The coin fl ip game described in this chapter is mathematically equivalent to a “ one -

dimensional random walk. ” What this means is that you fl ip the coin; if you get heads, you take a step forward; if you get tails, you take an equal - sized step backward. The number of steps forward you get is equivalent to dollars won; the number of steps backward is equivalent to dollars lost. If you start at position +1, it ’ s equivalent to starting with

$1 in your pocket; if you start at +2, it ’ s equivalent to starting with $2 in your pocket; and so on.

Try it. You can either actually fl ip a coin and take steps or you can do it on a spreadsheet.

Most spreadsheet programs have a random number generator that gives you a random number between 0 and 1. Generate a column of, say, 100 of these. Then in the next column, use an if statement: If your random number is > 0.5, put +1; otherwise, put − 1. In the third column, keep a running total of all the numbers in the second column.

Start the column with a number which is the amount of money you started the game with. Show how long you can play without getting wiped out.