Department of Statistics Informal Seminar
North Carolina State University

presents

Donald Richards

University of Virginia

"The St. Petersburg Paradox and the Crash of the Dot.Coms"

ABSTRACT

Peter repeatedly tosses a fair coin until it comes up heads. He agrees to pay Paul $2 if a head appears on the first toss, $4 if he gets the first head on the second toss, $8 if he gets the first head on the third toss, and so on. How much should Peter charge Paul as an entrance fee to this game so that the game is fair to both players? This game, the classic example of a St. Petersburg game, was first described in 1713 by Nicolaus Bernoulli in a letter to Remond de Montmort. It is paradoxical that no finite entrance fee can make the game fair to both players.

We will discuss the history of St. Petersburg games and some recent examples of modified St. Petersburg games, such as the game show "Who Wants to be a Millionaire?", and Cleveland Indians major league baseball player Ken Harrelson (who offered to play the entire 1969 baseball season without salary except for 50 cents doubled for every home run he hit; so his salary would be 50 cents if he hit only 1 home run, $1 if he hit 2 home runs, $2 if he hit 3 home runs, and so on).

Finally, we will see how the St. Petersburg paradox easily predicted the eventual crash of tech stocks. (For the record, I did warn a few people.) If you know anyone who lost money in the dot.com crash, please invite them to attend this talk; it will be a(nother) learning experience.

Thursday, February, 07, 2002

2:35 - 3:50 pm

106 Patterson Hall