Hi there !
Here, we study the random walk of a drunk knighto over a chessboard. Let's say the knights starts its walk on the a1 square (bottom-left), we try to compute the first time return of the knighto in a1. We'll bring some maths here later to also show the rigorous demonstration without approximation.
In this program, we simulated 1.000.000 walks, and found that in average, the drunk-knighto gets back to a1-square on move 893.
Drunk paramater can be modified, we arbitrarly chose 0.3.