Homework on Expected Value – Due Feb 10, 2009

This work needs to be done independently. It is “open book”. You can use any references you like though I think that the class notes should be sufficient. You may not consult any other persons by any means of communication.

When you submit your answers (Feb 10), please print out this sheet and sign it.

Because I understand that graded homework is to be done independently, I have not consulted with anyone else on this assignment.

________________________________________________

Your signature above.

For each of the following two games (Game A and Game B) you are to answer the following questions and show exactly how you obtained your answer. Use and calculation of “expected value” and the “don’t get outguessed” principle are essential to this assignment. In both games, the players show a head or a tail and the payoff (plus for Topsie, minus for Lefty) is shown.

1. What is Topsie’s best strategy and Lefty’s best strategy?

2. Who has the advantage? How much advantage? Or, is this a “fair game”?

Game A:

Payoff Matrix		Topsie’s choices
		H	T
Leftie’s choices	H	+4	-3
	T	-2	+1

Game B:

Payoff Matrix		Topsie’s choices
		H	T
Leftie’s choices	H	+2	-3
	T	-2	-1

Note that Game B is peculiar in that there is a fairly obvious winning strategy for Lefty. (What is it?) But can you prove or disprove that this is Lefty’s “best” strategy?