# The Oil Wildcatter

In this example, an oil wildcatter must decide either to drill or not to drill. He is uncertain whether the hole is dry, wet or soaking in oil. The wildcatter can make seismic soundings that will help determine the geological structure of the site. The soundings will give a closed reflection pattern (indication for much oil), an open pattern (indication for some oil) or a diffuse pattern (almost no hope for oil).

The wildcatter has two decisions to make, namely whether to test with seismic soundings costing k$10 and whether to drill costing k$70. The utility gained from drilling is determined by the state of the hole (dry, wet or soaking).

The domain of this problem is modeled by the influence diagram in figure 1. Note the arrow from Seismic to Drill. Since a decision node has no table assigned this arrow does not represent a causel dependency. In stead it shows the system that when the decision of Drill has to be made, the state of Seismic is known. If this is not specified, the calculations will not be correct. In fact, it will be impossible for the system to know which of the decisions of Drill and Test will be made first. The HUGIN System needs to know the sequence of decisions in an influence diagram, and if this is not clear, no compilation will be performed.

Figure 1: Influence diagram modeling the oil wildcatters decision problem.

In figure 1, the chance node Oil has states "dry", "wet", and "soak", the chance node Seismic has states "closed", "open", and "diff", the decision node Test has actions "test" and "not", and the decision node Drill has actions "drill" and "not". In table 1 and 2, the cpts of the nodes Oil and Seismic are shown. In table 3 and 4, the utility tables of the utility nodes Pay and Cost are shown.

Oil="dry" | Oil="wet" | Oil="soak"
0.5 | 0.3 | 0.2
Table 1: P(Oil).

| Test="test"
Oil="dry" | Oil="wet" | Oil="soak"
Seis.="closed" | 0.10 | 0.30 | 0.50
Seis.="open" | 0.30 | 0.40 | 0.40
Seis.="diff" | 0.60 | 0.30 | 0.10
| Test="not"
Oil="dry" | Oil="wet" | Oil="soak"
Seis.="closed" | 0.33 | 0.33 | 0.33
Seis.="open" | 0.33 | 0.33 | 0.33
Seis.="diff" | 0.33 | 0.33 | 0.33
Table 2: P(Seismic | Oil, Test).

Drill="drill" | Drill="not"
Oil="dry" | Oil="wet" | Oil="soak" | Oil="dry" | Oil="wet" | Oil="soak"
-70 | 50 | 200 | 0 | 0 | 0
Table 3: U(Pay).

Test="test" | Test="not"
-10 | 0
Table 4: U(Test).

The influence diagram is now constructed using HUGIN Runtime and after compilation, the results can be seen in the initial state of figure 2. The only important values to read at this point are those of Test. HUGIN has no way of knowing whether the wildcatter chooses to test or not. Thus, the values of the nodes depending on Test will not be correct.

You need a java capable browser to see this figure.
Figure 2: The results of propagating the influence diagram. You can click the states of Seismic to read the expected utility of drilling given the result of the seismic soundings. Initially, the figure shows the result of a propagation before anything is known about whether the wildcatter will test with seismic soundings or not. At this point, the values of the other nodes cannot be calculated correctly and should be ignored.

We see that the expected utility of testing is k$22.5 while the expected utility of not testing is only k$20. This implies that it will be best for the wildcatter to test with seismic soundings which will give him the states of Seismic. If you try to click at the state names of Seismic in the figure, you can see what happens to the expected utility of Drill when the seismic test has come up with a result. If you choose "closed", the expected utility of drilling is k$77.5. Else, if you choose "open", the expected utility is k$22.9 and if you choose "diff", the expected utility is k$-40.5. In the last case, it will obviously be better not to drill only giving expected utility k$-10.0.

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