A Short Lesson in Bad Decision-Making

In business school I had to take an introductory class in statistics that we colloquially called "D&D." The official course name was Data & Decision-making.

In retrospect, it was a truly valuable class (one of very few I encountered in b-school). If you can figure out how to use statistics to determine the most probable outcome from a set of scenarios, or find predictive correlations from within a sea of data, that's real power. You can take a lot of the guesswork out of decision-making and consequently make the "right" call much more often.

I performed miserably in this class. But I had a lot of company; it was perennially voted the hardest in the school's core curriculum.

While I sometimes fantasize (masochistically) about taking the class again to master the black magic of statistics, I realize that I did learn a valuable lesson: Humans are innately poor at estimating probability.

This was proved to me time and again throughout that course, starting on the very first day.

A gifted young professor taught D&D. I was 27 at the time, and he was only a year or two older than I. Wicked smart guy.

Given his age, he had a few things to prove to us on that first day of class. He wanted to demonstrate he was a little more fun and hip than the stuffy older profs who taught our other courses. He also intended to show that even though he was the same age as us, his was the Alpha cerebrum in the room.

So as we took our seats for the first time, he asked: "Who wants to bet me $5 that two folks in this room have the same birthday?"

We all looked at each other. There were about 65 students, plus the prof. We were all thinking: "365 days in a year. Only 66 people. Those odds don't seem so bad..."

A hand went up, taking the bet. The prof asked the folks in the back row to start shouting out what their birthday was, one at a time. We got about 6 people in before someone in the middle of the room said, "That's my birthday, too." A $5 bill was passed up to the teacher.

"Anyone willing to bet me again?" he asked.

Another hand went up, figuring the odds just got much better as the "fluke" overlap had been removed.

The exercise repeated. It only took a few more shoutouts to hit another shared birthday. Another $5 was handed over.

"Anyone else?" said the professor.

Another brave student made the bet and lost his $5.


This time we students were much more tentative. But after a while I shot my hand up. "What the heck," I figured. "He's got to be running out of luck."

Wrong. I lost my $5 in about ten seconds.

What I later learned was that the professor was making an exceptionally safe bet that only appeared risky because we students were grossly misjudging his probability of being wrong.

In fact, as long as there were 57 students left, the prof's chances of winning the bet were over 99%(!). The odds would continue to be overwhelmingly in his favor all the way down to 23 people, at which point they would be 50/50.

It turns out this is a classic probability exercise known as The Birthday Problem. And it apparently has kept the beer funds of statistics professors well-capitalized for ages. 

The lesson I took from the experience is this: Probability estimation is non-intuitive. If you need to make an important decision about the odds of something occurring, don't go with your gut. It will be often wrong (sometimes wildly so). Get data, crunch the numbers, and consult a professional if you can't figure things out on your own.

This caution with regard to decision-making has served me well over my career. I've lost count of the number of times I began with a strongly-felt guesstimate that was torn to shreds by the time I did the math and learned how far reality was from my gut instinct.

And what worries me – scares me, is more accurate – is that I don't observe this same caution in the actions of the people making the truly big decisions. Like the Fed, Congress, and many of our state governors. Instead, I see people – many of whom don't have strong empirical skills or practical business experience – making rash decisions about debt, deficits, taxes, money supply, interest rates, pensions, etc. that will have implications on a staggering order of magnitude. I myself can't wrap my brain fully around some of these (classic example: The Crash Course Chapter 11: How Much Is a Trillion?). And even though I'm by no means the smartest guy in the room, I have little confidence that a career politician is able to comprehend these gargantuan repercussions at a materially higher level than I can. 

Sure, it's easy if you're an elected official to simply print more money. Or run trillion-dollar deficits. Or raise taxes instead of cutting spending. Or mint the coin. Or burn more oil. But these are not short-lived decisions. Their implications will manifest over generations.

And as the system becomes more unstable, the gut decisions will come faster and more furiously, made by those with the most hubris.

If only it were $5 of beer money that was on the line, instead of our global standard of living.

This is a companion discussion topic for the original entry at https://peakprosperity.com/a-short-lesson-in-bad-decision-making/

Thanks Adam. That does sound like a course that I need to take. 

My first thought was "Evolutionary pressure should have been in the opposite direction. It should have given us a keen sense of risk”. This is another anomaly along with the need for sleep.

Both these attributes should have been weeded out strongly. There is nothing subtle about their survival disadvantage.


Interesting point, Arthur.
My (unqualified) guess is that our species is probably well-wired to assess risks of the most immediate and mortal kind (e.g., the snarling saber-toothed tiger). It's the second-order, frequently longer-term, risks that we're blind to (why we'll avoid eating the rotten fruit so we don't keel over from Campylobacter enteritis,  but we'll pursue a steady diet of junk food that simply kills us more slowly)

It would be interesting to hear from any biologists or behaviorists reading this.

I have no clue what the hell you Dudes are talking about. I 'll try again tomorrow. Maybe not. surprise

The brain power and commitment of so many here are most definitely a motivation to me.


…have decided to slooowwwly move away from the lap top, close its cover as I move, as I am now frieghtened beyond belief!!! LOL


That was a nicely written essay.  You made an important point well.  I agree with your response to Arthur.


Adam, the essay is sage advice, no question about that. Baseball is stats, stats, stats, and I get your message loud and clear.
Your bantering with Arthur was awe inspiring as you both are favorites and I'm glad you have each others in situations like this because honestly, I still have no clue how Arthur could garner his thoughts out of your essay, and THEN you responding. Education is knowledge, that's for sure.

OK, less scarred this morning and have wondered myself why we haven't evolved the ability to grow and retract our body hair as needed, over time, as on some of these cold days it sure would be nice! Am I in the ball park? Then again, we do have our razor! LOL!

Truly,… Respectfully Given


I think this is a very nice description of the problem with making assumptions based simply on what seems to be obvious. Some of the basic principles of economics 101 are just believed because they seem to make sense. Hence the "dismal" label - the scientific method does not seem to get applied in a transparent manner.
Everything needs to stand up to repeatable scientific measurement,  experimentation and review before it can be safely taken to be true - even the absolutely bleeding obvious. Eg it's obvious that heavy things fall faster than lighter things - until you measure their fall (Galileos famous experiment). As Adam says, intuition can be way off.

Its another angle on the fact versus belief concept that Chris has mentioned many times. 

…the issue for me is separating the shaft from the corn. Let me explain: I can due the math, get the numbers right but then comes along a Princeton Professor who continuously baffles the process with Bullshit where North is now South and Up is in fact Down. Then doesn't share his findings. So, garbage in is garbage out and making sense of it all is just a gut feeling. If it's a gut feeling (that's bad but not always a losing proposition) then it's better to learn how to quantify bullshit, and exactly how does one write a formula for that? Yet, intuitively (again, statistically a bad formula) we KNOW something has to give and it will be monumental at least that's what my gut tells me as measuring these extraordinary times are just impossible (no math to definitively even guess, we just know it's unsustainable).David and Goliath? My observations would have been wrong.
Respectfully Given

All in due time… the risks we are facing (high-debt loads, investment failure, living beyond means) have not been with us long enough to invoke evolutionary change.  If we survive we will learn.

Back when my sons were in grade school, they did a science project abut the intuitive response to the laws of proability. It helped that their scoutmaster was a PhD mathematician who worked for Northrop Grumman, and he walked them through it; math is not my best skill, but I knew enough to know that this would be an interesting experiment.
The kids had eight flashlight batteries in a basket, and an empty flashlight. Two were fully charged, six of the batteries were dead: emptier than a politician's promises. The person viewing the exhibit was asked to guess the odds of getting the two charged batteries into the flashlight. Upon lifting a flap, the actual odds were revealed. Everone was shocked that the odds were 36 to 1. It was not intuitive, even for the science fair judges, who should have known better.

The exhibit was also covered with things like lottery tickets and pictures of casino games, with the odds of each game below a flap.

An interesting mathematical rant on the odds of winning a pick-six lottery is here. The short version?  A Pick-Six lotto gives you 1 chance in 13,983,816. Odds of 1/13,983,816. (That's a .000007% chance of winning and a 99.999992% chance of losing).

Humans are simply bad at assessing risk. That's why they gamble.

I remember my econ statistic courses! I wasn't the best at them either (econometrics…uggh). One thing I think worth mentioning is context is everything. Scientific scrutiny is always good but intuition and context can be the balance to that scientific analysis if things in your gut are telling you that the data is somehow flawed. I don't see it as either or but rather the two working together. I think there is a difference between assumptions and intuition.
Adam, the example assumes that birthdays are random and that all students will be honest, and that's a pretty common sense assumption for a $5 bet. But if your prof had put more risk on the line, say $1000, how would that have changed the nature of the outcome? (probably no one would have taken the risk, I mean it is college, but hypothetically, would everyone have been honest?) I always found the assumptions on which much of the foundations of economic markets are based are flawed. We do not have instantaneous product information and even if we did, most people are not going to be "fully" informed, there's just not enough time or human will. I used to sit in my econ classes looking at those supply = demand graphs and say to myself…well yes that looks very mathematical and I can see it on the graph there, but is that really what the price 'should' be?  Then we run what we think are scientific models based on those assumptions and call them facts. I think this is where economics has real problems, it's impossible to scientifically reduce human behavior to fixed models when context is continually changing. The EEEs is a testament to this and why CM's (and many of us) gut is telling him there is something really wrong with the data.

Bob, baseball is all stats, but in the new context of the steroid use, now that we look back, what do those statistics mean? Who really deserves to be in the HOF? Do we have to go back and group the players that used and not used into different categories and run the stats over. Do we have a steroid HOF now?

A funny example…I received a call from a political pollster before the election (federal). He asked if I would take a a quick survey for a poll they were conducting. I was breathing pretty hard because I just stepped in the door after taking a run. He asked why I was breathing so hard, so I told him. He continued on and asked his first question…" Do you believe your town is moving in the right direction? What I mean is…is it getting better or worse for you locally?" I responded that some things were better and some were worse. There was a long pause as he looked at the available answers on his sheet and realized he didn't know what to ask next. I had not given him a better or worse answer. He responded "well it seems you're pretty tired after your run, I'll let you go, thanks for taking the call." I tried to say, no I'm fine, please go on, but he hung up.

As I watched the FOX news Carl Rove melt down on election night, I'm sure his data told him that Romney was supposed to win, and that's when I thought back to my phone call. How many people were cut off because they didn't answer the question within the confines of the script? Maybe it fit into the "margin of error," but then maybe not. I would guess human beings are predictable under certain circumstances, i.e. when the hockey stick is running on it's flat plane, but when curcumstances hit the steep curve, well, who knows?

Oh and Arthur I hate to think of sleep as an anomoly…I love my good night's sleep! lol

Thank You


Fascinating, can't wait to try it.  But, an econ prof has access to school records and would have the opportunity to check beforehand.  I know I would.  Just saying.

"Bob, baseball is all stats, but in the new context of the steroid use, now that we look back, what do those statistics mean? Who really deserves to be in the HOF? Do we have to go back and group the players that used and not used into different categories and run the stats over. Do we have a steroid HOF now?"Geez I really could write quite the piece here Brother so I'll attempt to be brief. Steroids to purists (of which I am) is an unknown, known (think Rumsfield). What did speed or other enhancements do to the stats of the 60's and 70's ballplayer? Drink, cocaine and other drugs of the early games (pre-1930's)? Less games and media attention, and commercial contracts are all time spent not preparing for the next game, and how is this reflected in game day stats? What if the umpire called a ball instead of a strike, when clearly the ball was right up the middle waste high. Stats are basically subjective unless the numbers are quantifiable and I just don't think they are for the most part when everything is moving in each and every direction. Fixed objects fine but moving objects are entirely different and when you add human error then the gut and intuition is all you have as a supplement to the equation. It is TIME where stats prove there worth and current stats are not reflective really of the true wealth effect.
So, what do we know, the game plays out in a 162 game schedule and statistically the player will perform at 300 BA. 20 dingers and 100 RBI if the season has two rain outs in April and if the medium temperature is 76 degrees because this particular player needs a couple days off and warm weather because for every degree the temperature falls it can be shown that his batting average and power production drops.
Stats tell the tape, and we must adhere to the stats to even out the score long term. The same stats today are obsolete tomorrow even using the same information. For instance: Babe Ruth can't hit a slider down and away so you pound him down and away. Then Ruth thinks, OK, I'll go deep to left then, crowds the plate, pulls in his hands, shortens his stride and pops it out to left. Assumptions are great and numbers are great until their not.
Like everything in life, Risk/Reward. I say you get caught then banishment and asterisks. Without rules, CHAOS. It's why I sat for 3 days recently, and rightfully so, I broke the rules. Man up time then.
Pete Rose, every one's fall guy bet on the game while HE MANAGED, and for me, this is a banish-able offense. Why? He cheated the game. Steroids, same thing, no matter that the improbability of hitting a Nolan Ryan fastball is near 0. As I think about this everyone, every ball player has cheated the game in some form or another. All bad but most all in what is called the grey area. It has yet to be determined if steroids fall in the grey area but because such effort is being made to cover it up tells me that extreme guilt and cheating is the motivation. The writers will vote and the talk will banter about forever as is the case with Shoeless Joe Jackson. It's what makes the game so great.

Nice article Adam:
  Reminds me of the Monty Hall Problem  (Let's Make a Deal!).  Amazing that the odds of picking the car behind door number 2 or 3, AFTER showing it's not behind door #1 are 2 out of 3 - not just 50/50.   (a perennial wrong door picker I hope I have that right - google it!).

  Gut feelings seem to me the obvious…  obviously not where the smart money is!! 

  Mama told me not to …


Brings up an interesting point inadvertantly and displays our cultural prejudices.  We have a lot of guys who graduated from top ivy league schools with amazing cerebral credentials running things at the moment.  Some of them spend their time inventing new financial "instruments" and writing new "algos" to work the markets.  They are the guys and gals who came up with terminator genes in seeds for Monsanto.  They are inventing new drone technology to fly around third world countries.  We have a lot of "smart" guys in charge, but things aren't going to well.
The average joe says to himself, well I'm not too bright, glad we have these really "smart" peolpe running things for us.  We don't do well in a particular academic subjects and assume that we are not the "alpha male (female)" in the group and defer to other "smarter" people.  But I would like to propose a very different view of things.

We all have our nature and inclination of how we view reality.  There are those who lean towards knowledge, a fragmented, linear, scientific, reductionist and mathematical view of the world.  They tend to go into math and sciences.  Then there are those who lean towards wisdom, wholistic thinking, intuitive learning, and big picture thinking.  They tend to move into the arts and literature.   Both are equally intelegent or "smart", but we have a whole cultural paradigm that has become self selecting towards one point view.  If a person doesn't do well in a hard science subject, they then tend to believe they are not smart.

We all of course are a mixture of both, but we are now self our leaders of society from one extreme.  Knowledge is about gaining power and Wisdom is about love.  We need both, but the wisdom of whether or not we should do something at all is primary to the power of how to do something.

If we don't move out of a paradigm that worships power to one that is drive by love and wisdom, the ship will surely sink.  We need to believe in our own intelligence what ever form it takes and not doubt our view of reality.

…I suppose he could up his odds a bit but if the stats say 99.9 percent then you bet it all, and live with the consequences are my thoughts. Then again, checking would confirm the .01 percent and is why $5 dollars is way different than $1000 dollars, so forth and so on.Welcome
OT Folks: My freezer alarm in the basement just blasted my home with a horrible sound that reminded me I had not shut the main freezer while stocking the refrigerator freezer with new supplies! I love that thing as sometimes we just forget to shut our freezer and that would have been a costly mistake. You can buy many different models for around $10 bucks! Do you have one?

Your point on "time" is a good one. Time is the great leveler in all areas of life isn't it? As you point out, with stats and scientific research over time, one small irritating new fact or revelation can render all of it obsolete. Godel's proof of incompleteness comes to mind…poor Whitehead and Russell…their enitre life's work negated by Godel's proof. Bummer!Baseball is a great analogy for what's going on in the world. We are all to blame, well most of us at least, in regard to the steroid scandal. Who didn't get caught up in the Sosa/McGuire contest? The stakes are very high in the big leagues, and money is at the heart of it unfortunately. The pressure is extremely high for individual players to perform, so the incentive to enhance/cheat is strong. A player's biggest fear is being sent back to the minors. The sad part is that the stats on steroids are pretty well researched. In high doses they are extremely harmful to a person's health. If we say it's okay to allow them (as some have suggested, not me) then what does that say about us as a society? Should we say…well hey if the player wants to harm his body that way to reach his maximum income, who am I to tell him no? To me, that's the equivalent of the colluseum days of Rome.
The same is true for those playing in the big leagues of finance, the stakes are high. High frequency trading is in some ways the equivalent of steroids. As CM (and Treebeard circuitously above…nice post!) has pointed out, this type of trading really has nothing to do with supply and demand, and is a way of gaming the system.  Humans can't compete with computer algos when it comes to quantity of trades, but   our insatiable desire for performance, not just cheating, may be the reason we look the other way.
Your point on rules and risk/reward is good and I agree. I would add the rules have to be constantly evaluated and tweaked in light of the current context (which is what the league is doing).  Similarly, we need to reevaluate the global rules within the context of our insatiable harmful addiction to more speed/performance, efficiency, profit, and productivity.
Treebeard, I agree whole heartedly with your post!
Thank You

I was watching my daughter in gymnastics class today. She and another girl were working on walking across the balance beam. There are three balance beams each at different heights. When crossing the lowest one, they both shared the beam equally. They would start at the same time from either end and walk toward each other in the middle. When they reached each other, they would each jump off and walk back to the end. They did the same on the middle height beam. But when they went to the highest beam, their behavior changed. They took turns starting at one end, going across the beam (same amount of real estate), and then jumped off. I thought it was interesting how the perceived risk of falling off changed their behavior (there were mats on either side making the risk neglible). Implied in this is that there was greater reward to walking across the higher beam, but essentially they were doing the same thing as they were on the lower beams. I find the analogy interesting and coincidental. Are the risks real or just perceived? I guess it depends on the height of the beam and if there's a mat (safety net).


I'm no biologist or behaviorist, but I have observed and noted both. Ironically, evolutionary pressure rewards optimists. Pessimists are less likely to take chances because they fear the possibility of negative outcomes. Optimists take chances because they hope for the reward coming. A pure optimist won't assess the severity of potential risks and will likely succumb before passing on genetic material. Likewise, a pure pessimist will never take a chance and will starve before procreating.

You don't need to be the fastest, strongest, smartest, etc. to survive. In some situations, being the second slowest is perfectly survivable. (My speculation) Humans' evolutionary success stemmed from our ability to work together. We can coordinate actions to behave like a much larger creature when needed. We can learn from others' mistakes (theoretically at least.) At the end of the day, we can separate and go our own ways. Some will die and most will live to see another day. The collective has to adjust in order to continue. It happened then and it happens now.

If you've ever seen a tweeker after a week of being awake, you'll see why sleep is rewarded by evolution. :wink: