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RewardandRisk Analysis
& Management 2012
Last revised: January 10, 2013

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analysis & Management--Overview

"All the world's a stage, ...[and] ... a casino ..."

William Shakespeare wrote, and fairly:

All the world's a stage,
And all the men and women merely players:
They have their exits and their entrances;
And one man in his time plays many parts, ...

We add this point:

All the world's a casino,
And all the men and women merely players.
Everyone, every moment, lives with many bets:
Some, not of his choosing;
Some, not fair;
Some, not winners.
And every day he bets his life.

So, let's go backstage at a fictional production that may remind you of events that really happened, that were on television, and that you saw. What follows is a fictional storyFn 1 about the fictional "Hank", as he watches (literally), as a new producer (figuratively) enters the theater, tears up everyone's script (figuratively) and sends papers flying through the air (literally), and informs Hank (in not so many words) that Hank has to start improvising, immediately!

Then, we'll review Hank's situation from the perspective of RewardandRisk.

A window on Hank's world

The time is 8:45, and Hank's show starts at nine, so people are wandering into the theater. He leads a small ensemble that does improv and always plays to a small audience. Hank is going through his pre-show ritual: He stands with a cup of coffee in one hand, looking out the window, facing an imaginary audience, establishing eye contact with person after imaginary person, silently mouthing his best sound bites from previous performances. Hank is feeling good. Everything is going well and on schedule, until ...

... he saw an enormous "fireball shoot out of the north tower and blow past" the windows of his northwest corner office. What the fuck? he thought. He has more important things to do than look at his watch, but it says 8:46:26 a.m. on September 11, 2001. Hank is high up in the south tower.

"September_11_attacks#Casualties" (Wikip., acc. 1/10/13)

Now, we know that (a) Mohammed Atta has just canceled Hank's morning meeting, flight American 11, 1 WTC, and more than 1500 lives, (b) nearly another 700 died aboard flight United 175, and in and near 2 WTC, and (c) that Hank--a major player for his firm--has just made his entrance as a bit player--an extra, really-- in a much larger production on a much larger stage.

Hank didn't know, then, what we know, now--that "Delay meant death on 9/11". What can we say about how Hank's RewardandRisk profile, analysis, and management might have changed, after 8:46:26?

We'll introduce the key concepts of RewardandRisk, RewardandRisk Profile, RewardandRisk Analysis, and RewardandRisk Management, and illustrate them with Hank's situation--what he knew and when he knew it.

RewardandRisk profile

A RewardandRisk Profile is a tabulation or other complete description that includes (a) a "list" of "events", everything that might happen at some time (or, at each time, depending on the case) in the future, and (b) the corresponding probability for each event in the list (or a way to compute it). A quantitative person (a "quant") might call the profile by a familiar name: a probability distribution. 

In Frank's story, as in life:

  1. At any moment, the list of possible events will be incomplete, and
  2. the probabilities will be SWAG estimates, at best.
  3. From moment to moment, the profile will change.
Before 8:46:26 ("Before")

Before 8:46:26, Hank would have focused his attention on events like losing his usual glib speech (from anxiety), having to take an unscheduled bathroom break (as a result of drinking much coffee), and identifying and handling unhappy campers in the audience. 

After 8:46:26 ("After")

At 8:46:26, Hank and about 2,000 others were above the 81st floor of 2 WTC. After that, Hank would focus his attention on events that might threaten his safety. He might wonder, What did I just see? Does it have consequences for me? Over time, this focus would narrow to particular events that might threaten his life. The probabilities of such events would change over time. Some would approach zero, and some would approach one.

RewardandRisk analysis

"Before", in a familiar situation, Hank would not have to do much analysis, which he had done long before.

"After", ideally, analysis would occupy almost all his time, at first. He would gather information by listening to people around him, listening to announcements over the public address system, looking at the north tower, making telephone calls (if he could get a signal), listening to a radio or watching television, etc. Maybe, he would explore his building, by entering an emergency stairwell. He might seek out the fire marshall for his floor.  

RewardandRisk management

A rational person wants to manage his RewardandRisk, so as to maximize his satisfaction or happiness (his "utility" or "expected utility"). RewardandRisk management is the process of choosing the best set of gambles from the available sets of gambles.


"Before", Hank had developed his speaking skills over years, joining Toastmasters International®, volunteering for "Table Topics", taking improv classes, etc. He was "practicing" his performance--as much as possible, given its improvisational nature--so as to further reduce the probability of stage fright, "brain freeze", etc. He drank coffee to boost his energy. He would visit the restroom before his entrance, "onstage", to avoid interrupting his "performance". He always told his audience that he would be available after the talk to answer any further questions they had.


"After", all of Hank's risk management plans from "before" were obsolete.

  1. If (a) Hank had an escape plan ready for just such an eventuality, (b) he had started descending, immediately, via either the elevator or emergency stairway, and (c) at 9:03 a.m. he were at street level or in the stairwell below floor 78, then he would have survived.
  2. If Hank had trusted the authorities, waited for instructions to leave, and were on or above floor 78, he would have died, almost certainly, with some 600 others of similar mind. (Some 1,400 others had fled, already.)
  3. If Hank were still above the impact zone at 9:03 a.m., then he would have had a front-row seat, ...
  "... when all hell broke loose."

"September 11, 2001 - As It Happened - The South Tower Attack" (Youtube, 8/30/07)

At about 9:03 a jet airliner crashed into Hank's building. Hank and about 600 others were above the 81st floor.

At this time and place, those 600 people did not realize that "certain escape" was not an available choice, that "How do I escape?" was not a problem to solve, that "escaping to safety" was, essentially, a pure gamble. The six main ways that Hank could manage his mortal risk boiled down to two choices:

  • use stairwell A, B, or C, and
  •  escape "up", or "down".

Now, it's a matter of luck.

"Stairwell A" (NYMAg, 8/27/11)

"Only four people who were above the 81st floor when the plane hit were able to use Stairwell A to escape [down to the street, not up to the roof]—each of them beating the worst possible odds of survival that day."

"Delay meant death on 9/11" (USAToday, 9/2/02)

The other 600 people who had remained above the 81st floor of 2 WTC died. 

Resolution of uncertainty

"9/11: South Tower "Collapse" video compilation" (Youtube, 2/13/07\)

At 9:59 things got worse. As the nearby video shows, the south tower collapsed.          


You may be able to manage some of the smaller gambles in a way that improves your overall situation, taking care that swapping one little gamble for another doesn't somehow worsen your overall situation. However, managing some gambles may worsen your overall situation. For example, if you exceed the speed limit to make an appointment, and you drive so fast that you lose control, you could die.

Summary and conclusion

The basic idea of RewardandRisk is that the world is a casino and your life is a big, complicated gamble. Sometimes, you're "all in", even if you never volunteered to be in that game.

Your RewardandRisk profile at a given time is the set of gambles that you are taking at that time.

You learn about your profile from Rewardandrisk analysis, the process of discovering your sets of available gambles. RewardandRisk analysis may allow you to get a better handle on the odds of any particular game, and do a better job of RewardandRisk management.

RewardandRisk management is the process of trading one gamble for another--or deciding to do nothing, because you can't trade up. You could manage your RewardandRisk without sufficiently analyzing your situation, but that may not be wise. RewardandRisk analysis may improve your RewardandRisk management.

So, a rational person would do the following:

  1. Recognize that life is a bunch of gambles, and that everything you have is at risk every moment.
  2. Analyze opportunities, the right amount, to define the sets of gambles that are available. Better analysis is expensive, but worse can cost even more.
  3. Manage life's gambles by picking the best available set of gambles, but don't lose sight of the big picture. Don't fix one problem, while making your overall situation much worse. could be a resource that helps you do a better job of analyzing and managing the RewardandRisk that is an inevitable part of your life.


"Inches decide life, death on the 78th floor" (USAToday, 9/3/11)

"Delay meant death on 9/11" (USAToday, 9/2/02)

"Four survived by ignoring words of advice" (USAToday, 12/19/01)

"Stairwell A" (NYMAg, 8/27/11)

"September 11, 2001 - As It Happened - The South Tower Attack" (Youtube, 8/30/07)

"The miracle survivors" (NYMag, )


1Fiction Disclaimer: This is a work of historical fiction, set in the World Trade Center on 9/11/01. The main character, "Hank", is a composite, based loosely on a person, who survived working in the WTC at the time of the 1993  bombing. 

The names, characters, businesses, organizations, places, events, and incidents either are the product of the author’s imagination or are used fictitiously. Any resemblance to actual persons, living or dead, in actual events or locales is entirely coincidental.