Door Prize: Fill & Download for Free

My favorite problem of this type:Suppose you are at a dinner party. The host wants to give out a door prize that is wrapped in a box. Everyone (including the host) sits around a circular table and each person is given a fair coin. Initially the host is holding the box. He flips his coin. If it is heads, he passes to the right. If it is tails, he passes to the left. The process is repeated by whichever guest is holding the box. (Heads, they pass right; tails, they pass left.) The game ends when the last person to receive the box finally gets it for the first time. That person gets to keep the box as the winner of the game.Where should you sit to maximize your chance of winning?In my experience, the initial intuitive response is, "On the opposite side of the table as the host." After a minute, people second guess themselves and say "Right next to the host." Eventually the give up - not knowing that they were right in both cases. In fact, the distribution is uniform. Every guest is equally likely to win the prize regardless of which seat they choose. (Given that you win the game, the expected length of the game is shorter when you sit next to the host and gets longer as you move further away, but the probability of winning is constant.)

This is not pretentious, but there isn't a question for selfish boss behavior. I once worked for a utility company. Each year, there was a large, expensive Holiday party for all employees. This was for the CEO and officers, and included everyone down to the lowest hourly wage employee. There were always lots of door prizes. The biggest prize was usually a washer & dryer. One year, the CEO's number was chosen for the top door prize. I watched in amazement as he just smiled and collected the prize. I was surprised that the officers even had entries in the drawing. I was amazed that he passed on the obvious choice to make a good show of insisting that another name be chosen. He just walked passed all those meter readers and collected the voucher for the appliances, smiling and looking like a winner all the way.

Given the thousands of people who descend on us at our model train shows, it is inevitable that a few will have “issues” with us.Our staff people wear “How Can I Help” badges identifying them as staff, but I frequently move around “in corn frito” so as engage visitors as if I were one of them.Now and then, I’ll encounter someone who is so pissed off as to be dehydrated, and I’ll ask about the problem.Which leads to a long tirade, a litany of faults and defects which no self-respecting show operator would ever permit. Eventually, the plaintiff exhausts himself, and I answer each of the complaints:The Maryland State Fair Grounds is not owned or operated by the State. It is privately held. But I will forward your parking issue to the management.The food is supplied by an outside vendor who has a contract with the Fairgrounds. We have no control over it, and we don’t make any money from food sales. Meanwhile, here is a coupon good for 15% off at a local pizzeria.The show does not accept credit cards, because it takes too long to process the sale and holds up the line. But you can write a check, and the cashiers will accept it.The door prize drawings are not rigged. If every winner actually claimed his prize, we would be out about $3 thousand every show.Eventually, the complainer asks to talk to a manager. I simply say, “I can do better than that. How about the owner?”The customer agrees. “Yeah, who is the owner?”And I say, “I am. Here’s my card, and here’s a pass for a free show, next time. Have a great day.”The visitor stands there in stunned silence, I give a slight bow and take my leave.