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Keep in mind that a surfer has two choices at any given page --- follow a link or go to a different web page. Our rules of Google-opoly will now reflect these options. When we jump to a web page in our network, we'll assume that every web page in the network is an equally likely destination. Brin and Page called this jumping teleportation.

Let's play again on the network of web pages from Figure 1. We will now use two dice with different coloring as we will need to distinguish between them. While the game is automated in the applet that follows, the rules of the game are now:

OBJECT Own the web page that is the first to collect $1,000 from the surfer.
SET-UP Each node in the graph represents a web page. Players (from 1 to 6) each choose a web page to own.
  1. The surfer begins at web page 1.
  2. Each player will move the surfer in turn as determined by the roll of the dice as detailed below.
  3. If the surfer is at a dangling node, then teleport by following these steps:
    • Roll both dice.
    • The number that appears on the die with black dots is the next web page for the surfer to visit, which may be the same web page. Go to step 4.
  4. To get to this step, the surfer is not on a dangling node. Roll both dice. This will determine if the surfer follows a link on the current web page or teleports and also the next web page to visit.
    • If the die with red dots is a 1 through 5, then
      • the surfer follows a link on the current web page;
      • the die with black dots indicates where to visit next according to the corresponding rule in Table 1.
    • If the die with red dots is a 6, then the surfer will teleport. In this case, the number that appears on the die with black dots is the next web page to visit.
  5. Whenever the surfer lands on a web page, the page's owner receives $1. A bar chart will keep track of the total amount of money collected by each web page.
  6. If no web page has collected $1,000 go to step 2.
  7. The game ends when a web page collects $1,000. If someone owns such a web page, that person wins the game.

Figure 4. The first Google-opoly game board with the option to teleport.

You can play this game with the applet in Figure 4. Play roll by roll for a bit by clicking the "Roll" button.

Now, let's do some fast rolling of the dice to randomly surf with these rules by clicking the "Roll continuously" button. In the histogram to the right of the game board, you should see that web page 1 and 4 are in a bit of a neck and neck race for the most revenue. With only $1,000 being the revenue that wins the game, either web page 1 or 4 might win. Even if web page 4 wins a particular round, if you allow the number of rolls to increase, the bar chart should settle down and indicate that web page 1 would receive the most revenue over more time. Depending on your sequence of rolls, this can take some time to observe.

Note, you can speed things up even further in the applet by clicking the "High Speed" option. You can also turn off teleporting by de-selecting the "Teleport" option in the applet. Experiment and see what you can learn!

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