Deal or No Deal (valuable lesson on Bayesian inference)
Deal or No Deal is a popular TV show, packed with suspense but also with valuable lessons on how Bayesian inference can help a person make better decisions. From Wikipedia:
The basic format of Deal or No Deal consists of a number of cases (usually 26, but varies in some countries), each containing a different amount of money. Not knowing the sum of money in each case, the contestant picks one case which potentially contains the contestant's prize. They then open the remaining cases, one by one, revealing the money they contained. At predetermined intervals the contestant receives an offer from the bank (run by "The Banker") to purchase the originally chosen case from the contestant, the offer being based on the potential value of the contestant's case. The contestant must then decide whether to take the deal from the bank, or to continue opening cases. If the contestant decides not to take the deal and reveals low value cases, then the next bank offer is likely to be higher (as the contestant's case is proven not to contain these low values). Alternatively, there is risk in revealing higher values, lowering future offers from the bank. The aim of this system is to try to make an exciting and suspenseful game. Each offer from the bank is typically significantly less than the expected value of the player's case.
===
Bayesian inference simply means that you update your degree of belief in light of new information.
Here's an example: I ask you to state a number while I roll a dice. If the number that comes up is the number you have voiced, then you win $600. Oh, I forgot to mention that to play this game, where you could potentially win $600, you have to pay me $100.
Question: Is it worth it for you to play?
Answer: You have to calculate the EMV, or expected monetary value, which is:
Probability X Payoff = (1/6) X $600 = $100.
Since this is EXACTLY the price for playing the game, you probably should not play the game.
However, if the price for getting the right number is $800, then EMV = (1/6) X $800 = $133.33
Since $133.33 is higher than the price of playing the game, or $100, then you should play the game. The odds of winning are in your favor.
Maybe this is not new to you, so here's a twist on how games are played in REAL LIFE:
Someone asks me to play the same game, but the stakes are higher: $1,000 to play, and $5,000 if I get the number right.
Using the above EMV equation, I get an EMV of $833.33, which is lower than $1,000, so logically, I should NOT play (because the odds are against me).
However, I'm quite rich, so I accept to play just for the fun of it. BUT I tell the person that he should throw the dice FIRST, and then I would state the number. My "official" reason for this request is that I have psychic powers and can read his mind AFTER he sees the number that comes up.
My real reason, in fact, is that my beautiful girlfriend is standing behind the man. If the number is odd, she would touch her lovely chin -- therefore, I would voice one of these numbers: 1, 3, 5.
If she doesn't do anything, then I know the number is even, and I would voice either 2, 4 or 6.
Either way, the odds of success for me has changed from 1 in 6, to 1 in 3.
The REAL EMV, therefore, is (1/3) X $5,000 = $1,666.66 (which is higher than the price of playing, which is $1,000).
Someone might say: "Well, Peter, you're cheating! Your girlfriend gives away information that you're NOT supposed to know!"
That's true. The only thing I can say is that it was HER idea! (kidding).
But seriously, there are tons of ways to get information so that you can, using Bayesian inference, update your calculation of the odds and, therefore, determine the REAL EMV.
This is the whole idea of the movie Wall Street, starring Michael Douglas and Charlie Sheen. The great financier Gordon Gekko recruits Bud Fox, a young stockbroker, to work him as a sort of spy.
He tells Fox: "Information is the most valuable commodity I know, wouldn't you agree?"
It's a great movie, but I don't think that you have to resort to illegal methods or ploys to get insider information. Read the fantastic book The Intelligence Edge, by George Friedman, to learn more about intelligence-gathering techniques (that are worthy of the CIA!).
The success secret here is to understand that every time we make a decision, we are in fact gambling. THE MORE WE KNOW, THE LESS WE GAMBLE.
(This is reminiscent of Gekko's quote from Sun Tzu: "Every battle is won BEFORE it's ever fought.")
If information is key to effective decision-making, how come the Internet (or Google, for that matter) doesn't seem to improve people's decision-making?
The answer is that information is just raw material. It is human intelligence that turns information into knowledge. This knowledge is what allows a person to clearly see the payoff as well as the odds of success, and then to decide accordingly.
There are two kinds of knowledge, when it comes to Bayesian inference: systemic knowledge and situational knowledge.
Systemic knowledge is universally applicable, often regardless of the situation at hand, whereas situational knowledge refers to the circumstances and details surrounding a particular decision.
Warren Buffett and Charlie Munger can be said to focus on systemic knowledge. For instance, they believe that a good business to invest in must have strong brand equity, good and solid management, high barriers to entry, etc.
Gekko, on the other hand, focused on situational knowledge which, of course, requires spies. This is not to say that he did not also master systemic knowledge. It's just that the movie focused more on the illegal ploys to uncover situational knowledge.
The basic format of Deal or No Deal consists of a number of cases (usually 26, but varies in some countries), each containing a different amount of money. Not knowing the sum of money in each case, the contestant picks one case which potentially contains the contestant's prize. They then open the remaining cases, one by one, revealing the money they contained. At predetermined intervals the contestant receives an offer from the bank (run by "The Banker") to purchase the originally chosen case from the contestant, the offer being based on the potential value of the contestant's case. The contestant must then decide whether to take the deal from the bank, or to continue opening cases. If the contestant decides not to take the deal and reveals low value cases, then the next bank offer is likely to be higher (as the contestant's case is proven not to contain these low values). Alternatively, there is risk in revealing higher values, lowering future offers from the bank. The aim of this system is to try to make an exciting and suspenseful game. Each offer from the bank is typically significantly less than the expected value of the player's case.
===
Bayesian inference simply means that you update your degree of belief in light of new information.
Here's an example: I ask you to state a number while I roll a dice. If the number that comes up is the number you have voiced, then you win $600. Oh, I forgot to mention that to play this game, where you could potentially win $600, you have to pay me $100.
Question: Is it worth it for you to play?
Answer: You have to calculate the EMV, or expected monetary value, which is:
Probability X Payoff = (1/6) X $600 = $100.
Since this is EXACTLY the price for playing the game, you probably should not play the game.
However, if the price for getting the right number is $800, then EMV = (1/6) X $800 = $133.33
Since $133.33 is higher than the price of playing the game, or $100, then you should play the game. The odds of winning are in your favor.
Maybe this is not new to you, so here's a twist on how games are played in REAL LIFE:
Someone asks me to play the same game, but the stakes are higher: $1,000 to play, and $5,000 if I get the number right.
Using the above EMV equation, I get an EMV of $833.33, which is lower than $1,000, so logically, I should NOT play (because the odds are against me).
However, I'm quite rich, so I accept to play just for the fun of it. BUT I tell the person that he should throw the dice FIRST, and then I would state the number. My "official" reason for this request is that I have psychic powers and can read his mind AFTER he sees the number that comes up.
My real reason, in fact, is that my beautiful girlfriend is standing behind the man. If the number is odd, she would touch her lovely chin -- therefore, I would voice one of these numbers: 1, 3, 5.
If she doesn't do anything, then I know the number is even, and I would voice either 2, 4 or 6.
Either way, the odds of success for me has changed from 1 in 6, to 1 in 3.
The REAL EMV, therefore, is (1/3) X $5,000 = $1,666.66 (which is higher than the price of playing, which is $1,000).
Someone might say: "Well, Peter, you're cheating! Your girlfriend gives away information that you're NOT supposed to know!"
That's true. The only thing I can say is that it was HER idea! (kidding).
But seriously, there are tons of ways to get information so that you can, using Bayesian inference, update your calculation of the odds and, therefore, determine the REAL EMV.
This is the whole idea of the movie Wall Street, starring Michael Douglas and Charlie Sheen. The great financier Gordon Gekko recruits Bud Fox, a young stockbroker, to work him as a sort of spy.
He tells Fox: "Information is the most valuable commodity I know, wouldn't you agree?"
It's a great movie, but I don't think that you have to resort to illegal methods or ploys to get insider information. Read the fantastic book The Intelligence Edge, by George Friedman, to learn more about intelligence-gathering techniques (that are worthy of the CIA!).
The success secret here is to understand that every time we make a decision, we are in fact gambling. THE MORE WE KNOW, THE LESS WE GAMBLE.
(This is reminiscent of Gekko's quote from Sun Tzu: "Every battle is won BEFORE it's ever fought.")
If information is key to effective decision-making, how come the Internet (or Google, for that matter) doesn't seem to improve people's decision-making?
The answer is that information is just raw material. It is human intelligence that turns information into knowledge. This knowledge is what allows a person to clearly see the payoff as well as the odds of success, and then to decide accordingly.
There are two kinds of knowledge, when it comes to Bayesian inference: systemic knowledge and situational knowledge.
Systemic knowledge is universally applicable, often regardless of the situation at hand, whereas situational knowledge refers to the circumstances and details surrounding a particular decision.
Warren Buffett and Charlie Munger can be said to focus on systemic knowledge. For instance, they believe that a good business to invest in must have strong brand equity, good and solid management, high barriers to entry, etc.
Gekko, on the other hand, focused on situational knowledge which, of course, requires spies. This is not to say that he did not also master systemic knowledge. It's just that the movie focused more on the illegal ploys to uncover situational knowledge.
posted by Super Peter at 12:06 AM
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