Random Acts: “Stop telling God what to do!” (part 1)

Let’s look at a few things that appear random, but have subtle underlying behaviors that turns magic into math.

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Computer Generated Random Numbers

True vs. pseudo-random numbers
There are two principal methods used to generate random numbers. The first method measures some physical phenomenon that is expected to be random and then compensates for possible biases in the measurement process. Example sources include measuring atmospheric noise, thermal noise, and other external electromagnetic and quantum phenomena. For example, cosmic background radiation or radioactive decay as measured over short timescales represent sources of natural entropy (as a measure of unpredictability or surprise of the number generation process).

The second method uses computational algorithms that can produce long sequences of apparently random results, which are in fact completely determined by a shorter initial value, known as a seed value or key. As a result, the entire seemingly random sequence can be reproduced if the seed value is known. This type of random number generator is often called a pseudorandom number generator.

Wikipedia

[When I worked at The Big House, the pseudorandom number generator was critical in our simulation of CPU designs. We’d run millions of simulations of random instruction sequences. When one failed, we’d use the seed from the initial simulation to recreate the test on a (hopefully) patched design.]

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Images

Let’s put our AI colleagues through their paces. We asked Gemini and Elder G to create totally random image prompts, ignoring any information they’d collected about us.

Good morning! It’s great to hear from you. Exploring the concept of “random” sounds like a wonderful way to start the day.

I’m happy to participate in this experiment. To generate this image, I’ve used a technique to create an unexpected scene without relying on any prior knowledge of your preferences or specific history. I simply let random variables combine to form a unique composition.

Gemini

Sora

Hot Pot

Elder G

Perchance

Perchance has a button that creates random prompts. The following are Perchance images based on the following prompts

[this prompt produced so many interesting images, we decided to include several]
woman, in a tattoo parlor, getting inked, excited, close-up

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Coin Toss

A coin toss looks random, but in strict physics it is not. A tossed coin obeys the very ordinary rules of classical mechanics: gravity, angular momentum, air resistance, and the exact way the coin leaves the hand.

If you knew all the starting conditions perfectly, Newton’s laws could predict the outcome.

In other words: A coin toss is deterministic, not inherently random. Humans simply lack the precision to measure and control all the variables.

Elder G:

Researchers Diaconis, Holmes, and Montgomery analyzed coin tossing and found that a typical toss has a slight bias toward the starting face, about 51% probability. The coin tends to land the way it began because of how it is caught.

So even normal coin flips are not perfectly 50/50.

Stage Magicians Go Further

Magicians can push this farther with techniques like:

• Thumb toss with controlled rotation
• Catch-and-flip methods (secretly turning the coin during the catch)
• Two-headed coins (the oldest trick in the book)

But even without trick coins, skilled performers can achieve very high success rates with controlled flips.

Here’s an interesting video where the secret of the predetermine coin flip is revealed. It is surprisingly simple, and after several hours of practice, we achieved a 50% success rate.

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Card Shuffle!

The number of possible combinations of a deck of cards is 52! (52 factorial). Big, big number!

Elder G does the hard part for us!

The Astonishing Size of the Number

The value is:

52! ≈ 80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000

In scientific notation: 52!≈8.07×1067. That is an 8 followed by 67 zeros.

There’s a magician’s trick where a deck can be shuffled 4 or 8 times and return to the original order. Again Elder G helps us out….

The Faro Shuffle

In a faro shuffle, the deck is cut exactly in half (26 cards and 26 cards), and the cards are interwoven perfectly, one by one.

There are two kinds:

1. Out-shuffle
The top card stays on top.

2. In-shuffle
The top card moves to the second position.

Magicians can do these with remarkable precision, though it takes a lot of practice.

The Famous Mathematical Result

For a 52-card deck:

• 8 perfect out-shuffles return the deck to its original order.

So if a magician performs eight flawless out-faro shuffles in a row, the deck is exactly the same as it started.

This result became widely known through the work of mathematician and former magician Persi Diaconis, who studied the mathematics of shuffling.

Why This Happens

Each shuffle performs a fixed permutation of the card positions.

If you repeat that permutation enough times, eventually you cycle back to the starting arrangement.

Mathematically, the permutation has an order of 8, meaning:

shuffle^8 = identity

So the eighth shuffle undoes the previous seven.

Elder G

The following Faro Shuffle video is provided so that you can either spot a dishonest card dealer, or become one yourself.