crashonly

To adress your first question (a bit): Here's a link to a brilliant talk by a brilliant physicist Lawrence Krauss, entitled . He talks quite a bit about how exactly it was that we found out that the universe was expanding, and how do we trace the expansion further and further back in time. He talks in lay terms, so that even a computer scientist (I know, as I am a student of CS myself ) will understand! EDIT: Oh, and feel free to skip through the introduction part by Richard Dawkins.

That's not an accurate depiction of the Monty Hall problem, which is what (I think) we're talking about here. If the rules were as you state, that: 1) the guy knows where the price is 2) can reveal -any- casket after you've made your pick, and you won't get to make another pick after he reveals your casket. Then indeed he would always reveal your chosen casket right away if you had picked an empty one, so as not to give you any additional chance of winning. You'd always have 1/3 chance of winning, and you should never switch.

It has everything to do with the man who is running the stall knowing where the price is, and always revealing an empty one that you did not pick. Your original pick is going to be right 1/3 of the time, and 2/3 of the time the price will be in one of the remaining caskets. So if we make the assumptions that the guy running the show knows where the price is and always reveals an empty one, 2/3 of the time the price is going to be in the casket you did not pick originally, and he did not reveal.

You are right that using a fraction such as 22/7 dynamically inside your code can give you more felxibility and more accurate results. You are completely missing the point, however, which is that 22/7 is a very bad value for Pi. 22/7 = 3.14285... so you see it goes off at 4th decimal already. So if 22/7 was the value you wanted to use, you would be correct, but as you want to be using an accurate value of Pi, any use of 22/7 will screw you over. This is simply wrong. 22/7 does not equate 3.14159, for some reason you seem to have replaced it with a 6 decimal approximation of Pi. This calculation is correct, and again it gives you a very bad answer, because you want to be using a more accurate approx of Pi than 22/7.