10 Mind-Blowing Comparisons: Chess Probabilities vs Atoms in the Universe

chess vs universe — Created with AI using OpenAI's DALL·E.

Chess is a game of astonishing complexity – so much so that Claude Shannon estimated there are on the order of $10^{120}$ unique chess game sequences. By comparison, astrophysicists estimate the observable universe contains only about $10^{80}$ atoms. In this article, we dive into the classic chess probabilities vs atoms in the universe comparison. We explain both numbers (the famous “Shannon number” for chess and the cosmic atom count) and put them in context. The result is a mind-bending look at how vast these numbers really are.

Chess Probabilities (The Shannon Number)

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Every time you play chess, you’re navigating a vast “game tree” of possible moves and countermoves. In 1950, Shannon estimated the game-tree complexity of chess – essentially the count of all possible games – at about $10^{120}$

In practice, early moves often have ~20 options each side, quickly rising to dozens later. For example: after White’s first move (20 options) and Black’s response (about 20), there are already ~400 possible positions. After 4 moves each (8 plies), the number of possible games exceeds 10^11, and it keeps skyrocketing. Ultimately Shannon’s back-of-the-envelope estimate gives $10^{120}$ as a round figure to express “astronomically many”.

For perspective, Chess.com notes that Shannon’s number $10^{120}$ is far larger than a googol ( $10^{100}$ ). In fact, even if a computer could examine a trillion positions per second, it would need far longer than the age of the universe to exhaust all $10^{120}$ games. The take-away: chess “probabilities” (possible games) is a way to say “the number of possible games” – and that number is effectively infinite for any realistic purpose. (Some experts refine Shannon’s value; for instance, using improved move branching they estimate as much as $10^{123}$

Key Chess Fact: The Shannon number is approximately $10^{120}$ , representing all distinct possible chess games (en.wikipedia.org). By comparison, the number of legal positions in chess is about $10^{47}$ – $10^{50}$ (chess.com), which is itself huge but still far smaller than the number of games.

Atoms in the Universe: How Many?

Now consider the other titan of scale: the number of atoms in the observable universe. Astronomers and physicists use the term “atoms” loosely to mean protons, neutrons, and electrons in ordinary matter. Based on measurements of the universe’s mass and composition, the consensus is on the order of $10^{80}$ such atoms (en.wikipedia.org). For example, current cosmological estimates (often using the Eddington number) put the count around $1.5×10791.5\times10^{79}$ to $10^{80}$ (en.wikipedia.orgen.wikipedia.org.)

How do they get this? A typical method: estimate how many stars (and galaxies) there are, multiply by an average star mass, and convert to atoms. One rough calculation is: ~10^11 galaxies × ~10^11 stars/galaxy = ~10^22 stars. If each star’s mass is $∼1030\sim10^{30}$ kg, and each kilogram has $6×1026~6\times10^{26}$ hydrogen atoms, the total is on the order of $10^{80}$ atoms. Indeed, one Live Science explanation works it out to about $10^{82}$ , noting that this involves assumptions (e.g. all mass in stars, mostly hydrogen) (livescience.com.) The exact factor (10^80 vs 10^82) isn’t critical – we’re talking eighty-something zeros.

Key points about cosmic atom count:

Observable vs Entire Universe: Scientists only count the observable universe (anything light has reached us from), because we don’t know if there’s more beyond. Even so, that observable sphere (~46 billion light-years radius) contains about $10^{80}$ atoms of matter.
Matter Fraction: NASA notes that ordinary atoms make up only ~5% of the universe’s energy/mass (the rest is dark matter/energy) (wmap.gsfc.nasa.gov). So the $10^{80}$ atoms account for the ordinary matter portion.
Variability: Estimates vary. Some use 10^80 as a round figure (en.wikipedia.org,) others get 10^82 (livescience.com.) All agree it’s around 80–82 zeros.

For context, consider sub-bullets:

An average human body has only about $10^{27}$ atoms (livescience.com), a tiny fraction of 10^80.
Earth’s mass (~6×10^24 kg) holds ~10^51 atoms (mostly iron/oxygen), still far below cosmic scale.
Point: Even if you counted all atoms on Earth, all stars, and all planets, you’re still around 10^80; adding them up to 10^82 doesn’t change that 80-zero scale.

Chess Probabilities vs Atoms in the Universe: Mind-Bending Comparison

So how do the two compare? Let’s put the numbers side by side:

Possible Chess Games: $10^{120}$ (Shannon number) (en.wikipedia.org)
Atoms in Observable Universe: $10^{80}$ (order-of-magnitude) (en.wikipedia.org)

That is, $10^{120}$ vs $10^{80}$ . Written out, chess games have 40 more zeros! In other words, there are about $10^{40}$ times more chess game possibilities than there are atoms in the entire observable universe.

Put concretely: if each atom in the universe was assigned one unique chess game, you would only cover a tiny fraction of all chess games (one in $10^{40}$ of them). Or flip it: if each possible chess game were to consume one atom, you would need $10^{40}$ universes’ worth of atoms.

Another perspective: a typical chess game might last ~80 moves. If you played one new game every second since the Big Bang (about $4×10174\times10^{17}$ seconds so far), you would have played ~ $10^{17}$ games. That’s a far cry from $10^{120}$ . In fact, even playing a trillion games per second wouldn’t scratch the surface. Each extra factor of time or speed is dwarfed by the cosmic gulf between $10^{80}$ and $10^{120}$ .

Bullet-list of mind-boggling facts:

The Shannon number $10^{120}$ is incomprehensibly large. For reference, a googol (10^100) is tiny by comparison (chess.com.)
The atom count $10^{80}$ is also huge, but relatively smaller. It means about 80 zeros after the 1 – already a number beyond practical counting or imagination (en.wikipedia.org.)
Difference: $10^{120}/10^{80} = 10^{40}$ . Ten billion trillion trillion is a factor of $10^{28}$ , and we have an extra $10^{12}$ on top of that!
Analogy: If each second of time were an atom, the universe’s age (~10^17 sec) is nothing compared to $10^{120}$ seconds (the chess number). The chess number is like counting to 10^120; even with the universe’s lifespan, we’d be at 10^17 – far short.
Chess.com/Chess Wiki: Chess resources highlight how “inexhaustible” the game’s beauty is, since the fraction of played games is essentially zero (chess.com.)

The upshot: while both numbers are enormous, the space of chess game outcomes vastly exceeds the count of atoms. This often-quoted comparison (“more chess games than atoms in the universe”) drives home how an abstract combinatorial count can exceed even cosmic totals.

Putting It All in Perspective

Numbers like $10^{120}$ and $10^{80}$ are hard to visualize. Here are some ways to feel the scale:

Human and Earth Atoms: A human (~70 kg) has ~ $10^{27}$ atoms (livescience.com). Earth has ~ $10^{50}$ atoms (mostly rock). The entire observable universe has about 10^80 atoms (en.wikipedia.org) – that’s 30 orders of magnitude more than Earth’s atoms.
Chess Games in Time: If our entire history of chess were played out, the total number of distinct games played by all humans (past and future) is negligible next to $10^{120}$ . Even iterating random games non-stop for the universe’s age would sample only a minuscule subset of all possibilities.
Probability Angle: Suppose you pick one chess game sequence at random. The chance that it is the “game that was actually played” in a famous match is virtually zero, given the enormous space of possibilities. Similarly, if you pick one atom from the universe at random, it could be hydrogen, helium, etc., but picking a particular atom (say, the 1-gram of iron in your blood) has probability on the order of $10^{-80}$ .

This cosmic and combinatorial comparison illustrates combinatorial explosion: as a system gains more parts (like moves in a game), the number of ways to arrange them grows super-exponentially. Chess, with its branching moves, quickly reaches stupendous magnitudes. Meanwhile, counting atoms grows slower (essentially proportional to mass, not combinatorial).

The phrase “chess probabilities vs atoms in the universe” highlights this astonishment: two gigantic figures in one sentence, one from game theory and one from cosmology. Both resonate with a sense of awe and complexity. For everyday purposes, they are both effectively infinite. But it’s still fun and enlightening to compare them!

Internal Link: For a deeper dive on extreme numbers, see our [link to related article] on the biggest numbers in science and nature. It covers googols, Graham’s number, and other mind-benders.
Fun Fact: Chess theory texts often mention this comparison to show that brute-forcing chess (trying every possible game) is impossible. Instead, chess engines use heuristics.

Conclusion

In summary, when we compare chess probabilities vs atoms in the universe, we discover a startling result: possible chess games far outnumber atoms in space. Claude Shannon’s rough estimate of $10^{120}$ chess games dwarfs the estimated ~ $10^{80}$ atoms (en.wikipedia.orgen.wikipedia.org.) It’s a wonderful reminder that huge numbers appear in many domains – from the cosmic to the combinatorial.

Whether you’re a science buff or a chess enthusiast, this comparison is both mind-boggling and thrilling. It shows how a 64-square board can in theory encode more information than the observable cosmos! Remember, when someone mentions “chess probabilities vs atoms in the universe,” they mean that the game of chess has an unimaginably vast number of possible outcomes – far beyond the count of atoms in all of space. That astonishing scale is part of what makes chess and the universe so endlessly fascinating.

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