If you ever want to get people of a mathematical bent shouting at each other you should try to get them to agree the solution to the Month Hall problem.
“Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice?”
There are lots of ways to approach the problem; I’ve just heard a new one from Hans Christian von Baeyer’s book, Information, which should convince any die hard “it makes no difference if you stick or switch” people.
“Imagine there are not three but, but a thousand curtains, and one car. Initially you pick, say, number 815 with a resigned shrug – realising that your chances of success are one in a thousand. The host (who knows precisely where the car is) now opens 998 empty cubicles. Not the one you have picked and not cubicle number 137. Now he asks politely: ‘Do you want to stick with your first guess, curtain number 815, or switch to curtain number 137?'”. What should you do? By changing the degree it makes it a lot more intuitive.