9781118041581

Decision Trees 505

Note that this expected profit is a weighted average of the possible outcomes,

the weight for each outcome being its probability. The greater an outcome’s

probability, the more weight it has in determining the overall expected profit

(i.e., the expected profit moves closer to it). For instance, if the strike chances

were .5, the expected value would be a straight average of the possible profit

and loss, or $200,000. Better strike odds produce a higher expected profit.

In Figure 12.1, the expected profit of $120,000 has been recorded at the

chance node of the tree. This indicates that, before the chance event has been

resolved (i.e., before the true outcome, oil or no oil, has been revealed), the

expected value of the risky drilling prospect is $120,000. According to the

expected-value criterion, the wildcatter’s optimal decision is to drill. The dou-

ble slashes through the decision tree’s “do not drill” branch show that this

choice has been ruled out.

CHECK

STATION 1

A firm supplies aircraft engines to the government and to private firms. It must decide

between two mutually exclusive contracts. If it contracts with a private firm, its profit will

be $2 million, $.7 million, or $.5 million with probabilities .25, .41, and .34, respectively.

If it contracts with the government, its profit will be $4 million or $2.5 million with

respective probabilities .45 and .55. Which contract offers the greater expected profit?

GOOD AND BAD DECISIONS AND OUTCOMES Suppose the wildcatter follows

the expected-value criterion and drills the site. Unfortunately, the site turns out

to be dry. The resulting $200,000 loss is a bad outcome.But this does not mean

that the choice to drill the site was a bad decision.Given what the wildcatter knew

then, the risk was worth taking. Roughly speaking, the chance of a very large

profit outweighed the chance of a smaller (although sizable) loss. Drilling was

a good decision that happened (unluckily) to end in a bad outcome. Alterna-

tively, suppose the wildcatter chooses to drill a second site instead of the first. At

the second, the outcomes are $550,000 and $220,000, with probabilities .3

and .7, respectively. The expected profit of the second site, $11,000, is barely

positive. Upon drilling the second site, the wildcatter strikes oil. Certainly this

is a good outcome. But even a lucky outcome cannot turn this into a good deci-

sion. In fact, the second site offers uniformly worse outcomes and worse odds

than the first. Accordingly, it never should be chosen over the first site. (If the

wildcatter has sufficient resources, both sites could be drilled profitably.)

The point is that a good decision must be judged on the basis of the infor-

mation available before the fact, that is, at the time the choice must be made.

Of course, hindsight is 20–20, but this is of no avail to the manager. Moreover,

20–20 hindsight is misleading when it comes to evaluating past decisions. A

bad outcome does not brand the decision as bad, nor does a good outcome

mark a decision as good. What matters are the chances of the foreseeable good

and bad outcomes at the point of decision. No matter how basic this point, it

is surprising how often it is forgotten by decision makers in business and

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