first, thanks to Marion and also to Jim Dixon; between the two of you I finally have an explanation that makes sense to me. It's called the Monty Hall problem 9hence Catspaw's reference) because it is identical with the procedure on "let's make a deal"-- M. Hall, host. If you go into Yahoo/Science/Mathematics you can get quite a discussion of this problem, under that name, but none of the explanations are as clear as the two I have seen! thanks.