SETO Fun Facts

1. Sixteen pieces. More than 20 trillion arrangements.

If all 16 SETO pieces are treated as unique and placed on the 16 squares of the 4×4 board, they can be arranged in:

16! = 20,922,789,888,000 different ways

At a rate of one arrangement per second, nonstop, it would take approximately 663,000 yearsto view them all.

2. Add one outside piece

In SETO, a piece may also occupy one of four outside positions.

Counting:

16 choices for which piece is outside
4 possible outside positions
every arrangement of the other 15 pieces and the empty square

The total becomes:

1,339,058,552,832,000 possible configurations

That is approximately 1.34 quadrillion possibilities.

At a rate of one configuration per second, it would take about 42.4 million years to examine them all.

3. Add two outside pieces

When two pieces are outside the board, with each occupying a different outside position, the number rises to approximately:

15,064,408,719,360,000 possible configurations

That is more than 15 quadrillion possibilities.

At a rate of one configuration per second, it would take approximately 477 million years to examine them all.

4. Then the game becomes even larger

Those figures count only where the pieces are located.

They do not yet count:

whose turn it is
which player has already used their Vault
legal and illegal movements
jumps
Switch moves
Break relocations
Return by Vacancy
Return by Pattern
the Ace and Relay pieces
repeated scoring patterns
different scores on the way to 7 points
the many different move sequences that can reach the same board position

Because several different move sequences can produce the same board arrangement, the complete number of possible SETO games would be vastly larger than the number of static configurations.

A 20-centimetre board. Sixteen squares. More possibilities than anyone could explore in a lifetime—or even in millions of lifetimes.

5. More Possible Games Than Stars?

Only 16 squares. Infinite imagination.

Imagine that, on average, a player has just 10 legal moves to choose from on each move.

After 20 moves: 10²⁰ possible move sequences (100 quintillion)
After 24 moves: 10²⁴ possible move sequences — roughly the estimated number of stars in the observable universe.
After 30 moves: 10³⁰ possible move sequences.
After 40 moves: 10⁴⁰ possible move sequences.

And that's using only 10 possible choices per move.

In a real game of SETO, the number of choices can be even higher thanks to different piece movements, jumps, Returns, Breaks, Switches, and Vaults.

The result? The number of possible SETO games may exceed the estimated number of stars in the observable universe.

For comparison, astronomers estimate there are roughly 10²² to 10²⁴ stars in the observable universe. That number is so vast that it is often compared to—and may even exceed—the total number of grains of sand on all the beaches and deserts on Earth.