Case: Ace-Face Card Game

My students found the idea of a decision matrix a bit strange and they had trouble understanding the "expected value strategy (Giere pp 273-274). These exercise seemed to make both the matrix and the EV strategy a little clearer. I did the exercise in two parts as indicated below.

Rock-Scissors-Paper Someone in the class will remember the rules of this came and they can explain it to the class and any international students. A Japanese student last time claimed to know it already. Then the student groups are asked to create a decision matrix for the game. Here's mine:

Decision Matrix

		States of the World
		Rock	Scissors	Paper
Your Options	Rock	0	+10	-10
	Scissors	-10	0	+10
	Paper	+10	-10	0

Students will use different value sets, but all should have the same general ranking of values. In the condition of complete uncetainty, all these choice have equal value {the game after all is to guess what your opponent will do next}.

But what if (from scouting reports) you knew that your opponent picked paper 80% of the time, and each of the others 10% of the time? Would the options still be equal? They should be able to verbalize the choice of "scissors" giving them the greatest expected success because they weight the paper state more than the others.

Ace-Face: a betting strategy game Each student is given a set of rules and a deck of cards. In the rules they are told to con

Ace-Face Decision Matrix Student groups should be able to construct this from the rules they are given, although they'll try to play without doing the calculations.

		States of the World				Expected Value	Satisfaction Level
		Ace p= 1/13 = 0.077	Face p= 3/13 = 0.231	High p= 4/13 = 0.308	Low p= 5/13 = 0.385	Expected Value	Satisfaction Level
Player's Options	Ace	+$30	+$10	-$5	-$10	-$0.78	-$10
	Face	-$10	+$15	+$5	-$5	+$2.31	-$10
	High	-$10	+$5	+$10	$0	+$3.46	-$10
	Low	-$5	$0	$0	+$5	+$1.54	-$5

Some groups will have to be coached to realize they know the probability of each State of the World from the number of cards in each category.

When the group has finished the matrix and can identify the options, they play the game. For the odds to remain constant, they need to return played cards to the deck and shuffle, but we ignored that complexity and it worked out. When the game is over, the expected value gave the best prediction of each player's winnings or losings. This fit well in 75 minutes, but there wasn't much game time in the 50 minute class. Perhaps it could be split over two sessions and combined with Chapter 10.