Betting strategies or betting systems are approaches to gambling intended to increase the odds of winning.

Independent Events

The following betting strategies have been recorded as being applied to games which operate on independent events. For such games, the odds of a particular outcome are identical for every bet played. No such strategy can beat the house edge (if any) in the long run, and all of them trade off many small wins for a big loss or vice versa.

• Martingale – doubling bet after each loss until a win is achieved (or fails when the amount of the bet becomes excessive).
• Kelly criterion;

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American mathematician Dr. Edward O. Thorp is considered the father of card counting. His 1962 book Beat the Dealer (ISBN 0394703103) outlined various betting and playing strategies for optimal blackjack play. Although mathematically sound, some of the techniques described no longer apply as casinos took counter-measures (such as no longer dealing to the very last card). Also, the counting system described (10-count) is harder to use and less profitable than the point-count systems that have been developed since. A history of how counting developed can be seen in David Layton’s documentary film, “The Hot Shoe.”

Even before the publication of Beat the Dealer, however, a small number of professional card counters were beating blackjack in Las Vegas and casinos elsewhere. One of these early card counters was Jess Marcum, who is described in documents and interviews with professional gamblers of the time as having developed the first full-fledged point count system. Another documented pre-Thorp card counter was a professional gambler named Joe Bernstein, who is described in the 1961 book I Want To Quit Winners, by Reno casino owner Harold Smith, as an ace counter feared throughout the casinos of Nevada. And in the 1957 book, Playing Blackjack to Win, Roger Baldwin, Wilbert Cantey, Herbert Maisel, and James McDermott (known among card counters as “The Four Horsemen”) published the first accurate blackjack basic strategy and a rudimentary card counting system, devised solely with the aid of crude mechanical calculators — what used to be called “adding machines”.

From the early days of card-counting, some players have been hugely successful, including Al Francesco, the inventor of blackjack team play and the man who taught Ken Uston how to count cards, and Tommy Hyland, manager of the longest-running blackjack team in history. Ken Uston, though perhaps the most famous card counter through his 60 Minutes television appearance and his books, tended to overstate his winnings, as documented by players who worked with him, including Al Francesco and team member Darryl Purpose.

In the 1970s and 1980s, as computing power grew, more advanced (and more difficult) card counting systems came into favor. Many card counters agree, however, that a simpler and less advantageous system that can be played flawlessly for hours earns an overall higher return than a more complex system prone to user error.

In the 1970s Ken Uston was the first to write about a tactic of card counting he called the Big Player Team. The book was based on his experiences working as a “big player” (BP) on Al Francesco’s teams. In big player blackjack teams a number of card counters, called “spotters”, are dispatched to tables around a casino, where their responsibility is to keep track of the count and signal to the big player when the count indicates a player advantage. The big player then joins the game at that table, placing maximum bets at a player advantage. When the spotter indicates that the count has dropped, he again signals the BP to leave the table. By jumping from table to table as called in by spotters, the BP avoids all play at a disadvantage. In addition, since the BP’s play appears random and irrational, he avoids detection by the casinos.

With this style of play a number of blackjack teams have cleared millions of dollars through the years. Well-known blackjack teams with documented earnings in the millions include those run by Al Francesco, Ken Uston, Tommy Hyland, various groups from the Massachusetts Institute of Technology (MIT) and, most recently, a team called “The Greeks”. Ken Uston wrote entertainingly about blackjack team play in Million Dollar Blackjack (ISBN 0897460685), although many of the experiences he represents as his own in his books actually happened to other players, especially Bill Erb, a BP Uston worked with on Al Francesco’s team. Ben Mezrich also covers team play in his recent book Bringing Down The House (ISBN 0743249992), which describes how MIT students used it with great success. See also the Canadian movie The Last Casino.

The publication of Ken Uston’s books both stimulated the growth of blackjack teams (Hyland’s team and the first MIT team were formed in Atlantic City shortly after the publication of Million Dollar Blackjack) and increased casino awareness of the methods of blackjack teams, making it more difficult for such teams to operate. Hyland and Francesco soon switched to a form of shuffle tracking called “ace sequencing”. This made it more difficult for casinos to detect when team members were playing with an advantage. In 1994, members of the Hyland team were arrested for ace sequencing and blackjack team play at Casino Windsor in Windsor, Ontario, Canada. It was documented in court that Nevada casinos with ownership stakes in the Windsor casino were instrumental in the decision to prosecute team members on cheating charges. However, the judge ruled that the players’ conduct was not cheating, but merely the use of intelligent strategy.

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Originally, martingale referred to a class of betting strategies popular in 18th century France. The simplest of these strategies was designed for a game in which the gambler wins his stake if a coin comes up heads and loses it if the coin comes up tails. The strategy had the gambler double his bet after every loss, so that the first win would recover all previous losses plus win a profit equal to the original stake. Since a gambler with infinite wealth is guaranteed to eventually flip heads, the martingale betting strategy was seen as a sure thing by those who practiced it. Unfortunately, none of these practitioners in fact possessed infinite wealth, and the exponential growth of the bets would quickly bankrupt those foolish enough to use the martingale after even a moderately long run of bad luck.

Analysis

Suppose that someone applies the martingale betting system at an American roulette table, with 0 and 00 values; a bet on either red or black will win 18 times out of each 38. If the player’s initial bankroll is $160 and the betting unit is $10, the player will make a win in approximately 96% of sessions, gaining an average of $4.30 from each winning session. In the remaining 4% of sessions, the player will “bust”, exhausting his bankroll, for a loss of $160. It follows then that the average session losses of a gambler employing this strategy are $2.27. Given a larger bankroll, the odds of making a win before running out of cash increase; however, the average winnings grow more slowly than the average losses, so the game remains a losing proposition.

Modern casinos generally have table minimums and maximums to prevent players from doubling their bets more than five or six times, rendering the martingale system obsolete.

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Card counting is a card game strategy used to determine when a player has a probability advantage. The term is used almost exclusively to refer to the tracking of the ratio of high cards to low cards in blackjack, although theoretically card counting can be used in some other card games.

How card counting works in blackjack

Card counting is based on the fact that high cards, and especially aces, are good for the player while low cards are good for the dealer. High cards are good for the player because they increase the chance of a player getting a “blackjack”, which usually pays 3 to 2. High cards also increase the player’s chance of success on his pair splits and double downs. Low cards are good for the dealer because they decrease the chance that the dealer will bust.

Card counters raise their bets when the ratio of high cards to low cards in the deck is skewed in their favor. They also make strategy adjustments based on the ratio of high cards to low cards. These two adjustments to their betting and playing strategy can give players a small mathematical advantage over the house.

Contrary to the popular myth, card counters do not need savant qualities in order to count cards, because they are not tracking and memorizing specific cards. Instead, card counters assign a heuristic point score to each card they see and then track only the total score. (This score is called the “count”.)

Different card counting systems assign different point values to various cards, but one of the most common systems, the Hi-Lo Count, is illustrative. In this system, the cards numbered 2 through 6 are counted as +1 and all tens (which include 10s, jacks, queens and kings) and aces are counted as -1. The cards 7, 8, and 9 are given a count of 0. The Hi-Lo system exemplifies a “level one” counting system; other counting systems also assign +2 and -2 counts to certain cards and are called “level two” systems. Many card counting experts agree that the additional accuracy derived from a “level two” system is offset by the increased difficulty of keeping count and the greater likelihood of making a mistake.

Another commonly used card counting system is the “K-O”, an unbalanced card counting system derived from Arnold Snyder’s unbalanced Red 7 count, published in 1981. The first blackjack researcher to publish an unbalanced card counting system was Jacques Noir, in his 1968 book Casino Holiday. Unbalanced card counting systems eliminate the need to estimate remaining decks to be dealt, a common source of player error in card counting.

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Albert Einstein is reputed to have stated, “You cannot beat a roulette table unless you steal money from it.”

And yet, the numerous even money bets in roulette have inspired many players over the years to attempt to beat the game by using one or more variations of a Martingale betting strategy, wherein the gamer doubles the bet after every loss, so that the first win would recover all previous losses, plus win a profit equal to the original bet. As the referenced article on Martingales points out, this betting strategy is fundamentally flawed in practice and the inevitable long-term consequence is a large financial loss. There is no way such a betting strategy can work over the long term. Another strategy is the Fibonacci system, where bets are calculated according to the Fibonacci sequence. Regardless of the specific progression, no such strategy can ever overcome the casino’s advantage; players trying them will inevitably lose sooner or later.

While not a strategy to win money, New York Times editor Andres Martinez described an enjoyable roulette betting method in his book on Las Vegas entitled “24/7″. He called it the “dopey experiment”. The idea is to divide your roulette session bankroll into 35 units. This unit is bet on a particular number for 35 consecutive spins. Thus, if the number hits in that time, you’ve won back your original bankroll and can play subsequent spins with house money. If your number never hits – well, it can take a great deal of time to spin the wheel 35 times; think of the fun you’ll have in that time! In practice, this dopey experiment often results in funny looks from the dealer at first; soon, however, every gambler at the table will be putting money on your number. This turns roulette into a group activity that can rival craps for cheers when the number hits. However, there is only a (1 − (37 / 38)³⁵) * 100% = 60.68% probability of winning within 35 spins (assuming a double zero wheel with 38 pockets).

There is a common misconception that the green numbers are “house numbers” and that by betting on them one “gains the house edge.” In fact, it is true that the house’s advantage comes from the existence of the green numbers (a game without them would be statistically fair) however they are no more or less likely to come up than any other number.

Various attempts have been made by engineers to overcome the house edge through predicting the mechanical performance of the wheel, most notably by Joseph Jagger, the man who broke the bank at Monte Carlo in 1873. These schemes work by determining that the ball is more likely to fall at certain numbers. Claude Shannon, a mathematician and computer scientist best known for his contributions to information theory, built arguably the first wearable computer to do so in 1961 [1].

To try to prevent exploits like this, the casinos monitor the performance of their wheels, and rebalance and realign them regularly to try to keep the result of the spins as random as possible.

More recently Thomas Bass, in his book The Newtonian Casino 1991, has claimed to be able to predict wheel performance in real time. He is also the author of The Eudaemonic Pie, which describes the exploits of a group of computer hackers, who called themselves the Eudaemons, who in the late 1970s used computers in their shoes to win at roulette by predicting where the ball would fall.

In the early 1990′s, Gonzalo Garcia-Pelayo, realizing that most roulette wheels are not “perfect”, used a computer to model the tendencies of the roulette wheels at the Casino de Madrid in Madrid, Spain. Betting the most likely numbers, along with members of his family, he was able to win over one million dollars over a period of several years. A court ruled in his favor when the legality of his strategy was challenged by the casino.

In 2004, it was reported that a group in London had used mobile cameraphones to predict the path of the ball, a cheating technique called sector targeting. [2] In December 2004 court adjudged that they didn’t cheat because their special laser cameraphone and microchip weren’t influencing the ball – they kept all £1.3m. [3]

Betting Only on Red

One conceivable strategy would be to bet on the ball landing in a red space for a certain number of spins, for example, 38.

There are 18 red spaces on a roulette table with 38 total spaces. Dividing 18 by 38 yields a probability of landing on red of 47.37%. This probability can be used in a binomial distribution and made into an approximate standard normal distribution.

Doing so indicates that, if one were to spin the wheel 38 times, there is a 99% probability that the ball would land on red at least 10 times. There is an 83% probability that in 38 spins, the ball will land on red at least 15 times. Out of 38 spins, there’s a 50% chance that 18 will be red.

However, the break-even point is 19 spins, since the bet on red is 2:1, and the probability of 19 red spins in 38 is only 37%. This indicates the difficulty of winning by only betting on red.

The results occur because, as indicated by the 18 divided by 38 equals 47.37% figure, the ball will land on red less than half the time. This percentage applied in the binomial and standard normal distributions creates the vast divide in probability from 18 red spins to 19 red spins out of 38 spins. Basically, it is very unlikely for anyone to spin much more than 18 red spins out of 38 spins.

Betting multiple times

This type of bet is a combination of the red bet and the martingale system. Except this bet also includes the odd. What you do is you start off with a bet of 1 on each the red and the odd (or you can do the black and even). You treat each bet seperately. When one bet loses, you double it. When one bet wins, you set it back to 1. The reason that this technique keeps you in the game so long is that there is a 25% chance of you winning both the red and the odd and theres a 50% chance that you will break even. Of course in order for this method to last, you would need an unlimited source of money.

Famous Bets

• In 2004, Ashley Revell of London sold all of his possessions, clothing included, and brought US$135,300 to the Plaza Hotel in Las Vegas and put it all on “Red” at the roulette table in a double-or-nothing bet. The ball landed on “Red 7″ and Revell walked away with his net-worth doubled to $270,600.

• In the 1942 film Casablanca, Rick’s Café Americain has a trick roulette wheel. The croupier can cause it to land on 22 at will. Rick (Humphrey Bogart) urges a Bulgarian refugee with whose case he becomes sympathetic to put his last three chips on 22 and motions to the croupier to let him win. After the man’s number dramatically comes up, Rick tells him to let it all ride on 22 and lets him win again. Although the details are not mentioned in the film (the croupier only notes that they are “a couple of thousand” down), it appears that Rick has given the man 3675 (3*35*35) francs.

• In the music video for Palace & Main by Kent, guitarist Harri Mänty goes to Las Vegas and bets the entire video budget on black. He wins, and the profits were donated to charity.

• In the third part of the 1998 film Run, Lola, Run, Lola uses all her money to buy a 100-mark chip. (She is actually just short of 100 marks, but gains the sympathy of a casino employee who gives her the chip for what money she has.) She bets her single chip on 20 and wins. She lets her winnings ride on 20 and wins again, making her total winnings 100,000 marks.

This guide is licensed under the GNU Free Documentation License. It uses material from the Wikipedia.