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and a circle. The rectangle represents a step or decision in the process, e.g. the arrival
of attendees or the accumulation of revenue. The circle represents an uncertain
event and the outputs of the circle are the anticipated results of the event. These
are the symbols that are also used in decision trees , but our use of the symbols is
slightly different from those of decision trees. Rectangles in decision trees represent
decisions, actions, or strategies. In our use of these symbols, we will allow rectan-
gles to also represent some state or condition, for example the collection of entry fee
revenue or the occurrence of some weather condition like rain. Exhibit 7.6 shows
the model for this new IFD modeling approach.
In Exhibit 7.6, the flow of the IFD proceeds from top to bottom. The first event
that occurs in our problem is the resolution of the uncertainty related to weather.
How does this happen? Imagine that Fr. Efia awakens early on October 6th and looks
out his kitchen window. He notices the weather for the day. Then he assumes that
the weather he has observed will persist for the entire day. All of this is embodied
in the circle marked Weather Condition and the resulting arrows. The three arrows
represent the possible resolution of weather condition uncertainty, each of which
leads to an assumed, deterministic number of participants. In turn, this leads to a
corresponding entry fee revenue varying from a low of $15,000 to a high of $40,000.
For example, suppose Fr. Efia observes sunshine out of his kitchen window. Thus,
weather condition uncertainty is resolved and 4000 attendees are expected to attend
Vegas Night at OLPS , resulting in $40,000 in entry fees.
7.4.4 Attendees Play Games of Chance
Next, the number of attendees determined earlier will participate in each of the three
games. The attendees either win or lose in each game; an attendee win is bad news
for OLPS and a loss is good news for OLPS. Rather than concerning ourselves with
the outcome of each individual attendee’s gaming results, an expected outcome of
revenues can be determined for each game and for each weather/attendee situation.
An expected value in decision analysis has a special meaning. Consider an indi-
vidual playing the WOD. On each play the player has a 35% chance of winning.
Thus, the average or expected winnings on any single play are $17.50 ($50 0.35)
and the losses are $32.50 ($50 [1–0.35]). Of course, we know that an attendee
either wins or loses and that the outcomes are either $50 or $0. The expected values
represent a weighted average; outcomes weighted by the probability of winning or
losing. Thus, if a player plays WOD 100 times, the player can expect to win $1750
(100 $17.50) and Fr. Efia can expect to collect $3250 (100 32.50). The expected
values should be relatively accurate measures of long term results, especially given
the large quantity of attendees, and this should permit the averages for winning (or
losing) to be relatively close to odds set by Fr. Efia.
At this point we have converted some portions of our probabilistic model into a
deterministic model; the probabilistic nature of the problem has not been abandoned,
but it has been modified to permit the use of a deterministic model. The weather
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