How does randomness work in games?

Yo, so you wanna know how randomness works in games? It’s all about something called a pseudo-random number generator, or PRNG. Think of it like a really complex mathematical formula. You feed it a starting number – we call that the seed – and it spits out a seemingly random number. The key word here is *seemingly*. It’s not truly random; it’s deterministic, meaning if you use the same seed, you’ll get the *exact same sequence* of “random” numbers every single time.

This is crucial for things like replayability. Imagine a roguelike – you want the same seed to give you the identical dungeon layout, enemy spawns, and item drops if you want to share a specific run with a friend. That’s the power of a PRNG with a known seed.

Now, different games use different PRNGs and seeding methods. Some games use the system time as a seed, giving a different sequence each time you play, but that can be easily manipulated (think: exploiting a game to get a specific outcome by waiting for a specific time). Others might incorporate player input or other game events into the seed to make it more unpredictable. High-quality games often go to great lengths to create more complex seeding mechanisms or even combine multiple PRNGs to enhance randomness and security.

The quality of a PRNG is super important. A bad one can produce patterns or biases in the “random” numbers, leading to predictability and potentially unfair gameplay. Think of those times you see the same enemy spawn in the same spot repeatedly – that’s a sign of a poorly implemented PRNG. Game developers put a lot of effort into making sure their PRNGs are robust and produce numbers that are truly unpredictable *for all intents and purposes*. That’s what keeps things exciting.

What is the disorder or randomness in a system?

Entropy: It’s not just disorder, it’s the *spread* of energy. Think of a perfectly ordered deck of cards – super low entropy. Shuffle it? Boom, high entropy! The energy, initially concentrated in the organized arrangement, is now dispersed across all possible arrangements.

Key takeaway: Entropy isn’t simply “messiness,” it’s a precise measure of how spread out energy is within a system. Higher entropy means more dispersed energy, more possible arrangements, and less predictability.

• Microscopic perspective: At a molecular level, high entropy means molecules are moving randomly and are spread out, whereas low entropy means they’re organized and confined.
• Macroscopic perspective: You can see this on a larger scale, too. A perfectly organized room has low entropy. A messy room? High entropy. The energy that went into organizing the room is now dispersed throughout the mess.

Why this matters: Understanding entropy is crucial in various fields:

• Thermodynamics: The Second Law of Thermodynamics states that the total entropy of an isolated system can only increase over time. Things tend towards disorder!
• Chemistry: Entropy plays a major role in determining whether chemical reactions will occur spontaneously.
• Information theory: Entropy is used to quantify uncertainty and information content. More randomness = higher entropy = less information.

Think of it this way: Entropy is the universe’s tendency towards maximum chaos. It’s a fundamental force shaping everything from the smallest particles to the largest structures.

What role does randomness play in game theory simulation?

Randomness is crucial in game theory simulations, particularly in modeling mixed strategies. A mixed strategy isn’t just about randomly choosing actions; it’s about strategically assigning probabilities to different pure strategies. This probabilistic approach is fundamentally important because predictable behavior is easily exploited. In games like Rock-Paper-Scissors (RPS), consistently choosing the same action guarantees a loss against a savvy opponent. A mixed strategy, however, introduces uncertainty. By randomly selecting actions according to pre-calculated probabilities – say, choosing rock, paper, and scissors each with probability 1/3 – a player can negate the advantage of predictability, thus leveling the playing field and achieving a higher expected payoff against opponents who might try to anticipate their moves.

This concept extends beyond simple games like RPS. In more complex scenarios, simulations employing randomness allow exploration of diverse strategic interactions. For instance, in evolutionary game theory, random mutations introduce variations in player strategies, driving the selection process and revealing strategies that thrive in a dynamic, unpredictable environment. Without randomness in these simulations, the evolutionary process would stagnate, failing to illustrate the power of adaptation and emergent behavior.

Furthermore, the use of Monte Carlo methods and other stochastic algorithms in game theory simulations allows the estimation of complex game outcomes. These methods, heavily reliant on randomness, enable efficient approximations of expected values and equilibrium points, especially in games with a large state space, where exhaustive analysis is computationally infeasible. The introduction of noise in the simulation itself—representing unpredictable factors within the game’s environment—can also highlight the robustness of specific strategies in the face of uncertainty and complexity.

What is the extent of randomness?

However, this is a macroscopic view. At the quantum level, randomness takes on a different character. Quantum mechanics introduces fundamental, irreducible randomness; events are probabilistic, not deterministic. This isn’t merely a matter of hidden variables or incomplete information – it’s a built-in feature of the universe. The uncertainty principle, for example, fundamentally limits our knowledge of certain pairs of properties (like position and momentum) simultaneously.

Therefore, while entropy provides a useful metric for randomness in classical systems, it doesn’t fully capture the inherent randomness at the quantum level. It’s a tool for describing statistical distributions of macroscopic states, not the underlying source of randomness itself. Furthermore, the concept of “randomness” can be subjective. What appears random to one observer might exhibit patterns to another with different knowledge or perspective. This highlights the importance of specifying the context and level of analysis when discussing randomness.

Finally, consider algorithmic randomness. A truly random sequence can’t be generated by an algorithm; any algorithm, by its very nature, introduces predictability and structure. This distinction is vital in computer science and cryptography, where generating sequences that appear random, yet are computationally unpredictable, is critical.

What is the main purpose of using randomness in an experiment?

The primary purpose of randomness in experimentation isn’t just about “preventing bias,” though that’s a crucial outcome. It’s about establishing causality. By randomly assigning subjects to different groups (e.g., treatment and control), we ensure that any observed differences between the groups are highly likely due to the treatment itself, and not due to pre-existing differences between the groups. This is the bedrock of inferential statistics, allowing us to confidently generalize findings from our sample to a larger population.

Selection bias, where certain individuals are more likely to be chosen for a particular group, is a serious threat to validity. Randomization mitigates this by giving every subject an equal chance of assignment, neutralizing the influence of known and unknown confounding variables. Accidental bias, stemming from unintentional inconsistencies in how the experiment is conducted, is also reduced; randomization ensures that any such inconsistencies are evenly distributed across groups, making their impact less significant.

Comparable groups are vital for accurate comparison. Random assignment, especially with a sufficiently large sample size, creates groups that are statistically equivalent at the outset, making it easier to isolate the effect of the intervention. Without randomization, differences between groups might be attributed to the treatment when they are actually due to pre-existing factors. Therefore, randomization isn’t simply about eliminating bias; it’s about building a robust foundation for drawing valid conclusions about cause and effect.

Consider the power of randomization tests. These statistical approaches directly leverage the randomization process to assess the probability of observing the experimental results under the assumption that the treatment had no effect. This provides a powerful, intuitive way to assess the significance of findings and understand the strength of the evidence supporting a causal link.

What is random used for?

Randomness is a fundamental concept with applications across numerous fields. In scientific research, particularly in randomized controlled trials, it ensures unbiased results by randomly assigning participants to different groups. This eliminates confounding variables and allows for a more accurate assessment of treatment efficacy. Think of testing a new drug – you wouldn’t want to accidentally give the drug only to people who are already healthier, right? Randomization prevents that bias.

Beyond science, randomness plays a vital role in cryptography. Strong encryption relies on the unpredictability of random numbers to secure sensitive data. Without true randomness, cryptographic systems become vulnerable to attacks. This is why generating truly random numbers is a big deal for online security.

In the world of gaming and gambling, randomness is essential for fairness and unpredictability. Imagine playing poker with a rigged deck! Random number generators (RNGs) are used to determine outcomes, creating an element of chance that is crucial to the overall experience. For instance, in video poker, the shuffling and dealing of cards rely on an RNG to mimic a real-life scenario. Poorly implemented RNGs can lead to biased outcomes, so developers invest heavily in ensuring these are truly random (or at least appear to be).

Furthermore, randomness finds its use in art and statistics. In art, it can inspire creative processes and generate unique patterns, textures, or musical compositions. In statistics, random sampling ensures that the selected data accurately represents the larger population. This prevents skewed results and allows for more robust conclusions.

Why is randomness important?

Randomness isn’t just about unpredictability; it’s about ensuring fair representation and avoiding bias. In stats, it’s crucial for establishing solid statistical properties – think confidence intervals and hypothesis testing. Without randomness, your conclusions are shaky at best.

Monte Carlo methods are where randomness really shines. These techniques use random numbers – often generated by algorithms, not true dice rolls – to solve complex problems. Imagine trying to calculate the area of a weirdly shaped object. You could throw darts randomly at a board encompassing it; the ratio of darts landing inside the object to the total darts thrown approximates the area. That’s the basic principle.

Here’s why it’s so powerful:

• Solving intractable problems: Many problems are too complex for direct analytical solutions. Monte Carlo offers a powerful approximation method.
• High-dimensional problems: Dealing with many variables simultaneously? Monte Carlo can handle it.
• Uncertainty quantification: It helps determine how much uncertainty is inherent in your results – a critical aspect of scientific accuracy.

It’s used everywhere in computational science, from:

• Physics simulations: Modeling particle behavior, fluid dynamics, etc.
• Financial modeling: Pricing derivatives, risk management.
• Machine learning: Training neural networks, generating synthetic data.

Important note: The “randomness” used is usually pseudo-randomness. True randomness is hard to achieve computationally, so algorithms generate sequences that appear random but are actually deterministic – they’re predictable if you know the starting seed. However, for most applications, this is perfectly adequate, provided the algorithm is good enough to generate statistically uniform random numbers.

What is the randomness effect?

So, the randomness effect, huh? It’s a big deal, especially in games. Think of it like this: you’re playing a game, maybe something complex like *StarCraft II*, where even the smallest input variation can drastically change the outcome. That’s intrinsic randomness – the subtle differences in your reaction time, your micro-adjustments, the ever-so-slight variations in your APM (actions per minute) all contribute to a non-deterministic result. No two games are *ever* exactly alike, even if you try to replicate your strategy perfectly. It’s like trying to perfectly recreate a speedrun – some runs will just be naturally faster due to inherent variations. It’s chaos theory in action, beautifully unpredictable.

Then you’ve got explicit randomness, the stuff you consciously introduce. Let’s say you’re playing that classic game, rock-paper-scissors. If you try to predict your opponent, you fall into a pattern. The best strategy here isn’t some deep calculation; it’s actually deliberate randomness. You actively *try* to be unpredictable, forcing your opponent to constantly adapt, thus disrupting their pattern recognition. Think of it as a form of strategic deception, the kind you need to master in games like *Poker* or *Magic: The Gathering*. You’re forcing your opponent to handle uncertainty, burning through their resources trying to counter your unpredictable choices. It’s all about managing information asymmetry – exploiting the fact they don’t know what you’ll do next.

In short, randomness in games, whether intrinsic or explicit, is a powerful tool. Mastering it, understanding how to leverage it, both in your own actions and to disrupt your opponent’s strategies, is a key to success in nearly every competitive game out there.

Why do we need randomness in simulation?

So, you’re asking why we need randomness in simulations? Think of it like this: imagine you’re playing a game, let’s say a roguelike, where every single event is predetermined. Every enemy spawns in the exact same spot, every item drops in the same place, every roll of the dice is the same. Boring, right? And you’d never truly know how difficult the game actually is.

That’s essentially what happens in a simulation without randomness. Every single run is identical. You’re not getting a fair representation of the possibilities. Instead, you’re only seeing one specific, pre-ordained outcome. In a real-world scenario – or even in a well-designed game – things are unpredictable. There’s an element of chance, of variation.

Randomness in simulation lets us model that unpredictability. We run the simulation multiple times, each with different random inputs. This gives us a range of outcomes, allowing us to calculate statistics like the average, minimum, maximum and standard deviation. This lets us estimate the true average outcome, and understand the variability inherent in the system. Without it, we’d just have one data point – which tells us practically nothing about the overall behavior of the system. It’s like trying to judge the difficulty of a roguelike after only playing one, perfectly scripted run. You need multiple runs to get a proper feel for the game’s variability, and the same applies to simulations.

What does random mean in games?

Random in games? That’s a loaded question, kid. It’s all about the RNG, the Random Number Generator. Think of it as the game’s digital dice, deciding everything from loot drops to enemy spawns. It’s the backbone of unpredictability, the very thing that keeps you coming back for more, or keeps you raging at your monitor, depending on the day.

Now, a good RNG is *crucial*. A poorly implemented one feels rigged, predictable, and utterly destroys immersion. You get the same crappy drops every time, the same predictable enemy patterns… It’s garbage. A truly *good* RNG feels fair, even when you’re on a brutal losing streak. You know it’s random, not secretly weighted against you (unless, of course, it *is*, and the devs are just *really* good at hiding it).

There are different kinds too. Some games use pseudo-random number generators (PRNGs), which are deterministic – meaning, given the same seed value, you’ll get the same sequence. This can be useful for testing or replayability, but it’s not *true* randomness. Then there’s the holy grail: true RNG, using external sources like atmospheric noise to generate numbers. It’s far harder to implement, but the randomness is, well, far more random.

• Loot Tables: RNG dictates what you find. High-level items are often lower probability, creating that coveted thrill of the rare drop. But poorly designed loot tables often just feel unfair, leading to hours of grinding.
• Enemy Spawns: RNG determines enemy placement, types, and numbers. A good RNG keeps things interesting, preventing predictable encounters. A bad one leads to the same three rats appearing every time you enter a dungeon.
• Critical Hits/Misses: RNG decides whether that attack lands, and whether it crits. The difference between a lucky win and a frustrating loss is often down to this.

So, yeah, “RNG” is more than just “luck.” It’s the invisible hand shaping the entire game experience. Learn to love it, learn to hate it, but above all, learn to *understand* it.

• Seed manipulation: Some games allow you to input a seed value, influencing the randomness. Knowing this can allow for some serious optimization or even cheesing.
• Statistical analysis: You can track your drops over time to see if the RNG appears biased (it probably isn’t, you’re probably just unlucky).
• Community research: Forums are packed with discussions about RNG mechanics. A lot of times, community effort can unveil hidden patterns, confirming or denying unfair weighting.

What is a simulation with randomness or probability which may affect the outcome?

A Monte Carlo simulation? Think of it like this: It’s how pro teams predict their chances of winning a tournament. Instead of just guessing, they run thousands of simulated matches, each with random elements like player performance fluctuations (think a star player having an off day), opponent strategies, and even map selection. Each simulation spits out a result – a win or a loss. By running tons of these simulations, they get a probability distribution – a clear picture of their likely win rate, not just a single guess. It helps them understand their weaknesses, identify high-risk/high-reward strategies, and make informed decisions on drafting, bans, and overall tournament strategy. The more simulations, the more accurate the prediction. Basically, it’s data-driven decision-making on steroids – minimizing reliance on gut feeling and maximizing chances of victory. This isn’t just for predicting the final outcome; it can also analyze individual match probabilities, helping with things like map vetoes and understanding the odds of winning specific matchups. It’s a crucial tool for any team aiming for the top.

What is an example of a random effect?

Imagine a massive PvP arena – thousands of players battling. We randomly select several large guilds (think elementary schools). Each guild has its own inherent skill level, a hidden stat representing their collective prowess. This is the random effect: the inherent difference in average guild skill compared to the overall arena average. It’s not something we directly control; it’s the unpredictable variation between guilds, representing factors like guild leadership, training methods, or even just luck in player recruitment. Crucially, this random effect isn’t just noise; it’s a structured component of variation, reflecting genuine differences in guild capabilities. A powerful statistical model would account for this guild-level random effect, allowing us to precisely estimate the true impact of specific strategies or gear upgrades, disentangling the inherent guild strength from the effects we’re actually studying. Ignoring this random effect leads to biased estimates – we might mistakenly attribute a strategy’s success to a particularly strong guild, rather than the strategy itself.

This random effect manifests in the data as unexplained variation *within* guilds after controlling for other factors. In our guild example, this could be the variation in individual player performance *within* each guild – even within high-skill guilds, some players will outperform others. However, the random effect specifically focuses on the *between-guild* variation in average skill, a crucial distinction when interpreting results.

A key characteristic is that these random effects are assumed to be drawn from a distribution (e.g., a normal distribution). This means that while we don’t know the exact skill level of each guild, we can model it probabilistically, making inferences about the distribution of guild skill levels across the entire arena. This allows for more accurate and robust inferences than simply ignoring this inherent guild-to-guild variability.

Is randomness good or bad?

Randomness? It’s a double-edged sword, man. For years, we’ve wrestled with it. Think unpredictable outcomes, the chaos factor – the stuff nightmares are made of in a high-stakes match. You’re looking at potentially game-breaking errors, a total collapse of strategy. It’s the ultimate wildcard. But, don’t be fooled. Randomness is also the secret weapon. It’s the unpredictability that keeps opponents guessing, throws off their muscle memory, their meticulously crafted strategies. Think of it like this: perfectly predictable gameplay is easily countered. The element of surprise, that unpredictable burst of aggression or a seemingly random skill shot – that’s where the real wins are hidden.

In esports, randomness manifests differently. It could be the server lag creating that crucial moment of latency, affecting aim or reaction times. Or, it’s the random loot drops, altering the entire meta of the game, forcing players to adapt their builds and strategies on the fly. It’s about using the randomness, not fighting it. Mastering the art of dealing with unexpected variables, making the chaos work *for* you – that’s what separates the pros from the noobs.

That’s where experience really shines. The more matches you grind, the better you understand the probabilities. You learn to mitigate the bad and leverage the good. That’s the true skill – adapting to the inherent randomness of the game and turning it into an advantage.

Does random mean by chance?

But here’s the kicker – true randomness is actually pretty hard to achieve, especially in computing. What we often call “random” is actually “pseudo-random.” That means it’s generated by an algorithm, making it predictable given the starting point (seed). However, good pseudo-random number generators (PRNGs) produce sequences that appear random for all practical purposes. This is crucial for things like cryptography and simulations – you need numbers that look random to be effective, even if they’re technically deterministic.

Then you have true randomness, often derived from physical processes like atmospheric noise or radioactive decay. These are inherently unpredictable, which makes them vital for situations needing maximum security or unbiased results. It’s a subtle but important distinction!

The word “random” is often used interchangeably with “chance,” and in everyday language, that’s perfectly fine. However, the technical distinction between pseudo-randomness and true randomness is crucial for many applications.

What is randomness in decision making?

Randomness in decision-making? Think of it as the chaos factor, the unpredictable stuff that throws a wrench into your perfectly planned strategy. In business, we’re trained to hate it. We see luck – good or bad – as irrational noise, something to be minimized, not embraced.

The Traditional View: The textbook approach is all about identifying and managing external forces that create this uncertainty. These forces, like market fluctuations or unexpected competitor moves, are viewed as risks. The goal is to quantify them, model them, and ideally, eliminate them. This is classic risk management 101.

But here’s the kicker: You can’t eliminate *all* randomness. Some of it is just inherent in the system. Trying to micromanage everything to eliminate chance creates inefficiency and misses opportunities. Let’s look at some examples:

• Market Volatility: Predicting the stock market with 100% accuracy is impossible. Random events, from geopolitical shifts to unexpected news cycles, constantly impact valuations.
• Customer Behavior: You can analyze trends and demographics, but individual customer decisions remain somewhat unpredictable. A viral marketing campaign could explode unexpectedly or flop completely.
• Technological Disruptions: The next big thing often comes out of left field. Being overly focused on controlling known risks can blind you to emerging opportunities that challenge the status quo.

A More Nuanced Approach: Instead of fighting randomness entirely, smart decision-making involves acknowledging its existence. This means:

• Scenario Planning: Developing multiple plans for various potential outcomes, including those driven by random events.
• Flexibility and Adaptability: Building organizational agility to respond effectively to unpredictable changes.
• Experimentation and Iteration: Embracing a test-and-learn mindset, accepting that some initiatives will fail due to factors outside your control.
• Stress Testing: Pushing your plans to their limits to identify weaknesses and vulnerabilities in the face of unexpected events.

In short: While minimizing controllable risks is crucial, complete elimination of randomness isn’t feasible. Accepting a degree of uncertainty, and building resilience to unexpected outcomes, is key to long-term success. It’s about managing the chaos, not conquering it.

How does entropy explain life?

So, you’re asking how entropy explains life? It’s a complex topic, but the core idea is that entropy, or disorder, *always* increases in a closed system. Think of it like this: your perfectly organized room (low entropy) will naturally become messy (high entropy) over time unless you actively intervene. That’s the second law of thermodynamics in action.

Now, life seems to defy this – we build complex structures, we organize, we create order. The trick is that life isn’t a closed system. We’re constantly exchanging energy and matter with our environment. We take in highly ordered food (low entropy), use its energy to maintain our structure, and expel waste (high entropy). The *net* entropy of the universe increases, even though we locally decrease entropy. This is why we need a constant input of energy – to fight back against the natural tendency towards disorder.

Consider a plant: it takes in sunlight (highly ordered energy), water, and nutrients to build complex structures, fighting against the decay dictated by entropy. But the process of photosynthesis, and the plant’s eventual decomposition, ultimately increases the overall entropy of the universe. It’s a constant battle against chaos.

This applies to everything from simple organisms to complex societies. Businesses fail because they lose the energy needed to maintain their structure and efficiency. Relationships crumble as the energy invested diminishes. Even stars, eventually, burn out, increasing the universe’s entropy.

Therefore, life isn’t an exception to the second law of thermodynamics; it’s a localized, temporary decrease in entropy sustained by a massive increase in entropy elsewhere. It’s a beautifully complex interplay of order and chaos.

Why is randomness important to experimentation?

Randomness in esports experimentation, like in any scientific endeavor, is paramount for reliable results. It’s not just about picking teams at random; it’s about ensuring the integrity of your data and the conclusions you draw from it.

Why? Random sampling – be it selecting players for a study on reaction time, picking matches for analysis of meta shifts, or assigning teams to different training regimens – dramatically boosts the external validity of your findings. This means your conclusions are more likely to hold true beyond the specific sample you studied, providing a more accurate reflection of the overall esports population.

Without randomness, biases creep in. For example:

• Selection bias: Choosing top-tier teams exclusively skews your results and prevents generalization to less skilled players or teams.
• Confirmation bias: Subconsciously selecting data points that support a pre-existing belief undermines objective analysis. Randomization helps mitigate this.

Consider A/B testing a new in-game strategy. Randomly assigning teams to either the control group (using the old strategy) or the experimental group (using the new strategy) ensures that any observed differences are likely attributable to the strategy itself, rather than pre-existing skill discrepancies. This strengthens the internal validity of your test.

Furthermore, random assignment allows for robust statistical inference. Stronger statistical power means you’re more likely to detect actual effects, reducing the chance of false positives (concluding a strategy works when it doesn’t) or false negatives (missing a genuinely effective strategy).

Specifically in esports, where subtle differences can significantly impact performance, random sampling is crucial for uncovering these nuances and avoiding misleading conclusions. It enhances the credibility and applicability of your research, informing better decision-making across all aspects of esports, from player development to competitive strategy.

• Proper randomization protocols are essential. This includes utilizing validated randomization techniques to avoid human error or unconscious bias.
• Sample size is crucial. Larger, randomly selected samples yield more reliable and generalizable results.
• Transparency is key. Clearly documenting your randomization methods allows for scrutiny and replication of your research.

How does randomization improve an experiment?

Randomization? It’s the ultimate clutch play in experimental design. Think of it as banning all the cheaters – selection bias is out of the game. It levels the playing field, ensuring both teams (groups) are equally matched, not just on the stats we know (known confounding variables), but also the hidden stuff we don’t even track (unknown confounding variables). This evens out the inherent advantages, preventing any team from getting an unfair head start. You wouldn’t start a match with one team having better gear, would you? That’s what randomization prevents.

It’s not just about fairness; it’s crucial for valid analysis. Randomization is the foundation upon which our statistical tests are built. It allows us to confidently apply those statistical methods, assuming that any differences we observe are due to the actual treatment, and not some pre-existing imbalance. We get a clean, reliable result that we can actually trust in our post-game analysis (statistical tests of equality of treatments). Without it, our stats are meaningless – like a win based on a game glitch. It’s the difference between a pro and a noob, a victory and a defeat, or a groundbreaking discovery and wasted effort.

What is a real life example of a random process?

Let’s talk randomness. A classic example is dice rolling. The outcome is unpredictable; we can’t foresee which face will land upwards. This inherent uncertainty is the hallmark of a random process. The probability of each outcome (1 through 6) is theoretically equal, assuming a fair die.

Coin flips are often cited too. While a meticulously controlled apparatus could theoretically produce a predictable result, a human flip introduces enough variability to be considered effectively random. The slight variations in how we flick the coin, the angle, the force – all contribute to a system that’s chaotic enough to generate seemingly unpredictable results. We often approximate this as a 50/50 chance of heads or tails, but minor inconsistencies impact the true probability.

It’s important to remember that true randomness in the real world is difficult to achieve perfectly. Even seemingly random events often have underlying factors influencing the outcome. However, the degree of unpredictability in dice rolls or human coin flips makes them excellent practical illustrations of random processes.