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The Café Bella-Roma love-seats A man and a woman go to Café Bella Roma either during the whole morning or whole afternoon, on just one random day every week. The thing is, if this man and woman ever sit opposite each other, they will fall in love, and the only chance they get to do this is sitting opposite each other at the Café Bella-Roma. They choose where to sit randomly. The Café has 3 tables, each with 2 chairs opposite each other, and never has any other patrons sitting at the tables when either the man or woman are there. What is the average number of days it will take them to sit opposite each other and fall in love? Suppose now that the Café has up to 6 patrons at any one time, and there is equal probability that the seats in the Café are occupied with any of 0 -6 of them. Now what is the average number of days it will take them to sit opposite each other and fall in love? Marcello, one of the owners, (both of whom secretly know all of this), at the beginning, Marcello wants to make an even bet that they will have met by a certain number of weeks. What number should he bet on so that his chances of winning the bet are 50/50?" The other owner, David, is more civic-minded and wants to know what the best thing he can do is to increase the chances of the man and the woman falling in love. His idea is to put in an extra table. Marcello reckons they should take a chair away from one of the tables. For this part, assume that still randomly 0-6 patrons are occupying the tables at any one time. There is standing room at the bar for extra's. Which idea is the best? edit: part c and d have been reworded for greater clarity.