# Chance News 11

## Quotation

"Then there was the man who drowned crossing a stream with an average depth of six inches." - W.I.E. Gates

## Forsooth

Here is a Forsooth from the December 2005 issue of RSS News.

The current rate of shrinkage they calculate at 8% per decade; at this rate there may be no ice at all during the summer of 2060
BBC News website

## Investing in a poker player

Texas Hold'em poker is sweeping the globe as a favorite pastime of gamblers, young and old, novices and experts.

The following web site discusses a proposition from an amateur poker player to gain financial backing for entry into the 2006 World Series of Poker.

### Questions

Can playing tournament poker be legitimately described as an "investment" (one with medium risk and potentially high return)?

What factors would you look for to determine the attractiveness of this investment opportunity?

## A game show for probabalists

A game show for the probability theorist in us all
New York Times, Dec. 14, A19
Gia Kourlas

This article describes the new NBC game show called "Deal or No Deal" The rules are described on the NBC website as:

The rules are simple. Choose a briefcase. Then as each round progresses, you must either stay with your original briefcase choice or make a "deal" with the bank to accept its cash offer in exchange for whatever dollar amount is in your chosen case. Once you decide to accept or decline the bank's offer, the decision is final.

To fully understand the game you should play it here. Choose "game" from the options and go to the bottom of the page that comes up and choose "Start game".

The Times article observes that it is not known how the bank determines its offers. Kourlas says that, at a meeting at his house to discuss the game, some thought the decisions my be based on probability concepts such as expected values and others thought that it had "psychological--but not logical--coherence.

Of course the game as played on the Internet the bank clearly has a strategy for determing the offers and if this were known we would have an optional stopping problem reminiscent of the famous secretary problem. This is obviously presents a nice challenge for students in a probability or statistics class.

### Questions

(1) The amounts that are in the briefcases at the beginning of the game are:

 $0.01$1 $5$10 $25$50 $75$100 $200$300 $400$500 $750 $1,000 $5,000$10,000 $25,000$50,000 $75,000$100,000 $200,000$300,000 $400,000$500,000 $750,000$1,000,000

(1) What is the expected amount in your initial suitcase?

(2) Assume that the banker always offers the expected value of the amounts in the remaining suitcases. Would any strategy give you a higher expected winning then just accepting the banker's first offer?

(3) If the bank does not offer the expected amount in the remaining suitcases, what is your optimal strategy to maximize your expected winning?

(4) Why might you not want to use expected value in deciding on your strategy for playing this game?

Sugested by Norton Starr and submitted by Laurie Snell.