# Chance, Choice, and Consequence

“Excellence is never an accident. It is always the result of high intention, sincere effort, and intelligent execution; it represents the wise choice of many alternatives – choice, not chance, determines your destiny.”— Aristotle

### The "Who Am I?" Game

• This game helps you to perceive probabilities in terms of sets of features.
• The "chance" is a randomly-drawn mystery card with the identity of one of the characters hidden.
• The "choices" are what questions you ask to eliminate characters from consideration, based on their features. By a process of elimination you can identify the mystery character.
• The "consequences" are the number of questions it takes for you to identify the character. This is your score. You can be lucky or unlucky but, if you play multiple times, it is your skill at choosing the right questions that determines how well you do in the long run.

## Are You Ready to Play?

• (Game appears on the next slide)

### Is the Screen Too Small?

• The circles are not meant to be overlapping like this:

### Is the Screen Too Small?

• Try switching your browser to full screen so it looks like this:

• You can do better at the "Who Am I?" Game by asking more sophisticated questions. These are questions like "Does the mystery character have brown hair but no beard?
• Select the feature "Has Brown Hair", and then click "SUPPOSE YES". All the people without brown hair are excluded from subsequent probability calculations.
• Next, select the feature "Has Beard" but this time click "SUPPOSE NO". All the people with beards are excluded.
• Now click "ASK THE QUESTION". If the mystery character matches the supposed features then all characters who do not match the supposed features are eliminated. On the other hand, if the mystery character does not match those features, then all characters who do match the combination of features are eliminated.

## Are You Ready to Play?

• (Advanced game appears on the next slide)

### What Are Those Probabilities?

• We compute some useful probabilities for you:

### How Is That Useful?

• With one question you can eliminate 50% of the characters:

### Some Questions Don't Make Sense

• If you ask a question we can't answer we allow you to clear one of your selections:

• Now play the game with your friends and keep track of your average score.
• Remember: you can be lucky or unlucky in any one game, but in the long run it is your skill at exploiting probabilities that will win the day!

• And remember your winning strategy the next time you are in a situation where your decisions will reveal information, such as:
• Choosing tests to diagnose your patient's illness;
• Checking suspects' alibis after a crime;
• Finding a reliable source of supply for a critical raw material...

### The Schedule Crasher Exercise

• This game helps you to understand some common concepts in project scheduling. The problem here is to "crash the schedule," that is, to complete it in less time than originally planned.
• We have a project with 7 activities. Some activities must be completed before other activities can start:

### What Makes This Interesting?

• You can crash a schedule by adding people to help on the different project activities. There are two problems with this:
• Each additional person speeds up completion of an activity by less and less. This is called "decreasing returns to scale." You are better to spread additional people out to different activities.
• You can add people to an activity and shorten its duration but it doesn't speed up the project as a whole. That is because you speeded up a "slack" activity: no other activity is waiting for it to complete. You are better to speed up "critical" activities: ones that prevent the project from completing early.

### What's The Goal?

• Your goal is to crash the schedule to 20 days:

### How Can You Do That?

• Add people to activities (but not too many):

## Are You Ready to Play?

• (Game appears on the next slide)

### What To Avoid?

• Don't add people to a 'slack' activity:

### Where to Focus?

• Add people to 'critical' activities only. They are shown in red:

### Can You Do Better Than This?

• It took 20 people to crash the schedule. Is there a better solution?

• Reset personnel to zero and play again, but, this time, follow the guides:

### The Guides Can Help

• Using the Guides led us to a good solution quickly:

### What is the Trick?

• The "Try Me!" guides were constructed using a technique called "marginal analysis." This is a common optimization technique known by many names:
• Incremental analysis
• Greedy algorithm
• Steepest descent
• "Most bang for the buck"
• This is just one of many techniques you will learn in the study of optimization. It is not guaranteed to find the optimal solution but it is often easy to construct.