Monty Hall and Probability 101
(1:00) - What The Framers Couldn't Imagine
(7:00) - Monty Hall: The Probability Brain Buster
(12:30) - Jeff Yass: The Power Of Rational Thinking
(18:30) - Breaking Down The Probability Of The Monty Hall Problem
(24:00) - Daniel Negreanu: Probability Simulation
(28:45) - Episode Roundup: Podcast@Zacks.com
Welcome back to Mind Over Money. I'm Kevin Cook, your field guide and story teller for the fascinating arena of Behavioral Economics.
Last week, I made a video presentation called Gaming the Stock Market with Poker Smarts where I drew some very important connections between the behavioral analysis of poker champion Daniel Negreanu and the work that I do in playing stocks.
I wanted to follow-up this week with an expanded discussion on the topic.
And then something happened over the weekend that made me more certain about what angle to take: the legendary game show host Monty Hall of "Let's Make a Deal" fame passed away at the ripe young age of 96!
Monty's fun and laughs with his infamous Big Deal to win a new car simply by choosing one of 3 doors became a fantastic probability brain buster because of the fact he always gave contestants a chance to switch their original choice -- and risk ending up with a goat.
But Hall helped you by opening one of the doors that had a goat, so now you knew there was one less goat lurking behind the door you chose and the other that he was offering you. In the 1970s and 1980s it became a big discussion in national newspapers about whether it mattered if you switched your original choice.
And many times it was math professors who got the answer wrong.
I learned to dissect this probability challenge from one of the great Market Wizards in Jack Schwager's books.
I'll explain both The Monty Hall Problem and the options trader who helped me understand it in a moment.
Prayers for Vegas
Before I dive into today's episode though, I want to be thoughtful and respectful with regard to one of the US kingdoms where this gambling math reigns: Las Vegas, NV.
Just two days ago, on Sunday October 1 at around 10pm Las Vegas time, a twisted coward opened fire with several assault weapons on a large concert crowd by the Mandalay Bay resort and casino, owned by MGM Resorts MGM.
At this time, nearly 60 people have lost their lives and hundreds more are injured, with dozens still fighting for their lives.
While there will be endless media coverage all week, all any of us really need to do is just imagine the horror of watching one of your friends or loved ones die in your arms. It makes me want to be very quiet, utterly speechless in sadness.
I have taken many moments of silence in the past two days for all that pain and suffering at the hands of some angry idiot with access to too much lethal military-grade destructive force.
But more importantly, in the aftermath of the tragedy as so many families in Vegas and beyond are hurting terribly, we have to lift up our heads and acknowledge all the police, fire, and medical personnel who helped and continue to help victims. Their lives will never be the same.
And then there are the strangers who helped one another, and those heroes who lost their lives trying to protect and save others. Strength and peace to all of them.
The Monty Hall Problem
In the mid-1990s as a clerk on the trading floors of the Chicago Mercantile Exchange, I was fortunate to come across two books by a thinking man's trader, Jack Schwager. His Market Wizards books were packed with interviews of great commodity, currency, and stock traders like George Soros, Paul Tudor Jones, and Monroe Trout.
In The New Market Wizards, Schwager talked to Jeff Yass who used a variation of Monty Hall's Big Deal to explain the power of probability-based thinking.
Do you know how to put the odds in your favor to win a car instead of a goat?
It's trickier than you think, even when you think Monty is trying to trick (or help) you.
That's where Jeff Yass, a billionaire trader and founder of options giant Susquehanna International, comes in to help us.
Yass built his options empire, with five other partners, near Philadelphia where he earned his wealth of trading experience as a member of the Philadelphia Stock Exchange in the early 1980s. This was just about the time that stock options trading was really taking off with the aid of computers.
And it was after Yass and his buddies made millions gambling the odds in Vegas.
In 2009, PhillyMag.com profiled Yass and gave a great intro to the Monty Hall Problem...
Let's play a game. Let’s say you’re a contestant on Let’s Make a Deal, Monty Hall’s game show from a generation ago. It’s your moment. There are three doors. Behind one door is a brand-new Camaro. Behind each of the other doors, there’s a goat. If you pick the right door, the Camaro is yours.
Silky-voiced Monty Hall gives you the big question:
“Do you pick door number one, door number two or door number three?”
The studio audience weighs in, and tension builds, as you think. Finally you pick, let’s say, door number one. But Carol Merrill, Monty’s assistant, doesn’t open it, not yet. Instead, Monty Hall directs Carol to open one of the other doors — door number two, say. Behind that door is … a goat. The audience titters nervously — that Camaro, still hidden, might yet be yours.
First, though, Monty is going to give you another choice. He’s going to give you both an option, and a dilemma:
“Would you like to stay with door number one,” he asks, “or would you like to switch to door number three?”
You ponder. But it’s a no-brainer, right? With two doors left, there’s a 50-50 chance the Camaro is behind either one. So you might as well stick with door number one.
(end of PhillyMag.com excerpt)
For the wisdom of Jeff Yass on the best way to think about this dilemma, be sure to listen to my podcast.
I also explain what inspired me to teach myself probability and statistics in my 30s (after spending the first 30 years of my life "allergic to algebra") and two reasons why everyone should strive to learn more of these essential maths:
First, because it has always been true that people can lie and fool you with statistics, whether from science or public policy.
Second, we have never been more inundated with data in the age of IBM, Microsoft MSFT and Alphabet GOOGL, the data-crunching and creating monsters, and their data workhorses, the semiconductor companies creating the future of advanced computing and AI, like NVIDIA NVDA and Advanced Micro Devices AMD.
Hence, being adept with probability and statistics will become an absolutely vital 21st century knowledge-skill set.
Disclosure: I own shares of NVDA and AMD for the Zacks TAZR Trader portfolio.
Kevin Cook is a Senior Stock Strategist for Zacks Investment Research where he runs the TAZR Trader service.
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