Beating Blackjack: How An Outsider Beat The House
Why was it that a gambling outsider like Ed Thorp figured out how to beat blackjack when it should have been insiders?
In the late 1950s, Ed Thorp defied conventional wisdom and developed a winning strategy for blackjack that anyone could then use. But what set him apart from those who came before?
For starters, he:
Incorporated more rigorous math/statistics into Blackjack than were then used
Deferred to rules-based decision-making
Stomached occasional “losses” on his journey, caused by random fluctuations
Ed Thorp and the Story of Beating Blackjack
The following excerpts are taken from Ed Thorp’s autobiography.
In the late 1950s, 26-year-old Ed Thorp was on his way to “lead the usual low-budget academic life” as a maths professor.
While teaching at UCLA, he and his wife, Vivian, were looking to get away one Christmas break. Las Vegas wasn’t too far away. While the dazzling city had been known for its gambling then, it had just recently turned itself into a bargain vacation spot.
“Since I knew of no one who had ever found a way to beat the casinos, gambling in Vegas wasn’t on my list of priorities.”
Fate intervened. A colleague, who had heard about their upcoming trip, told Thorp about a new Blackjack strategy. This new strategy claimed to give a player the best odds, though it fell just short of beating the game.
“Just before we left for our vacation, my colleague from Professor Robert Sorgenfrey told me about a new strategy [The Baldwin Strategy] for playing blackjack that claimed to give players the smallest house edge [0.62% house edge] of any casino game...Devised by for mathematicians during their time in the army, the strategy covered several hundred possible decisions a player might face.”
Thorp was intrigued. The Baldwin Strategy clearly showed that Blackjack had some underlying logical structure, with nearly break-even odds. And so, Thorp decided to check out the Baldwin Strategy for himself. He condensed the strategy’s main features onto a card, for use during gameplay (which was allowed).
Ed Thorp Goes to Las Vegas
“I knew virtually nothing about casinos, their history, or how they operated. I was like a person who had glanced at recipes but never been in a kitchen.”
Thorp showed up to Las Vegas that fall as an outsider, with little feel for the gambling world. But he wanted to find out for himself what Blackjack was like and see just how well the Baldwin Strategy fared in practice. Would this theory work in practice?
“When I held up a game by consulting my strategy card, the dealer made patronizing “helpful” suggestions on how to play my hand and indicated to the crowd that he was dealing to someone (and with) just in from the farm.”
Unfazed by the dealer’s ridicule, he was fascinated by the superstitious and dogmatic thinking that permeated Blackjack, which even the best insiders seemed to possess.
Winning and losing at Blackjack was determined by random fluctuations in the cards; a player would need a luck on their side to win—so it seemed to the insiders. Yet, while players around him saw randomness, Thorp saw some structure.
“But now, to Vivian‘s dismay, I was hooked on blackjack—though not in the usual sense. The atmosphere of ignorance and superstition surrounding the blackjack table that day had convinced me that even good players didn’t understand the mathematics underlying the game. I returned home intending to find a way to win.“ (emphasis added)
Beating Blackjack by Card Counting
“Had I been more knowledgeable about the history of gambling in the centuries of effort devoted to the mathematical analysis of games, I might not have tackled Blackjack.”
Fortunately, because of Thorp outsider’s status, he wasn’t aware of centuries of efforts to beat the game, nor was he burdened by conventional wisdom. His lack of “insider knowledge,” along with his ignorance of past efforts to beat Blackjack, ended up an asset.
“The belief that casinos must come out ahead in the long run was supported by conventional wisdom, which argued that if blackjack could be beaten, the casinos would have to either change the rules or to drop the game. Neither had happened. But, confident from my experiments that I could predict roulette, I wasn’t willing to accept these claims about blackjack. I decided to check for myself if the player could systematically win.”
He returned from vacation eager to analyze the game. Upon his return home, a novel idea struck Thorp.
“As my eyes gobbled up equations, suddenly I saw both why I could beat the game and how to prove it. 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 with any other during play. This cut the houses edge to just .62%, the best out of any game being offered. But I realized that the odds as the game progressed actually depending on which cars were still left in the deck and the edge would shift as play continued, sometimes favoring the casino and sometimes the player.” (emphasis added)
Thorp’s hunch was this: both the player and house odds actually moved back and forth during gameplay, as cards were removed from a deck. It turned out the good and bad fortunes of gameplay weren’t entirely random, not when you kept track of prior cards.
So if the Baldwin strategy was a rounding error away from beating the house, what would happen if you kept track of the cards, in addition? Perhaps the inside view the “house always wins” wasn’t written in stone.
Developing a Rules-Based Approach to Blackjack
“Attempts to find winning systems over the following centuries stimulated the development of the theory, eventually leading to proofs that winning systems for casino gambling games were, under most circumstances, impossible. Now I benefited from my habit of checking it out for myself.”
In June of 1959, Ed Thorp and Vivian moved to Cambridge to continue academic life at MIT. Around the same time, programmable computers were entering universities.
While Blackjack insiders weren’t well positioned to see the implications of emerging computer technology then, Ed Thorp, the academic, was. He saw how he could use MIT’s IBM computer for simulating gameplay, along with estimating the odds in Blackjack—if he could program it.
“My hand calculations were going to take hundreds, perhaps thousands of years. At that point I learned that MIT had an IBM 704 computer and, being a faculty member, I could use it. Using a book from the computer center, I taught myself to program the machine in it’s language, Fortran.”
With the IBM 704, he was able to quickly simulate how eliminating specific cards improved or reduced the player’s odds.
“The math also showed me that 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 players should have a big advantage.”
And so, Thorp showed that luck wasn’t the only way a player could win at Blackjack. A player merely needed to have a feel for which cards remained in the deck.
After further simulations, he developed a practical, rules-based, strategy which would beat Blackjack, if he could stick to it.
“My analysis using MIT’s IBM 704 had produced the basic results they gave me the Five-Count System, most of the Ten-Count System, and the ideas for what I called the ultimate strategy. The latter assigned a point value to every card, proportional to its effect on the game, with aces each counted as -9, 2s counted as +5, and so on down to Tens counted as -7. Though this was too difficult for almost anyone to keep track of mentally, many simple accounting systems worked out quite well. What was the best compromise 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.“
Returning to Las Vegas, Beating Blackjack, and Living with “Losses”
“For actual casino play, I built a much more powerful winning strategy based on the fluctuation in percentage of ten-value cards in the deck can’t even though my calculation showed the impact of a 10 was less than that of a five, since there were four times as many tens. The larger fluctuations in 10 richness that resulted gave the player more and better opportunities.”
Returning to Las Vegas, Thorp—this “someone just in from the farm”—was ready to beat the house.
He decided to employ his rules-based Ten-Count system to beat blackjack, but this favorable strategy came with a caveat: short-term losses had to be stomached.
“… The cards ran badly, I lost steadily, and after four hours I was behind $1700 and discouraged. Of course, I knew that just as the house can lose in the short run even though it has the advantage in a game, a serious card counter can fall behind and this can last for hours or, sometimes, even days. Persisting, I waited for the deck to become favorable just one more time.“
But Thorp wasn’t ready to walk. While gameplay with card counting was an emotional rollercoaster, he figured that the bitter, short-term, losses he suffered—brought about by randomness, were simply unavoidable.
The “winners” would inevitably pay for the “losers”.
So he didn’t mind losing a $1,500 hand because he understood that—with this long-term favorable approach—he’d inevitably finish the night up $10,000. Thorp kept playing.
“It happened a few minutes later as the deck suddenly produced a 5% advantage… The deck continued to be favorable, calling for a big bets, and the next deck quickly became good as well. In a few minutes I had wiped out my losses and went ahead $255. Then we quit for the evening.”
”For the second time, the Ten-Count System has 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.” (emphasis added)
Thorp stayed true to his system. In the long run, the strategies’ “winners” did pay for the “losers”.
And so, this Blackjack outsider, “just in from the farm” proved a player could beat the house.
“…when we returned to our hotel that you mean with my winnings, we were ahead $13,000 so far on the trip. My daily calls to Vivian has shown her that we were winning more each day.”
Ed Thorp: Master of Blackjack
“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. I chose to investigate blackjack. As a result, chance offered me a new set of unexpected opportunities.”
At this point in his arc, Thorp goes on to continue beating the house at Blackjack, even though the casinos tried to thwart his winning ways. He let the genie out of the bottle and published Beat the Dealer, in 1962, detailing his card-counting method to the general public. Now, everyone could be a card counter.
In the end, the outsider Thorp, demonstrates the value in finding out for ourselves in the face of conventional wisdom, applying math or statistics in new ways or in new places (increasingly with the help of computers), using rules-based decision-making when possible, and stomaching “losses” or unlucky streaks that are an inseparable part of “a random series of favorable bets”.
After Beating Blackjack, Ed Thorp goes on to beat Financial Markets too. But that’s another story.
Author’s Note
All quotes are taken from Ed Thorp’s Autobiography: A Man for All Markets: From Las Vegas to Wall Street, How I Beat the Dealer and the Market