Is this a "good enough" random algorithm; why isn't it used if it's faster?

Uniformity: The unsung hero

The charming simplicity of a primitive algorithm like QuickRandom might tempt you with its lightning-fast speed. But remember, speed isn't the holy grail. A truly fair and robust algorithm requires uniform distribution—a fundamental feature that ensures all outcomes are equally probable. Card games, statistical simulations, and cryptographic systems, for instance, need to guarantee unpredictability and fairness. That's where complex algorithms like Math.random() and SecureRandom shine—they're designed to fend off correlations and predictable patterns.

Initial Seeds: Choose wisely

The initial seed in your RNG is like the Big Bang—it sparks off the sequence of numbers to come. A simplistic algorithm like QuickRandom can have wildly varied outputs, contingent on the initial seed. A different seed can drastically alter the distribution, thereby asking randomness to take a back seat. Sophisticated RNGs ensure that the quality of randomness does not depend on the choice of the seed, thus guaranteeing consistent results.

Shielding Predictability with Complexity

Complexity can be your friend. At first glance, Math.random() might look like an over-complicated mess. But with each added complexity, it strengthens its defense against predictability. Think of it as a labyrinth—it grows more challenging to solve with each additional twist and turn. Features like hidden states and longer periods render guessing the next output a Herculean task, which is what you want, especially when creating security tokens or shuffling algorithms.

Taking RNGs seriously - especially in games!

In the context of game development, the importance of a sound RNG cannot be overstated. Fairness and unpredictability are vital for compelling gameplay. If players can predict your patterns, then you might as well call it 'pattern recognition' instead of a 'strategy game'. RNGs with a short period and recognizable patterns could spell disaster for your gaming experience.

Speed vs. Quality: An eternal struggle

Sure, fast is good. But what if your fast is imperfect? A quick succession of generated numbers might seem impressive unless their randomness is flawed or predictable. Similarly, in games, predictable outcomes can be as fun as watching paint dry.

Tried, tested, and trustworthy RNGs

Established RNGs like Math.random() or SecureRandom have had the fortune of undergoing rigorous testing and improvements over years. Their persistence isn't due to old habits or stubborn developers, but because they have consistently proven their worth, proving to be a safe and thoughtful balance between speed and randomness quality.

Custom RNGs: Challenging but risky

Individual developers often have a penchant for optimization, and this leads them down the rabbit hole of implementing custom RNGs. However, without the necessary expertise and a compelling reason, this exercise can be a risky one. Often times, the threat of undetectable patterns and biases outweighs the fleeting gains in performance that a custom RNG might offer.

True randomness: The holy grail

For an RNG to serve its purpose, its values need to be as predictable as a sneeze in a silent library, i.e., utterly unpredictable and uniformly distributed. Moreover, RNGs should ensure a long period with no discernible sequences or patterns. This is what makes an RNG genuinely random, and thus useful.

Randomness Quality: The key considerations

When choosing an RNG, remember these 3 golden rules:

• Uniformity: Every number should have an equal chance of popping up.
• Indistinguishability: The next number should be a mystery, irrespective of the past numbers.
• Period: The RNG should run for an extremely long time before repeating the sequence.

Feel free to utilize resources that offer rigorous empirical testing methods to ascertain these attributes in an RNG.