自然科学类纪录片，BBC 频道 2004 年出品，是 BBC Horizon 系列其中之一。
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http://www.bbc.co.uk/programmes/b00jmzdk
In the mid-1990s, a team of American science students took on the might of the Las Vegas casinos, and came home with millions of dollars. Hardworking engineering students during the week, they became high-rolling gamblers by the weekend and proved that, in one game at least, the house doesn’t always win.
The game was blackjack, and the students were from the world-renowned Massachusetts Institute of Technology (MIT). Their audacious winnings marked the climax of an arms race between casino and player that began 40 years earlier with maths professor Edward Thorp. He realised that the one feature of blackjack that made it different from other casino games also made it possible to beat.
In most gambling games - roulette, dice, slot machines, the lottery - events in the past do not determine the future. The odds are the same on every roll of the dice or spin of the wheel. Winning streaks or losing streaks may occur, but they are only one possible result from the set of all possible outcomes. A fair coin that has shown heads ten times, still only has a 50% chance of showing heads on the next flip.
Casinos and bookmakers make certain that the odds are always stacked slightly in their favour. In other words, over time, the house will always win.
Changing odds
Thorp realised that because of the unique way blackjack was played, the odds were not always the same in every round. After each hand is played, the used cards are put to one side, and not shuffled back into the deck. They are effectively removed from the pool of available cards in the next round.
So in any given hand, the odds of getting an ace will decrease if an ace has been played in previous rounds. Aces are beneficial to the player, so having a smaller proportion of aces in the deck shifts the odds further in favour of the house. Previous gamblers had realised this fact, but no one had the insight to come up with a practical system to take advantage of this phenomenon.
The basic rules of blackjack are simple. To win a round, the player has to draw cards to beat the dealer’s total and not exceed a total of 21. The dealer must draw cards until a total of 17 or greater is reached.
Thorp calculated that as the game continued and cards were removed after each round, if the remaining deck became richer than average in certain types of cards, it became advantageous to the player. Although the winning margin is still subject to the luck of the draw, this meant that using perfect strategy, with a large bankroll and playing enough hands, the player was more than likely to come out on top.
A player would start off each deck playing minimal stakes. Then by keeping track of the cards leaving the deck, they would determine a point when the odds switched in their favour and lay down larger and larger bets as the deck became more and more favourable. Playing perfect basic strategy without card counting, the player’s average expectation is between -0.6% and 0%. Using perfect high-low card counting and playing perfect strategy, the player’s average expectation is between +0.4 and +1.14%. So a £100 bet will yield on average £101.14 in return, playing a single deck game.
Testing the system
Thorp announced his strategy at the American Mathematical Society in 1960 and news quickly spread. He was approached by the mysterious ‘Mr X’, a gambler and businessman with strong links to the underworld, who was eager to see whether his strategy could make real money. Mr X put up $10,000 to test the system. Unaware of Mr X’s mobster links, Thorp agreed, and playing according to his strategy in Reno casinos, managed to more than double his bankroll in two days of play!
In 1962, Thorp published Beat the Dealer - A Winning Strategy for the Game of Twenty One. Immediately casinos in Nevada were inundated with wannabe card counters, eager to make a quick buck. Four years later, the second edition outlined the new high-low count, a system with just as much power but easier to use.
The casinos, terrified of losing money, decided to change the rules to make life harder for the card counters. They increased the number of decks, they shuffled more often and at one point even changed the winning payoffs. Dealers and pit bosses learned how to spot card counters, and asked anyone suspected of counting to play another game or leave the casino. Life for card counters became increasingly tough, and the counting systems became more complicated in order to try and keep up a marginal edge over the casinos. Card counting became a hazardous and unprofitable occupation.
In 1971, Keith Taft, an electronics engineer from California, was frustrated at his low winnings from counting. He decided to develop a portable computer that could count cards for him. With his son Marty, he built ‘George’, probably the world’s first portable computer, specifically to count cards at blackjack. The player tapped in the value of each card played using their toes, and the computer would buzz back the amount to bet and whether to stick or twist each round.
The computer was able to calculate precisely the advantage or disadvantage each card gave to the player, and thus accurately predict the optimum playing strategy. The Tafts’ computer allowed them to move back to the winning margins that Thorp had enjoyed 10 years earlier. Keen to capitalise on their success, the father and son team set up a home workshop to design and build new computers, which they sold for $10,000 apiece.
But it didn’t take long for the casinos to catch up with the Tafts. In May 1977, after a long winning streak, Marty Taft was escorted into the backroom of a Nevada casino. Security guards forcibly searched him, found his computer, and sent it away to the FBI. Soon after the law was changed to ban all computing devices in casinos.
Raising the stakes
In the early 1990s, however, a new breed of counters emerged. They had a greater level of resources, training and attention to detail than the casinos had ever encountered. Semyon Dukach, Katie Lilienkamp and Andy Bloch were all studying at MIT when they heard of card counting as a way to make extra money. MIT had a history of card counting. Indeed, Ed Thorp himself had developed the original system whilst at MIT, using one of the most powerful computers in the world at that time.
MIT counters played in teams, usually of three or more. Each individual was given a specific role. Some would simply watch tables, and wait for favourable situations to appear (the ‘spotters’). They would call in the expert strategist (the ‘controller’) who would fine-tune exactly when was the optimum moment to play, and how much to bet according to the cards being played. The controller would secretly signal to a ‘big player’ who would then join a table and place a massive bet at exactly the right moment.
The key was that by only betting when the odds were well in the big player’s favour, the big player could maximise potential profit, and also avoid being spotted as a counter. By watching a number of tables at any time, the team could select only those with the greatest promise of a good return. The big player simply looked like a rich, arrogant young gambler who got lucky on a single bet.
The MIT players went to great lengths to conceal both their own identities and their team play. They would work relentlessly to exploit any edge they could find - inexperienced dealers, poor shuffling or lax security. They also recorded exactly how much profit they managed to make from each situation, and honed their skills to be incredibly close to optimum play.
The trio played blackjack all over the world on and off throughout most of the 1990s, making money wherever they played. Their exploits only came to an end when Griffin Investigations, a private agency hired by casinos, identified the members of the MIT teams after months of surveillance. From that point on a team player even entering a casino would be swiftly ejected.
Card counting still occurs wherever blackjack is played, though as casino technology advances it becomes harder and harder to make anything but a small profit. Facial recognition technology, computerised blackjack tables and rule changes are slowly eating away at the small advantage possible through counting. But the lure of easy money makes it unlikely the casinos have seen the last of the counters. For 40 years they have found ways to make profit, and their ingenuity is bound to succeed again.
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