One of the subjects I teach is Financial Economics. During the last year, I’ve made considerable use of the insights of Nassim Taleb, who wrote one of the most prescient analyses of the current financial crisis in his great book “The Black Swan,” which is complex, but can be comprehended easily by any reader who has an understanding of basic economic theory and probability theory. Taleb made his fortune by taking advantage of general ignorance of probability theory, and exploiting arbitrage opportunities that arise when people underestimate the probability (and expected negative returns) of extremely improbable, undesirable events occuring. At any rate, his insights got me thinking about a purely academic excercise related to smuggling. These insights are not proprietary knowledge; by now, every respectable smuggler in the world gets the basic point I’m making here, but I thought I’d spell it out as simply as I can, simply for the erudition of other forum members. In order to "get’ the point I’m making, you have to try to think statistically. In order to keep the math simple, I’m using an example where the “expected” value of something could never occur in a single instance; it’s rather a representation of a statistical value (kind of like, “the average American family has 2.2 children;” no individual family has 2.2 children, but it is still the average family size from a statistical standpoint). I am NOT encouraging anyone to engage in illegal activity; I’m just suggesting that smugglers tend to use their understanding of economic theory and probability theory to greatly increase their earnings (just like investment bankers do), and here’s basically how they do it: Suppose you are thinking about importing 20 one pound containers of snuff into the United States, but you don’t want to pay tobacco taxes on them. Let’s assume the probability of any single shipment being stopped at customs and taxed is 50%. If you ship all 20 containers to the US in a single shipment, the expected tax (from a statistical standpoint) is the tax you would pay on 10 pounds, since the expected untaxed portion of the shipment is 10 pounds. Now, suppose you divide your containers into 2 shipments, and the probability of either one of them being stopped at customs remains 50%. Now, the probability of both of them being seized falls to 25%. So your expected tax bill is the tax you would pay on 5 pounds of snuff. Divide the containers further into 4 shipments, and your expected tax bill declines exponentially. Now, the probability that all 4 shipments will be seized falls to .4% (that’s right, less than 1/2 of 1%), given that the probability that any single shipment will be seized remains at 50%. Your expected tax bill now has fallen to the tax you would pay on .08 pounds, which is about 36 grams of snuff. Of course, one would want to weigh the expected tax savings against the additional shipping charges of dividing up your desired purchase into smaller orders, as well as other factors that could change the probability of any of your shipments failing to clear customs in the manner you desire. But it doesn’t alter the basic principle at work here, which is roughly the same principle that investors use when attempting to reduce risk by diversifying their portfolio’s. In common parlance, the principle is usually stated as “Don’t put all your eggs in one basket.” The DEA uses these principles to estimate the amount of illegal drugs smuggled into the US. Their basic assumption is that the average seizure is very small relative to the total amount of illegal drug trafficking because smugglers pay actuaries to do very sophisticated calculations like the very simple representative one above. Also, If you were paying close attention during Steven Soderbergh’s great film “Traffic,” reference to these principles was made during a fictional interrogation near the movie’s beginning. Another interesting use of this principle is the “expert” ruse. You start out with 1 million people and send a prediction to half of them, and the direct opposite prediction to the other half. Now, 500k people have received one “correct” prediction from you. Do it again. Now 250k people have received 2 correct predictions from you. Do it again. Now 125k people have received 3 correct predictions from you. Do it again. Now 75k people have received 4 correct predictions. Do it again, just to be on the safe side. Now 37.5k people have received 5 correct predictions in a row from you. Now, you offer to sell them your “expertise” for $1000 per year. You just made $37.5 million dollars, simply by knowing how to toss a coin. Class over.
This was a great class!
mate I do not see how they can enforce no tobacco in the us mail system if they cannot stop powder or a bit of weed. and by a bit I am talking 120k worth.
@LHB I learn so much from you, I think your best was comparing food scented snuffs to watching porn with your hands tied behind your back, Now that was a classic! Good points.
sorry to hijack this thread a little but still on statistics … when the lottery is on tv they say your chance of winning the jackpot is 1 in a million say then when no one wins it for 5 weeks and the jackpot goes away up … they say your chance of winning is now 1 in 5 million say … no doubt more people do the lottery when the jackpot is huge but the way i look at it is your chance of winning stays the same no matter how many people do it as there is still only 39 numbers or whatever the number is … i dont do the lottery btw
LHB, you are mistaking expected profit with risk of ruin. Profit expectation remains the same, but what has increased is your chances of remaining in business. Smuggler A scratches and saves 50 large to buy a product and have it sent over-seas knowing that if it gets through he could sell it for $500 G’s, but if it gets stopped (50% chance) he is out of business. Scenario 1 it gets through and he makes $450,000 profit. Scenario 2 it gets stopped and he is out $50 G’s and out of business. (1 * .5 * 450,000 = 225,000 +1 * .5 * -50,000 = -25,000 for an expected profit of $200,000.) Smuggle B does the same thing but splits up his product into 20 different deliveries knowing that half will still get caught: (20 * .5 * 22,500 = 225,000 + 20 * .5 * -2,500 = -25,000 for an expected profit of $200,000) What is the difference? The expected profit is the same but Smuggler A didn’t diversify and is risking his business life on a 50/50 shot. Smuggler B will live to play the game again. By splitting up his shipments, he hasn’t increased his profit margin but he has exponentially decreased his chances of his risk of ruin.
@ robbo I really appreciate your input. Your scheme is similar to a portfolio diversification strategy that reduces risk without changing the portfolio’s expected return. It’s a great example of risk reduction through diversification, which doesn’t change the portfolio’s expected return, but which makes it more desirable nevertheless by reducing its riskiness. In my example, I’m also talking about increasing your expected return through understanding the way probability theory works. I would argue that in the real world, you have actually reduced your risk AND increased your expected return. The reason is that the probability of each event happening is independent of the other, but the order in which they happen to YOU matters to you. So there’s no logical reason to assume that if the probability of one package being seized is 50%, that the probability of all of them being seized in succession is 50%. If the probability of a single even occuring is 50%, the a priori probability of identical successive events decreases exponentially, even while the probability of the single event occuring in isolation doesn’t change. You should not think about this stuff unless you’ve been drinking, and it’s a little too early for me. In my problem, I was talking about reducing the risk of bad outcomes occuring in a situation where the order in which they occur, and the person to whom they occur, matters, AND with increasing the expected returns of engaging in the activity associated with the undesirable outcome. In short, if the probability of an adverse event occuring is 50%, the a priori probability of the same adverse event occuring to you 5 times in a row is .5 raised to the 5th power. Which helps explain why those drug cartels make so much money, and why people in the financial community who appear to be winners for a few years are almost invariably out of business in a few more. @jspsks As far as the lottery example goes, the probability of winning depends on nothing more than the numbers and the probability that each of them will come up simultaneously. It doesn’t make any difference how many people buy tickets, although that affects the expected payoff matrix. Whether or not a lottery ticket is a “good” buy or not depends on the size of the jackpot. If the odds of winning the lottery are 18 million to 1 and the jackpot is $1m, a $1 ticket isn’t a good value because its expected value is only 18 cents. But as the jackpot rises, the ticket becomes a better bet. Given these odds, the ticket becomes a good bet when the jackpot rises to over $18 million, because at that point the expected value of the ticket is exactly $1. These statistical puzzles confound people with far more mathematical sophistication than I have on the statistics and econometrics forums, so I don’t want to drag it out. I will simply concede the point that you can significantly reduce your risk of an undesirable outcome by diversifying. If an investment strategy doesn’t change your expected return, reducing risk is a good thing since just about everyone is risk averse. Don’t put all your eggs in one basket. When you go out to a bar, focus on several women rather than just one. Odds are, you’re not gonna be nearly as unlucky as you would otherwise be!
And remember, 90% of the population is right-handed. By focusing on several women, the probabilities are I will get slapped on the left side of the face rendering it numb in short order, making the whole process not too bad. Always be alert to what hand they are using to hold their grog, though.
You said, “So there’s no logical reason to assume that if the probability of one package being seized is 50%, that the probability of all of them being seized in succession is 50%” I understand this point, but this is not what I was saying. If the probability for 1 package being caught is 50%, it is not outlandish that the first few could get through or get seized - but the more that are sent out the greater the tendency to regress towards the mean of 50% You know that when you flip coins you can get a decent length string of either heads or tails, but it does not change the fact that the next flip is still a 50/50 chance. One shouldn’t fall for the fallacy that just because they got 5 tails in a row that they can bet big that they will flip a head next because there is only a 1.5% chance of flipping 6 tails in a row - the coin has no memory and the next flip is only 50/50. When you said this: "Now, suppose you divide your containers into 2 shipments, and the probability of either one of them being stopped at customs remains 50%. Now, the probability of both of them being seized falls to 25%. So your expected tax bill is the tax you would pay on 5 pounds of snuff. Divide the containers further into 4 shipments, and your expected tax bill declines exponentially. Now, the probability that all 4 shipments will be seized falls to .4% (that’s right, less than 1/2 of 1%), given that the probability that any single shipment will be seized remains at 50%. Your expected tax bill now has fallen to the tax you would pay on .08 pounds, which is about 36 grams of snuff. " What you are arguing is the exact opposite of reality - the more shipments that are sent out the greater the tendency to regress to the 50% mean. Meaning with time, your expected tax bill will get closer and closer to the tax bill on 10lbs of snuff. In other words, if 10 packages are sent, it is entirely possible that only 2 might caught. If 1000 separate packagers are sent, it is MUCH LESS likely that only 200 might get caught. The numbers will get closer to 50% It is RoR that decreases, not expected profit that increases.
While you’re at it you’d have to figure in the increased shipping costs too. I’m only kidding, of course.
Don’t behave as if the unlikely will be impossible, and if you do, be prepared to deal with the consequences. This is a lot of wisdom you have. I assume you know all about William Bernstein and the Efficient Frontier. It’s rare to come across people with this knowledge, compliments!
The Martingale often features in books on mathematics and probability. Indeed, the mathematics of probability stems from gambling rather than smuggling - most famously the association between one Chevalier de Mere and the great 17th century philosopher and mathematician Blaise Pascal (of Pascal Triangle fame). The Chevalier, a dice gambler, reasoned like this: The chance of getting a 6 in a single throw is 1 in 6. Therefore, the chance of getting a 6 in 4 rolls is 4 x 1 out of 6 or 2 out of 3. With this scheme he was successful as the probability of a 6 is actually found in 3.8 rolls of the dice. As he was so successful no one would accept his gamble. He then started to offer the same bet on scoring a double-six on 24 rolls of two dice using the same reasoning - the chance of double six in one roll is 1 in 36, therefore a double six in 24 rolls is 24 x 1 out of 36 or 2 out of 3. As his losses mounted he sought counsel from Pascal via the Mersenne Solon who, as a result of this trivial encounter, corresponded with Pierre de Fermat (famous for his last theory) and the modern Theory of Probability was born. Unfortunately for the Chevalier he should have gambled on a double six in 25 rolls as the probability of a double six, as Pascal told him, occurs with 24.61 throws. Fortunately for casinos, bookies and owners of slot-machines Pascal’s advice on probability is generally disregarded - as was Pascal‘s advice to the unfortunate Chevalier de Mere.
Dear Fellow Forum Members, I should never have posted the original post on a Saturday Night at about 3AM (hint, hint). I made a serious error in the math, and was embarrased to return to admit it, but here it is: the sum of the probabilities of all possible events must sum to “1” in order to caculate the expected gains or losses of a particular “gaming” strategy. I would have knocked one of my students down a letter grade for having committed a similar mistake, if I wasn’t such a screw up in my own life. Please, let this thread sink, and pardon me for my stupidity. The general principle still holds, however: you reduce risk by diversifying. And the other general principle is “Never underestimate the importance of randomness and luck in your own success.” At least that’s the way I console myself (by telling it the other way around; never underestimate the importance of randomness and luck in your own failure) on nights like these. @ PhillipS, robbo, nicola037, et al., Brilliant! Which is why someone eventually had to come up with Discrete Mathematics. This is my problem, and one of the reasons why I “lost” in my estimation above: I’m habituated into thinking in terms of continuous functions, differential equations, etc. But every roll of the dice is a discrete event, just like every pass through customs is a discrete event. Using continous mathematics to attempt to predict outcomes in the case of discrete events is a recipe for disaster. I hope to meet up with all of you in The Afterlife sometime! A bunch of aesthetes with brains of steel. Who would have thunk it. You too, Nicola037, despite our small past disagreements. To be honest, I’ve never heard of William Bernstein and The Efficient Frontier, and I don’t believe in cheating by Googling it, so you’ll have to inform me! I thank everyone for bearing with me, and sincerely apologize for wasting everyone’s time.
Well that’s alright, LHB we’ll overlook it… this time 
(hint: you apologizing for this is pretty much like when I’m riding in a car with somebody and they announce something like “sorry, I took a wrong turn, I shoulda went the other way it would have been shorder” etc – as if I’d even notice or have known if they’d never said anything at all lol) I had thought about trying to bring up the M. Savant “Lets Make a Deal” theory to discuss in here (but then thought better of it)
I glossed over the actual math and didn’t check it, but the math is not important for the understanding currently as the concept of risk, and how people tend to be overconfident and have apetite for risk at the wrong times. The fact you appreciate this is indicative of a very high level of culture and reading. It took me a lifetime to grasp this and only now I am able to really wrap my hands around this principle. I have not read Taleb’s Black Swan, but I have read a lot of books of people whose ideas/recommendations/thoughts are based in the same ideology. THIS is what should be taught in colleges and universities!