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Your second game: Cycling

Now, let's play on the game board in Figure 3 that does not contain a dangling node. Playing with this new board necessitates adjustments to Table 1, which dictates where to go after each roll. Google-opoly assumes that a surfer is equally likely to visit any link on a web page. If you are at web page 1, then you must visit web page 4. Therefore, all rolls should lead from web page 1 to web page 4. Now, web page 4 has 3 links. So, there is a 1/3 chance of visiting any of its linked web pages when a hyperlink is followed from web page 4. In order to match this probability, rolling a 1 or a 2 will result in moving from web page 4 to web page 2. Can you think what entries would work for the remaining parts of the game? Keep in mind that in many cases the answers aren't unique. For instance, we could have set a rule that rolling a 3 or a 4 results in moving from web page 4 to web page 2. You will see one such set of adjusted rules in Table 2.

at page
roll a 1
visit page
roll a 2
visit page
roll a 3
visit page
roll a 4
visit page
roll a 5
visit page
roll a 6
visit page
1 4 4 4 4 4 4
2 1 1 1 1 1 1
3 1 1 1 1 1 1
4 2 2 3 3 5 5
5 6 6 6 6 6 6
6 5 5 5 5 5 5
Table 2. Rules of Google-opoly for the game board in Figure 3.

With the adjustments to the table complete, we are ready to play on the new board! So choose a web page to own and start rolling with the applet in Figure 3.

Figure 3. The second Google-opoly applet.

For this board, you should notice that you are guaranteed to eventually bounce back and forth between web pages 5 and 6 without any option of escape. This type of network structure is called a cycle. Keep in mind that a cycle could have more than 2 web pages. What is the winning guess? Web page 6 is a good guess but actually will acquire $999 at the point web page 5 collects $1,000 since web page 5 is always visited first and will be visited the same or one more time than web page 6. This can also be seen by experimenting with the applet in Figure 3.

So now we have played Google-opoly on two game boards. This is what led to Brin and Page's billion dollar business? Actually, no. Part of the success of Google is that its rankings are based on a model of internet activity. Let's think more critically about our current rules for Google-opoly and how well they reflect randomly moving around the web.

Suppose you were surfing on the network in Figure 3 and entered a cycle. By the current rules of our game, any surfing session that lands on web page 5 gets stuck bouncing between pages 5 and 6. Alternatively, let's return to the issue of the dangling node in Figure 1. Our current rules have us stuck at that web page forever! Better be careful visiting a music or video file under this model as that would be your last page to visit. This behavior doesn't reflect how people actually surf the internet. When you reach a dangling node or enter a cycle, you either enter another web page's address or click the back button. So, we will introduce a new idea into our game that will lead to an altered set of rules that better reflect surfing behavior and also make for a more interesting game of Google-opoly.

Your first game
Your second game
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Markov's strategy
Google's game


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