Probabilistic (randomized) algorithms before "modern" computer science appeared Edit: I choice the answer with highest score by December 06, 2012.

This is a soft question.

The concept of (deterministic) algorithms dates back to BC. What about the probabilistic algorithms? 

In this wiki entry, Rabin's algorithm for the closest pair problem in computational geometry was given as the first randomized algorithm (year???). Lipton introduced Rabin's algorithm as the start of the modern era of random algorithms here, but not as the first one. I also know many algorithms for probabilistic finite automata (a very simple computational model) discovered during 1960s.

Do you know any probabilistic/randomized algorithms (or method) even before 1960s? 

or

Which finding can be seen as the first probabilistic/randomized algorithm?
This is discussed a bit in my paper with H. C. Williams, "Factoring Integers before Computers"

In a 1917 paper, H. C. Pocklington discussed an algorithm for finding sqrt(a), modulo p, which depended on choosing elements at random to get a nonresidue of a certain form.  In it, he said, "We have to do this [find the nonresidue] by trial, using the Law of Quadratic Reciprocity, which is a defect in the method.  But as for each value of u half the values of t are suitable, there should be no difficulty in finding one."

So this is one of the first explicit mentions of a randomized algorithm.