Carl Bialik, author of "The Numbers Guy" for the Wall Street Journal, has posted a reader quiz about probability. Question 4 is of particular interest to me.
4. In baseball, suppose the American League champion is better than the National League champion, such that it has a 55% probability of winning each game against the NL champ. Then the NL champ nonetheless will win a best-of-seven-games series four in 10 times. What is the smallest odd number, X, for which a World Series between these two league champs that is best-of-X will ensure that there’s a 95% probability of a just result — the superior AL champ winning?
I think I have successfully written a program that calculates the answer. My programming skills are suspect, but it seems to produce the right results for the simpler cases, if my rusty probability is correct. I am going to hold off giving my answer as to not post an answer key and skew the poll's results. (How's that for arrogance! Like my mom is going to read this and then start an avalanche of poll responses.)
I get for a 3-game series the AL champ wins 57.5% of the time. In a 7-game series that result rises to 60.8%. Any guesses as to what X is?