring, and a reproducible result does not prove that randomness played no role. It may simply mean that the same pseudorandom sequence was replayed.

How it works

To use randomness responsibly, specify the possible outcomes, their probabilities, and any dependence between draws. A computer simulation typically starts a pseudorandom generator from an internal state derived from a seed. Sampling routines transform its output into values from a chosen distribution.
Reusing the same seed can reproduce a sequence when the generator, software behavior, and sequence of calls are controlled. Changing the order or number of random calls can change later results. Reproducibility of an entire AI pipeline may also depend on data versions and other computational details. A statistical simulation generator should not be assumed suitable for generating security secrets.

Three practical examples

A training experiment can use recorded seeds to investigate how much model initialization changes its evaluation score.
A simulation can draw service times from a specified distribution to explore variation in a hypothetical queue.
A graph-layout tool can randomize its starting positions, allowing different drawings of the same unchanged network while preserving the underlying connections.

Think of it this way

Think of a well-specified lottery: you know the possible tickets and the selection rule even though you do not know the next winner. The analogy is limited because pseudorandom computer sequences are deterministic once their state is fixed, and real sampling procedures can contain biases that an ideal lottery model leaves out.

Worked example

Consider an original experiment of four independent fair coin flips. There are 2⁴ = 16 equally likely complete sequences. HHHH is one such sequence, so its probability is 1/16. HTHT is also one specific sequence, with the same probability 1/16. The orderly appearance of one pattern does not make it individually less possible than the other.
Now ask a different question: what is the probability of exactly two heads, regardless of order? There are six qualifying sequences, so the probability is 6/16 = 0.375. There are two all-identical sequences, HHHH and TTTT, giving probability 2/16 = 0.125. A property of many sequences and a single exact sequence are different events.
After three heads, the fourth flip still has probability one half of being heads under the independent fair-coin model. The coin is not required to compensate for the earlier imbalance.
For an AI experiment, suppose three predetermined seeds produce illustrative accuracy scores of 81%, 83%, and 82% on the same test set. Their mean is 82%, and their range is two percentage points. These three invented results reveal variation in this small experiment, not a precise confidence interval or proof of general performance. Reporting only the 83% run would conceal the less favorable outcomes. Replaying that seed helps reproduce one run, while evaluating several seeds helps examine sensitivity.

Illustrative case study

Fictional case: Hazel Models compares two training methods. One analyst reports a single favorable run for the newer method, while another cannot reproduce the comparison because initialization and data shuffling were uncontrolled.
The team defines its evaluation procedure before rerunning, records the generators and seeds, and compares methods across a planned set of runs. It also keeps the test data separate from choices about which method to tune. This fictional case illustrates reproducibility and fair comparison; it does not establish that any particular number of seeds is sufficient for every project.

Common misconceptions and mistakes

Do not equate random with uniform. A biased coin is still random under its stated model. Do not equate randomness with independence either: a stochastic process can contain strong dependence between successive observations.
A sequence that looks irregular may come from a deterministic rule, while a valid random sequence may contain striking patterns. Statistical tests can reveal departures from specified properties but do not prove every desired form of randomness. Fixing a seed does not remove sampling uncertainty, and selecting a lucky seed after inspecting results can distort a comparison. Different seeds are useful experimental settings, not evidence by themselves that all runs are independent in every respect.

Business use

Businesses need to understand randomness when AI results vary between training runs or when simulations support decisions. Identify which sources of variation are intentional, which should be controlled, and which represent uncertainty in the real process.
Separate repeatability from reliability. Repeatability helps diagnose a particular result; reliability requires checking whether conclusions persist across relevant data and computational variation. Record enough context to reproduce important experiments, and report the spread of outcomes when it affects the decision. Choose generators suited to the application rather than treating all functions called “random” as interchangeable.

Check your understanding

Why is exactly two heads more likely than the specific sequence HTHT?

Answer: Exactly two heads includes six sequences, whereas HTHT names only one. Their probabilities are 6/16 and 1/16 respectively.

Related terms

Probability distribution
Independence
Sampling
Stochastic process
Monte Carlo simulation
pseudorandom number generator
random seed
reproducibility

Learn next

List all eight sequences of three fair flips and group them by the number of heads. The group counts are 1, 3, 3, and 1. Then explain why a group probability differs from the probability of any one sequence within it.

Sources

Sources: Harrell, Glossary of Statistical Terms, randomness: https://hbiostat.org/glossary/ . NumPy, Random sampling documentation, deterministic generators and seeds: https://numpy.org/doc/stable/reference/random/index.html . NetworkX, Randomness documentation: https://networkx.org/documentation/stable/reference/randomness.html .

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