Is this some sort of joke?

The algorithm you settled upon is known as a Bozosort, and is one of the algorithms studied in the infamous paper, Sorting the Slow Way: An Analysis of Perversely Awful Randomized Sorting Algorithms. That's right -- the algorithm that involves swapping random elements until the list is in order is considered not just awful, but perversely awful. "Perverse: showing a deliberate and obstinate desire to behave in a way that is unreasonable or unacceptable, often in spite of the consequences." .... that Perversely Awful -- So bad that one must be intentionally selecting the algorithm for its awfulness.

In that paper, this algorithm is shown to have an average run-time of O(n!), so in the case of your 20 numbers, on average it will take 432902008176640000 iterations to achieve a sorted solution. In the worst case it might never finish, since the solution is left to chance. In practical terms, as iterations increases toward infinity the probability of never finding a solution declines toward zero, meaning that if you are given infinite time a solution is virtually guaranteed. Who has infinite time?

If you are looking for an algorithm that is pretty simple to reason about, search for Bubble Sort. It's not terribly efficient, but it is also not perversely awful, and tends to be one of the easier sorting algorithms to comprehend and commit to code.