ChatGPT:
1. How many possible deck orders are there?
A standard deck has 52 unique cards.
The number of different ways to arrange them is:
That number is:
52! ≈ 8.07 × 10^67
That’s an 8 with 67 zeros after it.
For comparison:
-
The number of atoms in Earth ≈ 1 × 10^50
-
The number of atoms in the observable universe ≈ 10^80
So the possible orders of a single deck are closer to the total atoms in the cosmos than to anything we ever deal with in daily life.
2. Age of the Universe vs. shuffles
The universe is about 13.8 billion years old.
That’s roughly 4.35 × 10^17 seconds.
Suppose a mythical being could shuffle and perfectly randomize a deck once per second since the beginning of time.
-
Total shuffles performed = 4.35 × 10^17
-
Fraction of deck orders explored =
That’s 0.000…(50 zeros)…054.
In other words, after the entire lifetime of the universe, you wouldn’t even scratch the tiniest fraction of possible deck orders. You wouldn’t even get close to one-billionth (10^-9). You’d still be unimaginably far away.
3. Chance of ever seeing a repeat
Another way to look at it is with the “birthday paradox” logic.
-
To have a 50% chance of seeing a repeat shuffle (two identical orders), you’d need around √(52!) ≈ 10^34 shuffles.
That’s an incomprehensible number of shuffles. Even all humans alive, shuffling every second, across all of history, wouldn’t come remotely close.
4. The takeaway
-
Every time you shuffle a full 52-card deck, you almost certainly create an order that has never existed before and will never exist again.
-
The sheer size of the number dwarfs human scales of time, activity, or even the universe’s lifetime.
It’s one of those places where math collides with intuition:
-
We feel like shuffling is mundane.
-
But in truth, each shuffle is generating a sequence that is as unique as a snowflake — multiplied by an unimaginable cosmic factor.
No comments:
Post a Comment