The point is, I do not dispute the formula. I dispute the argument that a calculated probability is "different" than that calculation. Buffon posed a question which is calculated. For a needle the same length as the separation of the parallel lines, the result is the value of 2/pi. Again, the summation can not be terminated, because if it is, the result is rational. That would be no different that stopping the dropping of needles and calculating the result. Buffon's question has a solution and it includes pi.
No, the point is that you made a claim which has been shown false but aren't man enough to admit it.