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30 Jun 2021, 08:16
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Hi GMATters,
Here is a sample of my newest blog post regarding Probability on the GMAT. There's more information where this came from, plus wait for a series of Probability videos I'll cross over on YT (/gmatcoach) and Instagram (@yourgmatcoach).
Rowan
------------
Probability was initially developed for gambling. Given the gamblers I know, that means it can’t be particularly complicated.
Why we base the global financial system on it is another question, but Quantum Mechanics uses it as well, so I’ll admit I’m being judgmental here.
Looked at one way, Probability attempts to give us a mathematical way to predict the future, which isn’t necessarily the most accurate. It’s a bit like trying to predict the weather if you live somewhere other than London (for me, it’ll be rainy and grim).
CORRECT Probabilistic Thinking is Not Common
Or maybe lots of people think that they are good at it, or they “have a system,” or some other nonsense, but they are actually completely terrible at it.
THAT PERSON IS NOT YOU.
What it means that other people are terrible at Probability is that you get a bunch of language tossed around freely that means pretty much nothing.
In short, these people confuse likelihood with Certainty and overestimate the upside of something while downplaying the ever-present possibility that something catastrophic could happen (cf. 2008).
Now, in a very Zen sense, we cannot of course predict the future, so just maybe injecting a “maybe” actually is a very useful idea. To paraphrase Socrates by way of Don Rumsfeld, “there are unknown unknowns” in the world, so a bit of agnosticism wouldn’t harm any of us.
The problem comes, of course, in situations where we overreach and accidentally end up in that confused (and wrong) Certainty. Situations where this is useful are few and far between, and usually involve gambling; that is, the House likes to make money, and people who are too confident are easy marks.
So... any time we hear the words odds, chance, likelihood, or any mathematical “prediction” of the future, it’s time to put the skeptic’s hat on. There exists a good chance (hahahaha) that a deep misunderstanding is afoot.
Let’s start with a definition of “chance.” And it isn’t going to work to go tautologous and say something like “likelihood.” Let’s step inside the local William Hill (or on to that riverboat if you’re in the US) and make a guess.
Probability was Designed for Gambling
This isn’t a conjecture; it’s a real thing. Probability was originally developed to help bookmakers create odds so that the reliable bettors would be encouraged, more effectively, to part with their cheddar.
Then it might be little surprise that many GMAT Probability questions continue to involve finite game systems. That’s what the math is invented for!
Now it just might be that playing the horses or pretending to be Daniel Craig at the baccarat table with your clip-on bow-tie can, over time, instill a keen intuitive sense of Probability in a person. Try it and let me know how that goes. I’ll be waiting here.
If there’s any truth in that conjecture, I’d wager (hahahaha) that it’s because bettors have skin in the game. If they don’t get fairly good at these things, they’ll lose their shirts! It always helps to have a bit of incentive.
If you don’t understand Probability, the GMAT will ruin you.
That’s your skin in the game.
Read the rest here: https://yourgmatcoach.com/gmat-probability-doesnt-have-to-be-hard/
Here is a sample of my newest blog post regarding Probability on the GMAT. There's more information where this came from, plus wait for a series of Probability videos I'll cross over on YT (/gmatcoach) and Instagram (@yourgmatcoach).
Rowan
------------
Probability was initially developed for gambling. Given the gamblers I know, that means it can’t be particularly complicated.
Why we base the global financial system on it is another question, but Quantum Mechanics uses it as well, so I’ll admit I’m being judgmental here.
Looked at one way, Probability attempts to give us a mathematical way to predict the future, which isn’t necessarily the most accurate. It’s a bit like trying to predict the weather if you live somewhere other than London (for me, it’ll be rainy and grim).
CORRECT Probabilistic Thinking is Not Common
Or maybe lots of people think that they are good at it, or they “have a system,” or some other nonsense, but they are actually completely terrible at it.
THAT PERSON IS NOT YOU.
What it means that other people are terrible at Probability is that you get a bunch of language tossed around freely that means pretty much nothing.
In short, these people confuse likelihood with Certainty and overestimate the upside of something while downplaying the ever-present possibility that something catastrophic could happen (cf. 2008).
Now, in a very Zen sense, we cannot of course predict the future, so just maybe injecting a “maybe” actually is a very useful idea. To paraphrase Socrates by way of Don Rumsfeld, “there are unknown unknowns” in the world, so a bit of agnosticism wouldn’t harm any of us.
The problem comes, of course, in situations where we overreach and accidentally end up in that confused (and wrong) Certainty. Situations where this is useful are few and far between, and usually involve gambling; that is, the House likes to make money, and people who are too confident are easy marks.
So... any time we hear the words odds, chance, likelihood, or any mathematical “prediction” of the future, it’s time to put the skeptic’s hat on. There exists a good chance (hahahaha) that a deep misunderstanding is afoot.
Let’s start with a definition of “chance.” And it isn’t going to work to go tautologous and say something like “likelihood.” Let’s step inside the local William Hill (or on to that riverboat if you’re in the US) and make a guess.
Probability was Designed for Gambling
This isn’t a conjecture; it’s a real thing. Probability was originally developed to help bookmakers create odds so that the reliable bettors would be encouraged, more effectively, to part with their cheddar.
Then it might be little surprise that many GMAT Probability questions continue to involve finite game systems. That’s what the math is invented for!
Now it just might be that playing the horses or pretending to be Daniel Craig at the baccarat table with your clip-on bow-tie can, over time, instill a keen intuitive sense of Probability in a person. Try it and let me know how that goes. I’ll be waiting here.
If there’s any truth in that conjecture, I’d wager (hahahaha) that it’s because bettors have skin in the game. If they don’t get fairly good at these things, they’ll lose their shirts! It always helps to have a bit of incentive.
If you don’t understand Probability, the GMAT will ruin you.
That’s your skin in the game.
Read the rest here: https://yourgmatcoach.com/gmat-probability-doesnt-have-to-be-hard/
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05 Jul 2021, 04:21
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ygcrowanhand
Do you have a source for this? I might be misremembering, but as I recall the earliest treatments of probability theory, they all adopted the point of view of the gambler, not the point of view of "the house", and the mathematicians involved were inventing probability not to help bookmakers, but simply to investigate interesting mathematical problems. Naturally oddsmakers found application for that theory, but it wasn't for oddsmakers that the theory was developed.
05 Jul 2021, 04:37
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Hi Ian,
Nice to hear from you again after a while!
Yes, and perhaps my statement is best taken with a pinch of hyperbole, as the history is rather complex but Ian Hacking addresses the story well in The Emergence of Probability: https://amzn.to/3qKRqqS
That said, I understand your point and as it's been many years since reading Hacking, I'll give him a re-read to understand whether that should be changed to Probability being "figured out by mathematical explorers of the topic and quickly adopted by bookmakers to their own advantage."
Rowan
Nice to hear from you again after a while!
Yes, and perhaps my statement is best taken with a pinch of hyperbole, as the history is rather complex but Ian Hacking addresses the story well in The Emergence of Probability: https://amzn.to/3qKRqqS
That said, I understand your point and as it's been many years since reading Hacking, I'll give him a re-read to understand whether that should be changed to Probability being "figured out by mathematical explorers of the topic and quickly adopted by bookmakers to their own advantage."
Rowan
