Sorting a deck of cards by throwing it into the air

Science · Published 19 October 2026 Swipe more like this →

In short: Imagine trying to organize a messy pile of items by simply throwing them into the air and picking them up at random over and over again. This is the literal logic behind Bogosort, a sorting algorithm so inefficient it serves as a mathematical monument to the

Bogosort, also known as permutation sort or "stupid sort," operates on a "generate and test" paradigm. Instead of using logic to move elements into their correct positions, it generates a permutation of the input and checks if it is sorted. If it isn't, it tries again. This process can be deterministic, enumerating every possible permutation, or randomized, where the algorithm shuffles the input randomly until a sorted sequence appears.

The mathematical reality of Bogosort is rooted in probability theory. For a list of distinct elements, there is only one sorted permutation out of $n!$ possible arrangements. The probability of success in a single trial is $1/n!$. To find the probability of success within $k$ shuffles, the formula is $P = 1 - (1 - 1/n!)^k$. This highlights the algorithm's extreme inefficiency: for even modest values of $n$, the probability of success remains vanishingly small unless $k$ is an astronomically large number.

While it is primarily a pedagogical tool used to contrast with efficient algorithms, Bogosort shares a conceptual link with the "infinite monkey theorem." Because there is a non-zero probability of achieving the correct permutation, the algorithm is guaranteed to finish in finite time given an unbounded number of tries. However, the work required is often impractical. For instance, while the expected number of comparisons in the average case for distinct elements is asymptotically equivalent to $n!$, the number of swaps grows even faster because shuffling the collection is proportional to its size, regardless of how quickly the algorithm detects the list is unsorted.

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