A Man for All Markets: From Las Vegas to Wall Street, How I Beat the Dealer and the Market

by Edward O. Thorp

The notion of a market value for the whole world reminds me of a sign I saw on an office door in the Physics Department of the University of California, Irvine. It read EARTH PEOPLE, THIS IS GOD. YOU HAVE THIRTY DAYS TO LEAVE. I HAVE A BUYER FOR THE PROPERTY.

I want to print this and leave it on the front door of The Spheres.

Forty-six years later, when I stopped by our high school reunion for a couple of hours, the “ins” seemed the same as they had so long ago, only older and mellower. High school had been the apex of their lives. Many had married one another and lived locally ever since, whereas for me high school was a launching pad for life’s great adventure.

I'm so glad I made it out of Redding.

My mother had been carrying on an affair with the husband of the family with whom we had originally stayed when we visited California for the first time during the summer before Pearl Harbor. Only recently did I learn from my brother that the affair started then, and that when my father eventually discovered it, this led to the divorce.

It’s always classy when the father doesn’t mention it, right?

Understanding and dealing correctly with the trade-off between risk and return is a fundamental, but poorly understood, challenge faced by all gamblers and investors.

I started with the fact that the strategy I had used in the casino assumed that every card had the same chance of being dealt as any other during play. This cut the casino’s edge to just 0.62 percent, the best odds of any game being offered. But I realized that the odds as the game progressed actually depended on which cards were still left in the deck and that the edge would shift as play continued, sometimes favoring the casino and sometimes the player. The player who kept track could vary his bets accordingly. With the help of a mental picture based on ideas from an advanced mathematics course, I believed the player edge must often be substantial. Moreover, and this also was new, I saw how the player could condense and use this information in actual play at the table.

Note to self: Every new shoe should begin with table minimums and only leverage up when calculate odds tip in your favor.

The IBM 704 had done a thousand man-years of hand calculations in just ten minutes of computer time. I looked at these results with great excitement, for they would very likely either prove I was right or dash my hopes. The result was a player disadvantage of 2.72 percent with all the Aces gone—2.51 percent worse than the overall 0.21 percent casino edge. Although this was a huge shift in favor of the casino, it was actually great news. It proved conclusively what I believed in that Eureka moment back in the UCLA library when I thought I could beat the game, namely, that as cards were played there would be huge shifts in the edge, back and forth, between the casino and the players. The math also showed me that if removing a specific group of cards from the deck shifted the odds in one direction, adding an equal number of the same cards instead would move the odds the other way about the same amount. This meant that with an Ace-rich deck rather than an Ace-poor deck, the player should have a big advantage. For instance, with twice the usual proportion of Aces, which happens when all four Aces remain among the last twenty-six cards (half the deck), the player ought to gain roughly 2.51 percent over his initial 0.21 percent disadvantage, for a net edge of about 2.30 percent.

It's worth remembering that 2.5% constitutes a "large edge." You still have to play correctly for a long time to take advantage.

One of the best compromises between ease of use and profitability was to count the small-value cards (2, 3, 4, 5, 6) as +1 as they are seen during play, intermediate cards (7, 8, 9) as 0, and large-value cards (10, J, Q, K, A) as −1. From the results of my computer runs anyone could work out the details of nearly all the blackjack card counting systems in use today.

Exactly as I was taught by my gambling buddies.

A young reporter for the Post named Tom Wolfe followed up after my talk with an interview. The Post ran his story, “You Can So Beat the Gambling House at Blackjack, Math Expert Insists.” He was curious rather than skeptical, sympathetic but probing. Wolfe later became one of America’s most famous authors.

It's great that Tom Wolfe gets this call-out for his curiosity. Maintaining curiosity rather than cultivating cynicism, should be everyone's challenge in life.

In the abstract, life is a mixture of chance and choice. Chance can be thought of as the cards you are dealt in life. Choice is how you play them.

Love this.

I finally decided to go to Nevada, partly to silence that irritating jeer often leveled at academics, “Well, if you’re so smart, why aren’t you rich?” As a matter of personal pride and honor I felt that I owed my readers proof that the theory really worked, despite scoffs from casinos that my claims were ridiculous. The clincher was the casino spokesman on television who, speaking of my system said, “When a lamb goes to the slaughter, the lamb might kill the butcher. But we always bet on the butcher.

Even though the Goliath I was challenging had always won, I knew something no one else did: He was nearsighted, clumsy, slow, and stupid, and we were going to fight on my terms, not his. The clincher was that Vivian, despite her reservations and her preference that I play it safe, thought I could do it.

Support from the homefront. "Honey, I'm going to go take-down Vegas" never seems to work for me...

This plan, of betting only at a level at which I was emotionally comfortable and not advancing until I was ready, enabled me to play my system with a calm and disciplined accuracy. This lesson from the blackjack tables would prove invaluable throughout my investment lifetime as the stakes grew ever larger.

Everyone play calmly and disciplined with your crypto, ok?

For the second time, the Ten-Count System had shown moderately heavy losses mixed with “lucky” streaks of the most dazzling brilliance. I learned later that this was a characteristic of a random series of favorable bets. And I would see it again and again in real life in both the gambling and the investment worlds.

This jibes with my own experiences as well. Luckily, I think I play pretty close to this system. I've always referred to it as "small-ball" but heavily weighted on the big hands where I think I have an advantage. Believe it or not, I've seemed to do OK. At worst, I've only had moderate losses.

How hard is it to count? The more I practiced, the better my times, and I found that if I was able to count one deck in twenty to twenty-five seconds I could easily keep up in any game I was in, so I simply checked to be sure I was up to this standard each time before I played.

The next time I go out, I need somebody to deal a couple packs for me.

A dealer making this hole-card check would typically bend up the corner of his two cards to see what was hidden underneath. Eventually the Aces and Tens would get slightly warped. If the dealer was especially careless or if decks weren’t changed often enough, the savvy player could spot the warps before they were dealt and know where the Aces and Tens were, a huge advantage.

Now that is devious.

With six chambers, only one of which is loaded, the chance of firing the cartridge would seem to be one in six. But for a properly lubricated and maintained weapon held upright with the cylinder parallel to the ground, gravity and the weight of the cartridge will cause the full chamber to tend to end up near the bottom, provided the cylinder is allowed to stop on its own. If the cylinder is then relatched, the player has shifted the odds in his (women are too smart to play) favor.

You try it.

When I sat down to play on the fourth night, the atmosphere had again changed, drastically. The pit boss and his minions were smiling and relaxed. They seemed pleased to see me. Then they volunteered “coffee with cream and sugar, just the way you like it.” I was deep into the first shoe happily winning and drinking my coffee when suddenly I couldn’t think. I could no longer keep the count. I was shocked because I had managed well enough through noise, smoke, conversation, the pressure of high-speed play, the excitement of losing or winning, and the impact of alcoholic beverages. Something unexpected had taken place.

It is absolutely frightening to think of being drugged by management at a casino.

The six of us left Las Vegas the next morning to drive back to Las Cruces. I was at the wheel as we went down a mountain road in northern Arizona. We were going sixty-five miles an hour when the accelerator pedal suddenly jammed. The steep downhill and the wide-open throttle were too much for the brakes. The car sped up to eighty miles an hour and the turns in the road became unmanageable. With little time to think and my foot pressing as hard as I could on the brakes, I also set the emergency brake, downshifted so the engine would help slow the car, and cut off power by turning off the ignition. I finally managed to stop in a turnout.

...and even more-so to think of flying off a mountainside because your accelerator was mysteriously stuck. Yeesh.

We had proven the system worked at the tables like it did in theory. As a result, both the Dunes and the Sands removed the natural 8 and natural 9 bets.

Sucker bets were more beatable, when there was a disciplined system. Something tells me casinos know these tricks now and have geared their sucker bets more accordingly. In an arms race with gamin establishments, player edges tend to be temporary.

While at New Mexico State, I invested money from book royalties and gambling winnings in stocks. But I was ignorant of the market as well as unlucky. The results were poor. I wanted to do better. Investments presented a new type of uncertainty, but the theory of probability might help me make good choices.

It's best to get this lesson with a small amount of money. Watching people blow inheritances on learning is a painful thing.

“First, you bought something you didn’t really understand, so it was no better or worse than throwing a dart into the stock market list. Had you bought a low-load mutual fund [no-load funds weren’t available yet] you would have had the same expected gain but less expected risk.”

Amen.

Then Vivian remarked on my second mistake in thinking, my plan for getting out, which was to wait until I was even again. What I had done was focus on a price that was of unique historical significance to me, only me, namely, my purchase price. Behavioral finance theorists, who have in recent decades begun to analyze the psychological errors in thinking that persistently bedevil most investors, call this anchoring (of yourself to a price that has meaning to you but not to the market).

I learned from this that even though I was right in my economic analysis I hadn’t properly evaluated the risk of too much leverage. For a few thousand dollars I learned from this to make proper risk management a major theme of my life for more than fifty years thereafter.

Leverage. Warren Buffett: "When leverage works, it magnifies your gains. Your spouse thinks you're clever, and your neighbors get envious," explained Buffett in his 2010 shareholder letter. "But leverage is addictive. Once having profited from its wonders, very few people retreat to more conservative practices. And as we all learned in third grade — and some relearned in 2008 — any series of positive numbers, however impressive the numbers may be, evaporates when multiplied by a single zero. History tells us that leverage all too often produces zeroes, even when it is employed by very smart people." - https://www.usatoday.com/story/money/markets/2014/01/19/how-warren-buffett-uses-leverage-to-invest/4638423/

I also learned from my losing silver investment that when the interests of the salesmen and promoters differ from those of the client, the client had better look out for himself.

Caveat emptor.

Back in Newport Beach, the die was being cast. I passed Warren’s test when I told him if the dice are numbered as A = (3, 3, 3, 3, 3, 3), B = (6, 5, 2, 2, 2, 2) and C = (4, 4, 4, 4, 1, 1) then calculations show that, on average, A beats B two-thirds of the time, B beats C five-ninths of the time, and C beats A two-thirds of the time. Other sets of nontransitive dice are possible as well. I have entertained people by marking a set of three dice like this and letting my opponent pick his die first. After trying all three dice in turn and losing each time, people are typically stumped.

Did you know you can buy non-transitive dice? https://www.amazon.com/Non-Transitive-Dice/dp/B00F4I8IW0/

Warren’s house in Emerald Bay became newsworthy later on during Arnold (“The Terminator”) Schwarzenegger’s successful 2003 campaign to become governor of California. Initially, Buffett was a supporter and an economic adviser to Arnold. One campaign issue was how to cut California’s budget deficit. The problem was caused largely by the anti-tax measure Proposition 13, adopted by California voters in 1978. This limited the tax on real estate to 1 percent of the assessed valuation with a cap of 2 percent per year on any revaluation upward. With California’s soaring prices, the tax on houses that weren’t traded fell over time to a small fraction of 1 percent of their current value, thus sharply eroding the tax base and expanding the budget deficit. A house was reassessed at the current market price only when it was resold. As a result, taxes on comparable houses varied greatly, depending on when they last changed ownership. This led to major inequities in the taxes paid by different homeowners. In addition, by drastically lowering the overall effective tax rate on residences, Proposition 13 reduced the annual expense of homeownership, which in turn fueled the excessive rise in California home prices.

Unintended consequences, written in to tax law. California is *still* messed up. Make your wealth elsewhere, I say. You heard it here first.

it is difficult to judge how relatively bad these were, compared with the incessant violations that have always been, and continue to be, endemic in business and finance, because only a few of the many violators are caught, and when they are prosecuted it may be for only a tiny fraction of their offenses. This contrasts with the case of Drexel, where the searchlight of government was focused to reveal as many violations as possible. It’s like the case of the man who was cited three times in a single year for driving while intoxicated. His neighbor would also drink and drive, but was never pulled over. Who is the greater criminal? Now suppose I tell you that the caught man did it only three times and was apprehended every time, whereas his neighbor did it a hundred times and was never caught. How could this happen? What if I tell you that the two men are bitter business rivals and that the traffic cop’s boss, the police chief, gets large campaign contributions from the man who got no traffic citations. Now who is the greater criminal?

This is called "real life".

The government released a list of more than thirteen thousand past and present Madoff account holders, ranging from hundreds of not very rich Florida retirees to celebrities, billionaires, and nonprofits such as charities and universities. If these legions of investors were easily gulled, often for decades, what does this swindle (and others) say about the academic theory that markets are “efficient,” with its claims that investors quickly and rationally incorporate all publicly available information into their selections?

It says that there are always inefficiencies, so the strictest interpretation of the efficient market hypothesis is clearly wrong, but as a model, it's damned accurate.

We were asking $5,495,000 and expected to get about $5,000,000. One offer was at $4.6 million, and the prospective buyer used his aggressive business partner to open negotiations. The partner’s in-your-face style and nitpicking criticism of the house was designed to beat down the price. He alienated us and our agent. The other offer was for $5 million from an agreeable family who loved the house “as is.” We accepted, upon which the other buyer begged us to reconsider, indicating he would meet or exceed the other price, and wouldn’t use Mr. in-your-face to close the deal. Too bad. Lesson: It doesn’t pay to push the other party to their absolute limit. A small extra gain is generally not worth the substantial risk the deal will break up.

Life's too short to deal with assholes. This is more timeless wisdom you can take to the bank. I just sold my 14 year old truck to 3 farmers from Duvall. They asked me what my fair price was, I told them, they bought the truck.

What the hagglers and the traders do reminds me of the behavioral psychology distinction between two extremes on a continuum of types: satisficers and maximizers. When a maximizer goes shopping, looks for a handyman, buys gas, or plans a trip, he searches for the best (maximum) possible deal. Time and effort don’t matter much. Missing the very best deal leads to regret and stress. On the other hand, the satisficer, so-called because he is satisfied with a result that is close to the best, factors in the costs of searching and decision making, as well as the risk of losing a near-optimal opportunity and perhaps never finding anything as good again.

My wife = maximizer. Me = satisficer.

This is reminiscent of the so-called secretary or marriage problem in mathematics. Assume that you will interview a series of people, from which you will choose one. Further, you must consider them one at a time, and having once rejected someone, you cannot reconsider. The optimal strategy is to wait until you have seen about 37 percent of the prospects, then choose the next one you see who is better than anybody among this first 37 percent that you passed over. If no one is better you are stuck with the last person on the list.

This is the entire hiring model for Amazon. We make each decision as to fit and viability individually. If you're rational about your criteria, it works, but I think it would be tough to do as an individual.

According to the theory of efficient markets (the EMH), the market sets prices so that they accurately reflect all available information. How does the collapse of 60 percent in fifteen minutes in response to false information represent the rational incorporation of information into the price? I also ask believers in the EMH to explain why the stock failed to recover in the eleven days after the hoax was exposed. The news for EMLX was good.

In 2014, Forbes ranked him as the 134th richest American, at $3.8 billion. One of his hires was Jeff Bezos, who, while researching business opportunities in 1994 for Shaw, got the idea for an online bookstore and left to start a company called Amazon.com. At $30 billion in 2014, Bezos was the fifteenth richest American.

Not anymore!

Ridgeline was closed a large part of the time to new investors, and current partners were often restricted from adding capital. To maintain higher returns, we sometimes even reduced our size by returning capital to partners.

It is the rare hedge fund that admits its methods have a ceiling cap.

For many years Berkshire had a shareholder-directed charitable contribution program. Each year the company allowed each A shareholder to donate $X, where $X was $1 a share at the start and gradually increased to something like $18 a share. Shareholders allocated their amounts to charities chosen by them, not management, and Berkshire sent the money. As a result of the antiabortion protests at this annual meeting and the related boycott of a Berkshire company, the program was discontinued. The antiabortion protesters succeeded in eliminating not only shareholder contributions supporting family planning, but those to other charities as well, including organizations the demonstrators themselves favored.

The law of unintended consequences.

The number of households worth at least $1 million was thought to be about ten million in 2015. With so many millionaire households, the goal of becoming one of them looks within reach. To see what might be done, imagine you’re an eighteen-year-old blue-collar worker with no savings and no prospects. What if, somehow, you could save $6 a day and buy shares in the Vanguard S&P 500 Index Fund at the end of each month? If that investment grows in a tax-deferred retirement plan at the long-term average for large stocks of about 10 percent, then after forty-seven years you can retire at age sixty-five with $2.4 million. But where do you find an extra $6 a day? The pack-and-a-half-a-day smoker who kicks his drug habit saves $6 each day. If the construction worker who drinks two $5 six-packs of beer or Coke each day switches to tap water he can save $10 a day, $6 of which he puts in an index fund and $4 of which he spends on healthy food to replace the junk calories from the beer or Coke.

Politicians, dimly aware of the awesome power of compound growth, have in many jurisdictions passed laws against perpetuities to prevent the enormous concentrations of wealth that might arise from investments compounding without limit. On the other hand, some states and counties welcome perpetual trusts, being more interested in deriving revenue from them now.

Multi-generational wealth is a larger problem, IMO, than the opposite. Creating a class of wealthy people who never contributed anything, is the source of a lot of strife in the country.

Each year, typically at the end of October, US equity mutual funds assign the year-to-date taxable gains or losses to their current investors. If you were to make an investment shortly before this in a year when the fund had a lot of gain, you could experience the inequity of paying taxes on an amount far larger than your real economic gain. On the other hand, in a year when the fund allocated large losses, a purchase shortly before the time to receive the losses could let investors reduce their tax bill without having had a corresponding economic loss.

Taxable investors need to review their holdings on a case-by-case basis. For instance, in 2015, with a cost basis of about $1,000 a share, a market price of $225,000 a share, and a combined federal and state tax rate of, say, 30 percent, I would net about $157,800 per share after a sale of my Berkshire Hathaway Class A stock. An index fund purchased with this smaller amount would have to do about 43 percent better than Berkshire in the future for me to catch up. This seems extremely unlikely.

Buy and hold, baby. Diversify with new funds and sit on your hands with old ones.

The threat to a buy-and-hold program is the investor himself. Following his stocks and listening to stories and advice about them can lead to trading actively, producing on average the inferior results about which I’ve warned. Buying an index avoids this trap.

The #1 benefit of a good advisor is behavior modification. If you have somebody who is more disciplined than you, sitting at a level of detach meant from your finances, you think twice about discretionary purchases and trading.

When Commodity Futures Trading Commission chairperson (1996–99) Brooksley Born wanted to regulate the derivatives that would later be a major cause of disaster, the PBS program Frontline detailed how she was blocked in 1998 by the triumvirate of Federal Reserve chairman Alan Greenspan, US Treasury Secretary Robert Rubin, and Deputy US Treasury Secretary Lawrence Summers, all of whom would later advise government on the 2008–09 bailout. Nassim Taleb asked why, after a driver crashes his school bus, killing and injuring his passengers, he should be put in charge of another bus and asked to set up new safety rules.

I need to read more Taleb.

imagine that Joe Sixpack offered to sell you a CDS on your $320,000 loan to your friend for $1,600 a year for five years. Joe is doing well, has a million-dollar house with no debt, and is therefore “good for the money.” Happy with $1,600 a year in extra income, Joe continues to sell CDSs on residential mortgages. Unregulated, he sells a thousand just like the one he sold you, and his income grows to $1.6 million a year. If these loans average $320,000 each, he is insuring a total of $320 million, all backed by his million-dollar house. You object, arguing that Joe couldn’t sell this many CDSs because once he’s sold a few of them people would realize there was a good chance he couldn’t pay off in a crisis. Ah, but what if Joe did this in a subsidiary and didn’t disclose the vast scale of his operations? Welcome to AIG.

How can we prevent future financial crises driven by the systemic and scarcely regulated use of extreme leverage? One obvious step is to limit leverage by requiring sufficient collateral to be posted by both counterparties when they trade. That’s what is done on regulated futures exchanges, where contracts are also standardized.

Institutions that are “too big to fail,” and have a significant risk of doing so, should be broken into pieces that are small enough to fail without jeopardizing the financial system. As Alan Greenspan finally admitted, “Too big to fail is too big.” This is a catchy sound bite but it misstates the real problem. It’s not the mere size of an institution that creates the danger. It is the size of the risk to the financial system from a failure.

Mnuchin was literally arguing to remove regulatory oversight for banks ($50B - $200B) at the end of January, and had no good answers to questions regarding how to assess the size of the risk this poses.https://www.thenation.com/article/here-comes-the-next-financial-crisis/

Education builds software for your brain. When you’re born, think of yourself as a computer with a basic operating system and not much else. Learning is like adding programs, big and small, to this computer, from drawing a face to riding a bicycle to reading to mastering calculus. You will use these programs to make your way in the world.

I have always been fascinated by the idea of programming yourself. Most people don't realize that they're self-installing bloatware and viruses.

Simplistically, there are two types of rich, those who use government to tilt the playing field in their favor and those who don’t. The former pay taxes at a rate well below the middle class and the latter pay at substantially higher rates. The blended rate of the two groups is similar to that paid by the upper middle class. But the politically connected rich typically point to the higher rates paid by their nonconnected rich fellows as a cover to demand still more tax breaks for themselves.