Narion, you are of course perfectly correct regarding the red/white problem. Martin Gardner , who writes (wrote?) for !Scientific American" published this problem in the 60's and was immediately heckled by a so-called professional gambler who insisted that the probability of red was evens,("only two possibilities , either red or white"). He even offered to meet Gardner and play for real money. Gardner refused, reasoning that his available capital was so much less than the gamblers capital that he could not afford the possibility of a freak run which as all statisticians know is certain to occur sooner or later.

Going back to the cups problem, my indebtedness to Jim comes by my extrapolating the problem from 1000 cups ( as he postulated) all the way down to four. In each case it is obvious that , when the house knows the correct cup, it makes sense to switch. I have to say that I still do not see it intuitively at the three-cup level, but I am familiar with mathematical patterns and I know your solution is correct.

I would just like to add that this is one of the most enjoyable threads i have ever encountered on the net.

Thank you FMaj7 for instigating it and thank you Marion for enlivening it. And thank you to all who still dont understand the correct solution for inducing a warm glow of smug self-satisfaction in those who do

Murray