24 Hours In Vegas or Debt in Venice?

Mail On Sunday


I flew into Vegas late on Thursday night, checked into the Venetian Hotel, ditched my luggage, and headed back downstairs to the blackjack tables. I stood peering over a player’s shoulder, firmly established the house rules in my mind, and then returned to my room without betting a cent. My brief trip to the tables was merely a scouting a trip, basic homework before a night of swotting, all of which was preparation prior to a 24 hour blackjack blitz.

Ever since I went to Reno in 1989, I have been a compulsive player of blackjack (otherwise known as pontoon or 21). Although blackjack offers the best odds of any casino game, even the perfect blackjack player is at a disadvantage against the house, and is destined to lose in the long run. However, on this trip I was determined to acquire a new blackjack skill, one that would give me an edge and which would allow me to potentially beat the casino.

There are four types of blackjack player. The ‘rookie’ has no clue what to do, is probably in Vegas to attend a conference, and inevitably loses. On average he will forfeit up to 10% of his stake by the time he leaves. The second type of player, the ‘amateur’, is more clued up, but still makes errors that mean he will lose about 3% of his stake. This is roughly same loss as that suffered by the roulette player, but there is a crucial difference. Whereas roulette is a game of complete chance and the player is locked into losing 3%, the blackjack player can to some extent influence the game and improve his odds. By making the right decisions, namely hitting and standing at the right times, the third type of player, the ‘expert’, can almost break even. The fourth type of player is the ‘card-counter’, who memorises the cards that have already been dealt to make predictions about future cards. By drawing upon this extra bit of information, the accomplished card-counter can consistently beat the casino. Card-counters present such a danger to the casinos that they risk being arrested for trespassing if the pit bosses spot what they are up to. My challenge was to master card-counting in one night, then employ it for 24 hours without getting arrested.


On the way back to my room I picked up a copy of “Casino Player” and skimmed it as I took the elevator up to the 34th floor. Arnold Snyder, otherwise known as the Bishop of the First Church of Blackjack and a world authority on the subject, had written a rather ominous article entitled “New Jersey’s New Anti-Counter Regulations”. Fortunately, I was in Nevada and I sensed that I would be safe as long as I kept a low profile and did not bet too much. The only other bit of the magazine that caught my eye was in the “Fun With Numbers” section; apparently, 119 is the number of dollars paid by George W. Bush to reserve the website bushsucks.com, in order to prevent any anti-Bush surfers from using it to embarrass him when as he ran for president.

Once in my room, I unpacked by blackjack books and piled them high on the desk. More has been written about blackjack than any other casino game; “Blackbelt in Blackjack”, “Blackjack Attack”, “Blackjack for Blood”, “Million Dollar Blackjack”, “Blackjack for the Clueless” and “A Woman’s Guide to Blackjack”. The last title focuses on how to use ‘feminine wiles’ to take advantage of casino culture and gain an edge in blackjack.

My first task was to identify the best card-counting strategy for the Venetian’s house-rules. The rules of blackjack change from country to country, from city to city, and even neighbouring tables can operate different regulations. For example, the player’s option to surrender (to admit defeat and thereby cut your losses) is not allowed in Britain, but is permitted at some Vegas tables. I soon established my strategy for the Venetian Casino’s version of blackjack, I memorised it, and then rehearsed it over and over again by dealing deck after deck. Eventually, at 4am, I decided that it was time to get some sleep.


Blackjack is played with groups of up to seven players competing against a single house dealer. Some players take the game far too seriously and some dealers at the end of a shift can get cranky, so I scoured the casino, looking for a table with a relaxed group of players and a friendly dealer. I also needed a table with cheap minimum bet. In order to test out my newly acquired card-counting skills, I needed to play as many hands as possible, but to minimise risk I wanted to bet $5, rather than $25, per hand.

I ended up with Henry, a rather avuncular dealer. Sat next to me on the player’s side of the table was Danny, the Minnesota Muffin King. Danny had made his fortune, sold his chain of muffin shops and was now investing his money in Vegas and on the futures market. I tried to partake in the table banter, but card-counting requires intense concentration, especially when you’re a beginner, and a result I was perceived to be the stereotypical silent, restrained Brit.

Blackjack played by a card-counter is the only casino game that guarantees long-term profit for the player, but on the other hand poorly played blackjack is the casino’s biggest generator of income. Most players, including Danny, follow their intuition and donate dozens of unnecessary chips to the dealer. When it comes to probability, human intuition is wholly unreliable and rates poorly compared to mathematical logic.

For example, if a player has blackjack (see box) and the dealer is showing an ace, there are two possibilities. Either the dealer also gets blackjack and no money changes hands, or the dealer does not get blackjack and the player wins $15 on a $10 stake. However, before seeing the dealer’s second card, the player can opt out and accept a $10 pay-off. The vast majority of players take this so-called ‘insurance’ option, because it is a guaranteed profit in the face of a dealer who only needs a picture card or a ten to draw. The desire for insurance is motivated by a gut instinct, but in fact insurance is a foolish option, one that should never be taken.

A bright 12-year-old could do the maths to show that a player should always reject insurance.The failure to make good blackjack decisions is caused by the same deceitful intuition that results in the birthday paradox, which begins with following question: how many people do you need to have at least a 50/50 chance that there will be at least two of them with the same birthday? With 366 possible birthdays, most people will guess that a group should include at least hundred people. However, the true answer to this probability problem, deduced using elementary mathematics, is a group of just 23 people. In other words, it is more than likely that there will be a shared birthday on a soccer pitch among the 22 players and referee.

I had no problem having to sit through Danny’s instinctive and flawed approach to blackjack, but after a while other things began to irritate me. First, he would use a mixture of pseudo-mathematics and superstition to support his strategy. Worse still, Henry the avuncular dealer deliberately gave duff information that only served consolidate Danny’s mistaken blackjack beliefs. After just two hours I decided it was time to move on. I had practised my card-counting and made a small profit, so I had nothing to complain about.

Profit = $27.50, Balance = +$27.50


I decided to take a short break before returning to the tables. I did not have time to visit any of Las Vegas’s tourist attractions, such as the Liberace Museum, the Casino Hall of Legends (also known as the Smithsonian of Showgirls) or Dr Naughty (“the world’s foremost X-rated comedy hypnotist”), so instead I spent half an hour exploring the delights of my casino, the Venetian Hotel.

Not only does the extravagant Venetian Hotel boast full size replicas of the 315-foot Campanile Tower, the Doge’s Palace and St Mark’s Square, but also the ceiling of the hotel lobby is adorned with recreations of the works of Bambini, Tiepolo and Veronese. The hotel’s most famous attraction is its canals, complete with real Venetian gondoliers. When I took the obligatory gondola trip, I was surprised that there was one bridge missing from the copycat canals, namely the Bridge of Sighs, so called because prisoners would pass over it and glimpse their last view of the city before being incarcerated. My gondolier explained that the casino designer had deliberated ignored the bridge, because it is not considered appropriate to have something so depressing in such a glitzy city.

** ** ** **

I returned to the blackjack tables and continued with my card-counting strategy. The father of card-counting was Edward O.Thorpe, a mathematician at the University of California at Los Angeles. He realised that the odds of dealing blackjack from a fresh deck are long, roughly 20 to 1, but if the deck contains an increased proportion of aces then the odds are significantly shorter. This growth in the likelihood of blackjacks helps the player rather than the dealer, because of the following reason. Imagine that the player is betting $10 per hand; if the dealer gets blackjack and the player does not, then the player simply loses $10; in contrast, if the player gets blackjack and the dealer does not, then the player wins $15. More aces mean more blackjacks, and blackjacks are more beneficial for the player.

Clearly it is illegal to artificially load a deck with aces, but Thorpe imagined a game in which a round of hands was dealt from a deck, which did not include any tens. The remainder of the deck is therefore naturally loaded with aces, and therefore the next round of dealing is likely to favour the player against the dealer. In short, Thorpe reckoned that it was possible for a player to sit at a table and bet $10 on the first deal of cards. If no aces appeared, then he would increase his bet to $20, because the next deal was likely to be biased in his favour. Alternatively, if the first deal included lots of aces, then the player would reduce his bet to $5 in the next deal. Thorpe believed that it was possible for the player to gain an advantage by betting heavily when the deck was loaded in his favour and betting lightly when it was against him.

Thorpe began his blackjack research in the early 1960s. He used what computer power he could get his hands on to do the complex calculations necessary to define an optimum card-counting strategy. It turns out that it is not the just the aces that work in favour of the player. He first published his results in the “Proceedings of the National Academy of Sciences”, and his research was declared to be “the greatest achievement in game theory since the sixteenth century”. In 1962 he published a more accessible account of his work in the notorious best-seller “Beat the Dealer”, his instructions for gaining an edge against the dealer. Most people believe that card counting relies on memorising all the cards that have been dealt, but Thorpe’s method focuses on tracking just a few cards, namely the tens and aces (which help the player) and the small cards (which hinder the player). It needs to be emphasised that Thorpe’s card-counting strategy gives the player the tiniest of edges, in fact less than 1%. This means that over the long term, after betting $10,000 dollars, the player can expect to earn less than $100. And in the short term, his bank balance will fluctuate by several hundred dollars in both directions. Thorpe declared that it was possible to consistently beat the casino, but players had to be prepared for a long, hard slog.

When Thorpe’s ideas caught on among serious gamblers, casinos fought back by changing the rules of blackjack to wipe out the card-counter’s meagre advantage. Blackjack players, both amateurs and card-counters, boycotted the game, forcing casinos to revert to the traditional rules. Instead, they barred specific notorious card-counters. By 1979, casinos posted signs that read: “Professional card-counters are prohibited from playing at our tables.” If a suspected card-counter entered the casino he would be given a warning, and if he returned he would be arrested for trespassing. This seems unjust. The card-counter is barred simply because he uses his skill, intellect and memory to compete against the casino. He is being penalised for being smart.

Equally frustrating for the card-counter is the fact that casinos are tending towards dealing from larger shoes. A shoe is a compilation of several decks, as many as eight, and the greater the number of decks, the tougher it is to card-count and to gain an advantage. After six or seven shoes, I realised that the 6-deck game at the Venetian was making my brain ache. The casino also had a 1-deck game, which is far better from a card-counter’s point of view, but the minimum bet was $25, fives times higher than the 6-deck minimum. I decided it was time to move next door to one of the seedier casinos, which had a 1-deck game with a $5 minimum. It seems to have been a sensible move, because I had a winning streak that continued right through the afternoon. At the end of the session, I treated myself to a deluxe sub sandwich at the Subway diner.

Profit = $133.50, Balance = +$161.00


When I returned to the table I had a bout of paranoia and decided that I needed to be a little more careful about my behaviour. The tell-tale sign of a card-counter is somebody who markedly raises or lowers his bet prior to a shuffle, because this is the moment that he has the best sense of what is left in the deck. I had been warned that pit bosses, who oversee the dealers, are trained to identify card-counters. Furthermore, some casinos also use spy cameras and computers to weed out Thorpe’s disciples. As the cards are dealt from the shoe, an electronic eye notes each card, works out which player receives it, and then identifies those players following card-counting strategies.

The casinos are always keen to eject card-counters, but I could reduce the risk of being spotting by adopting a more subtle betting strategy. If the deck became rich in tens and aces, then I would gradually build up my stake, rather than increasing it in one obvious leap. Although this form stealth card-counting is safer, it is also less profitable, and it is petty and infuriating that card-counters have to resort to this. The casinos are trying to ban a perfectly legitimate strategy. It is not as though card-counting is cheating. It is not in the same league as the gambler who built a plastic ice cube containing a tiny prism, which he placed in his drink at the corner of the table, so that he could spy on the dealer’s supposedly hidden card.

If card-counters are ever driven out of the game, then mathematicians and players will have to resort to other means to gain an edge. Professors Dave Bayer and Persi Diaconis, now at Columbia and Cornell Universities respectively, have already demonstrated that there is another chink in the casinos armour. If a player memorises the cards dealt in one shoe, it is still possible to predict with some success the order of some of the cards in the next shoe, despite the shuffling that goes on in between. Their research on shuffling depends on a deep understanding of mathematical calculations done in 52-dimensional hyperspace.

In theory, casinos could combat this strategy by shuffling for longer. In practice, however, time spent shuffling is time when the casino cannot win money from the average punter. Hence, an more shuffling would beat shuffle trackers, but it would reduce the overall profits of the casino.

Ultimately, blackjack players might resort to technology in order to beat the system, just like the team who won at roulette by cramming microprocessors in their shoes. Doyne Farmer and his colleagues were ex-physicists and members of the “Chaos Cabal”. The science of chaos is all about making predictions in apparently unpredictable (or chaotic) situations. Farmer would watch the spinning roulette wheel, and when the ball crossed the zero on its first two revolutions he would tap a button inside his shoe with his big toe. Using this basic information to calculate the ball’s speed, his magic shoe could predict roughly where it would fall into. Farmer’s shoe would beam a radio signal to a co-conspirator who was also wearing special shoes, causing pins inside to prick his foot and indicate where to place the bets. The magic shoe brigade made significant profits before quitting Vegas in favour of setting up The Prediction Company, which makes even more money by selling predictions to the biggest gamblers of all, namely stock-market traders.

I could have done with the help of a pair of magic shoes during the evening session, because my fortunes were declining. I took a break, indulged in a couple of large coffees and a sad cabaret performance, and hope that I could reverse the trend during the late night session.

Loss = $15, Balance = +$146


I returned to the blackjack tables at 11 pm, when the tables were crammed, and continued through till 4am, by which time there were just one or two sad cases per dealer. It was a highly profitable session, spoilt only by one obnoxious character. He was a bad player and a bad loser, haemorrhaging $100 chips and, worst of all as far I was concerned, cursing continuously. It eventually came to the point when either he or I had to leave the table, and fortunately the pit boss sided with me and escorted him out of the casino. It seemed ironic that the casino was, unknowingly, protecting a card-counter.

I chatted to the dealer, Margot, who also played blackjack from time to time. She explained that she occasionally bumped into similarly odious characters. In fact, she sometimes sought them out and deliberately played badly. Mr Nasty is then forced to witness occasions when he might lose $1000 because Margot hits a card when she should have stayed. She felt that it was worth losing a $5 chip in order to see the look of frustration on Mr Nasty’s face.

Profit = $164, Balance = +$310


My 24 hour challenge was to end at 10 am. I tried to wake up early in order to cram in one last session, but it was a short and unprofitable period of play. In the end, I made a total profit of $285, which might sound impressive, but I would discourage readers from trying to replicate by efforts. First, it took me 18 hours of concentrated play to win this much, which works out to only $16 or £10 per hour. When you take into consideration dealer and waitress tips, along with the cost of the room, then the profit is halved.

Furthermore, I had to bet a total of $5000, which is a major investment. Worse still, my profit of $285 was largely down to luck, rather than card-counting. In the short-term, over say 24 hours, the fluctuation due to good or bad luck can be as much as $500 in either direction, and the actual profit due to card-counting is less than $50 dollars. In other words, the only way to iron out the effect of the luck and guarantee a win is to bet more and play for longer, which means a bigger bankroll and more effort.

I am relieved that I made a profit, but I realise that the most sensible way to make a profit on a trip to Vegas is to persuade a newspaper to pay all your expenses and a fee up front. There is the myth that blackjack card-counters can beat the system, but the reality is that the profit is small, and most card-counters lack the memory, intellect, concentration and stamina to make the system work. In fact, casinos like to encourage the myth that blackjack can be beaten, because it encourages would-be hustlers with their flawed card-counting to visit Vegas and squander large amounts of cash.

Perhaps it is worth bearing in mind what happened to the card-counting guru Edward Thorpe. His research into the mathematics of blackjack earned him a fortune, but not because he pursued his system to any great extent. He soon stopped playing for money when the casinos drugged his drinks on two separate occasions and barred him. He was quick to realise the best way to make money would be to sell his blackjack system to would-be card-counters.

Profit = $25, Balance = + $285