Why do you get an answer which makes sense, when it is pure chance?
How come you can actually use the answer, even though it is centuries old?
There are two books, which address these questions. One is "The Field" by Lynne McTaggart, the other is "I am right, you are wrong" by Edward de Bono. He wrote many books, but I will quote from this one. His insights are so practical and effective that they are mandatory in Brazilian schools as the base of teaching.
According to De Bono the brain thinks in the same way as the flow of water. There is a catchment basin, in which all rivulets flow towards the same lowest point, on their way joining into rivers, big rivers and eventually a sea or ocean. Everything in that basin is "logical": if one goes from the end of the river back to the sources, they all make sense.
But if you can step out of that basin, you enter another catchment basin. An idea will flow towards a different sea, another ocean. Or, if you step back to your problem, suddenly you bring with you a very different idea into your original basin, one which could not be reached as long as you stayed inside. You created a new source!
When you try to solve a problem and you cannot reach a solution, then find a source which "makes no sense", which comes from another basin. Open a dictionary or the bible and take the first noun you encounter. Or look around and take the first image you see. Or cast a hexagram...
Now you are looking at your problem from two sides. The original logical one and the weird one which makes no sense. But this other side changes your problem, or maybe only your way of looking. Suddenly the snake bites its tail, or an apple falls on Newton's head, or Archimedes jumps out of the bath, shouting "eureka". They took a step out of the catchment basin and connected that fresh thing to their problem.
A different catchment basin is a paradigm shift. Your horizon expands.
And who knows, chance might not be just chance after all:
Lynne McTaggart researched many experiments of the past 50 years, about the influence of the mind. There is substantial evidence that the mind can influence matter. Especially when there is only a small influence needed to make something change direction.
So the idea of coins or sticks answering your deepest thoughts or wishes or intuition is not weird. It explains as well why especially a computer-casting gives good answers.