# MCS-177 optional assignment

One application of computer programs is performing simulations. In this assignment, your goal will be to simulate investments or wagers.

This assignment differs from other assignments in that I will not specify what procedures you should write or in what order you should write them. You'll make all the decisions. This assignment is not relevant to the current reading in the textbook, though I suggest you read through Chapter 7 before you begin. You may use any material from earlier in the course you might find helpful. Feel free to discuss this assignment freely with classmates to strategize, but do the programming work and data collecting on your own.

I will not specify how much this assignment will affect your final grade. It's my hope that you undertake the assignment because it interests you, and that the affect on your grade is of secondary importance. Although the assignment is due by the last day of classes, please try to turn it in earlier.

## All or nothing wagers

Suppose you have one dollar, and you are allowed to make a bet. Half the time you win, and you get back \$1.60, but if you lose, you only get back \$.60. You can place this over and over again, but each time you play you have to bet all the money you have. If you win, you get back 160% of what you started with. If you lose, you get back only 60% of what you started with. This might seem like a good bet since you stand to win 60% and lose only 40%.

## Diversified wagers

Suppose that instead of betting all your money each day on one bet, you can bet half your money at a time on two separate bets. So, if you start with \$1, you'll bet \$.50 twice. There are four equally likely possibilities:
WIN-WIN You'll end up with \$.80 + \$.80 = \$1.60 You'll end up with \$.80 + \$.30 = \$1.10 You'll end up with \$.30 + \$.80 = \$1.10 You'll end up with \$.30 + \$.30 = \$.60
Once again, you bet all your money each day, but in two separate bets. This is like diversifying a financial portfolio.

Investigate which wager is better for a typical person to make: The all-or-nothing or the diversified wager. You should write procedures to help investigate this question. You should assume that a person will bet all their money each day for a while. Make any assumptions you find helpful, including how many days the person bets.

## What to turn in

You should write a short report consisting of the data you collected and the conclusions you drew concerning the two types of bets. Be sure to present the data clearly enough so I can easily figure out what it means. Include copies of the procedures you wrote to help investigate the questions. Naturally, any procedure you write (which is not self-explanatory) should have a comment clearly explaining what it takes as arguments and what it returns.