Seeking Wisdom

by Peter Bevelin

  According to the National Transportation Safety Board the number of passengers killed in air accidents in the U.S. during 1992 through 2001 was 433 (including the 232 aboard the four hijacked flights on September 11, 2001). For reference, in 2001, the annual number oflives lost in road traffic accidents in the

  U.S. was 42,119.

  That people feel safer driving than flying makes sense since we are oriented towards survival. As Antonio Damasio says in Descartes' Error, "Planes do crash now and then, and fewer people survive plane crashes than survive car crashes." Studies also show that we fear harm from what's unfamiliar much more than mundane hazards and by things we feel we control. We don't feel in control when we fly.

  Why do we lose money gambling? Why do we invest in exotic long shot ventures? We often overestimate the chance of low probability but high-payoff bets. For example, how likely is it that anyone guesses a number between 1 and 14 million? What is Mary's chance of winning "Lotto 6/49" if there are 14 million outcomes? What must happen? She must pick 6 numbers out of 49 and if they all match she wins. What can happen? How many numbers can she choose from? The possible number of ways she can choose 6 numbers out of 49 is 13,983,816. The probability that someone chooses the winning combination is therefore one in about 14 million. Merely slightly better than throwing heads on 24 successive tosses of a coin.

  Imagine the time it takes to put together 14 million combinations. If we assume every combination on average takes 1 minute to put down on paper, and Mary pick numbers for 24 hours a day, it will take her 27 years to write them all down.

  Even if Mary invests $14 million to buy 14 million tickets in the hopes of winning a $20 million jackpot, she may have to share the jackpot with others that picked the winning number. If just one other person picked the winning combination, she would lose $4 million (20/2- 14).

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  Why do people play a game when the likelihood of losing is so high? Even if we exclude the amusement factor and the reinforcement from an occasional pay off, it is understandable since they perceive the benefit of being right as huge and the cost of being wrong as low - merely the cost of the ticket or a dollar. Remember the advice of Benjamin Franklin: "He that waits upon fortune, is never sure of a dinner."

  Mathematical expectation

  A lottery has JOO tickets. Each ticket costs $10. The cash price is $500. Is it worthwhile for Mary to buy a lottery ticket?

  The expected value of this game is the probability of winning (1 in 100) multiplied with the price ($500) less the probability of losing (99 out of 100) multiplied with the cost of playing ($10). For each outcome we take the probability and multiply the consequence (a reward or a cost) and then add the figures. This means that Mary's expected value of buying a lottery ticket is a loss of about $5 (0.01 x $500 - 0.99 x $10).

  We need to separate between few games and many games. Since probability means the number of times an event is likely to happen during a large number of trials, the expected value is the amount Mary should expect to win or lose per game if she made the same bet many times. Expected value tells Mary that she on average should expect to lose $5 every time she plays if she plays the same lottery over and over. Not what she can expect from a single game. Mary has a 1

  % chance of winning the lottery and if she wins, her gain is $490. She has a 99

  % chance oflosing $10.

  Most of our decisions in every-day life are one-time bets. Choices we face only once. Still, this is not the last decision we make. There are a large number of uncertain decisions we make over a lifetime. We make bets every day. So if we view life's decisions as a series of gambles, we should use expected value as a guide whenever appropriate. Over time, we will come out better.

  John placed $38 dollar on the roulette tabk.

  Mathematics and human nature make it impossible for us to beat the roulette wheel for any considerable length of time. If we play at a casino once we may be lucky and in the short run win some money, but we should expect to lose in the long run. The casino has the advantage.

  There are 38 different numbers (including double zero) on the roulette wheel. When the croupier spins the wheel there is an equal chance of the ball landing in any one of the 38 slots. John puts $1 on a single number. If his number comes

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  up, he wins $35. On average his expected value of a one dollar bet is a loss of 5.26 cents (1/38x$35 - 37/38x$1). Over the long run John loses an average of 5.26 cents for every dollar he places on the table. The odds are set so they average out in the casino's favor.

  ''If I just stay at the table long enough, the odds turn in my favor and I will win back everything I lost. "

  But this is what the casino wants us to believe. The casino can't predict the outcome of any particular bet but as soon as there are a large number of individual players making bets, the casino will make money. As a casino operator said: "What I love is the risk. Some nights we make money, and other nights we make more money."

  Even if we win in the short run, human nature turns us into losers. Nearly all of those who win big continue to play until they have lost their gains, and perhaps more. This is well illustrated by Henry Howard Harper in his book, The Psychology of Speculation:

  It is said to be a proven fact that the chances are so much against the player, that a roulette wheel can be run at a profit, even if the percentage in favor of the house is entirely eliminated. This is due to the fact that the excitement of play causes a certain confusion of mind, and players are prone to do the wrong thing; for instance, double their bets when in an adverse run of luck and "pinch" them when luck is running favorably. Or, on the other hand, players who have pressed their advantage and doubled in a run of favorable luck will continue stubbornly to plunge long after their luck has changed. Precisely the same psychology applies to trading in stocks.

  Chance has no memory

  "My luck is about to change. The trend will reverse. "

  We tend to believe that the probability of an independent event is lowered when it has happened recently or that the probability is increased when it hasn't happened recently. For example, after a run of bad outcomes in independent events that appear randomly, we sometimes believe a good outcome is due. But previous outcomes neither influence nor have any predictive value of future outcomes. There is neither memory nor a sense of justice.

  Mary flipped a coin and got 5 heads in a row. Is a tail due? It must be, since in the long run heads and tails balance out.

  When we say that the probability of tossing tails is 50%, we mean that over a long

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  run of tosses, tails come up half the time. The probability that Mary flips a head on her fifth toss is 50%. The coin has no sense of fairness. As the 19th Century French mathematician Joseph Bertrand said: "The coin has neither memory or consciousness." Mary committed the gambler's fallacy. This happens when we believe that when something has continued for a certain period of time, it goes back to its long-term average. This is the same as the roulette player when he bets on red merely because black has come up four times in a row. But black has the same chance as red to come up on the next spin. Each spin, each outcome is independent of the one before. Only in the long run will the ratio of red to black become equal.

  Every single time Mary plays, the probability it lands on heads is 50% and lands on tails 50%. Even if we know that the probability is 50%, we can't predict if a given flip results in a head or tail. We may flip heads ten times in a row or none. The laws of probability don't count out luck.

  "J got a speeding ticket yesterday, so now I can cross the speed limit again,"said john. Even criminals suffer the gambler's fallacy. Studies show that repeat criminals expect their chance of getting caught to be reduced after being caught and punished unless they are extremely unlucky.

  Mary finds it comforting knowing it will take another 99 years until the next giant storm happen.

  What is a" 100-year storm?" To predict storms we look at past statistics i.e., how often
in the recorded past a storm of a certain magnitude has occurred. We also assume that the same magnitude of storm will occur with the same frequency in the future. A 100-year storm doesn't mean it happens only once every 100 years. It could happen any year. If we get a once in 100-year storm this year, another big one could happen next year. A 100-year event only means that there is a 1% chance that the event will happen in any given year. So even if large storms are rare, they occur at random. The same reasoning is true for floods, tsunamis, or airplane crashes. In all independent events that have random components in them, there is no memory of the past.

  Controlling chance events

  The craps table was filled with people tossing their die soft and asking for a low number.

  We believe in lucky numbers and we believe we can control the outcome of chance events. But skill or effort doesn't change the probability of chance events.

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  "Change tickets! Are you crazy! I would feel awfol if my number comes up and I'd traded it away. "

  In one experiment a social psychologist found that people were more reluctant to give up a lottery ticket they had chosen themselves, than one selected at random for them. They wanted four times as much money for selling the chosen ones compared to what they wanted for the randomly selected ticket. But in random drawings it doesn't make any difference if we choose a ticket or are assigned one. The probability of winning is the same. The lesson is, if you want to sell lottery tickets, let people choose their own numbers instead of randomly drawing them.

  Gains, losses and utility

  The 18th Century Swiss mathematician Daniel Bernoulli said: ''A gain of one thousand ducats is more significant to a pauper than to a rich man though both gain the same amount." This means that the utility or personal value of an outcome differs for different people and at different stages in life. For example, our preferences change as our state of wealth changes.

  Often when we make financial decisions we don't consider our total wealth. Instead we judge a decision by evaluating changes measured in terms of short term gains and losses.

  "Should I invest?"

  "There is a 50% probability that I gain $10,000. There is a 50% probability that I lose $4,000. "

  "Since I get pleasure from gains and the expected value ($3,000} is positive, I decide to invest."

  Instead we should take a more long-term view and think in terms of wealth. We should add our current wealth to all possible financial outcomes and choose the alternative that has a higher expected utility (considering our own psychological nature, talent and goals).

  ''My present wealth is $1,000,000. Do I choose $1,000,000 for sure or $996,000 or

  $1,010,000 with equal probabilities?"

  "Since the expected utility resulting from integrating the favorable investment with my wealth is lower than the expected utility of my current wealth, I don't invest. " Remember that the concept of utility is about the personal value of potential consequences and is therefore different for different individuals. An individual who finds that the expected utility resulting from integrating the mentioned

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  investment with his wealth are higher or about the same as the expected utility of his current wealth, will choose the favorable investment.‌

  Ask: What do I end up with? How much will I have ifl succeed and how much will I have ifl fail? How certain am I? What is the expected utility?

  The consequences of low frequency events

  Imagine the following scenario:

  Outcome A OutcomeB

  Probability Cost of consequence

  10% -90

  90% -10

  Expected value

  -9

  -9

  Both outcomes have the same expected value but differ hugely in their cost of consequences. We can't only look at how likely an unwanted event is to happen. We must also rate the magnitude of its consequences. Before taking an action, ask: What are the benefits and costs? What might go wrong? How can it go wrong? How much can I lose? What is the probability and consequence of failure over time? How can the probability and consequence of failure be reduced?

  What if the probability of success is high but the consequence of failure is terrible?

  The consequences of being wrong

  Take no chance whatsoever with food poisoning, and stay away from places where others have been recently killed, regardless

  of what the mathematical laws of probability tell you.

  - Edward Wilson (Professor Emeritus, from Consilience)

  "Pascal's Wager" is Blaise Pascal's argument for believing in God. Pascal reasoned as follows: If we believe in God, and God exists, we would gain in afterlife. If we don't believe in God, and God exists, we will lose in afterlife. Independent of the probabilities of a God, the consequences of not believing are so awful, we should hedge our bet and believe.

  Pascal suggests that we are playing a game with 2 choices, believe and not believe, with the following consequences:

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  Probability (p) Believe

  Don't believe

  God does exist

  p

  Saved (good) Damned (bad)

  God does not exist (1 - p)

  Inconvenience Normal life

  If God exists, and we believe God exists, we are saved. This is good. If we don't believe, and God is unforgiving, we are damned. If we believe but God doesn't exist, we miss out on some worldly pleasures. If God doesn't exist and we don't believe that God exists, we live a normal life.

  Expected value of believing= p (the value of being saved) + (1-p)(the cost of inconvenience)

  Expected value of not believing = p(the cost of being damned) + (1-p)(the value ofliving a normal life)

  Pascal said: "If I lost, I would have lost little. If I won I would have gained eternal life." Our choice depends on the probabilities, but Pascal assumed that the consequences of being damned is infinite, meaning the expected value of believing is least negative and therefore he reasoned that believing in God is best no matter how low we set the probability that God exists.

  john wants to make extra money and is offered to play Russian Roulette.

  If John wins he gets $10 million. Should he play? There are 6 equally likely possible outcomes when he pulls the trigger - empty, empty, empty, empty, empty, bullet. This makes the probability 5/6 or 83%. This is the same as saying that John is playing a lottery with only 6 tickets where one ticket is lethal.

  Should he play this game once? The probability is 83% that he gets $10 million. The probability is only 17% that he loses.

  Let's look at the consequences: If John doesn't play and there was a bullet he is glad he didn't play. If he plays and there is a bullet, he dies. If he doesn't play and there was no bullet he loses the pleasure which the extra money could have bought him. If he plays and there is no bullet he gains $10 million which would buy him extra pleasure. To play is to risk death in exchange for extra pleasure. There is an 83% probability that John is right but the consequence of being wrong is fatal. Even if the probabilities favor him, the downside is unbearable. Why should John risk his life? The value of survival is infinite, so the strategy of not playing is best no matter what probability we assign for the existence of "no bullet" or what money is being offered. But there may be exceptions. Someone that is poor, in need of supporting a family who knows he will die of a lethal disease within 3 months might pull the trigger. He could lose 3 months of life,

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  but if he wins, his family will be taken care of after his death.

  We should never risk something we have and need for something we don't need. But some people pull the trigger anyway. This is what Warren Buffett said about the Long-Term Capital Management affair:

  Here were 16 extremely bright - and I do mean extremely bright - people at the top of LTCM. The average IQ among their top 16 people would probably be as high or higher than at any other organization you could find. And individually, they had decades of experience - colle
ctively, centuries of experience - in the sort of securities in which LTCM was invested.

  Moreover, they had a huge amount of their own money up - and probably a very high percentage of their net worth in almost every case. So here were super-bright, extremely experienced people, operating with their own money. And yet, in effect, on that day in September, they were broke. To me, that's absolutely fascinating.

  In fact, there's a book with a great title - You Only Have to Get Rich Once. It's a great title, but not a very good book. (Walter Guttman wrote it many years ago.) But the tide is right: You only have to get rich once.

  Why do very bright people risk losing something that's very important to them to gain something that's totally unimportant? The added money has no utility whatsoever - and the money that was lost had enormous utility. And on top of that, their reputation gets tarnished and all of that sort of thing. So the gain/loss ratio in any real sense is just incredible... Whenever a really bright person who has a lot of money goes broke, it's because of leverage... It's almost impossible to go broke without borrowed money being in the equation.