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Arguably, the most successful casino gambler ever is Anargyros Nicholas Karabourniotis, otherwise known as Archie Karas, or simply ‘The Greek’, who, in December, 1992, embarked on an unprecedented winning streak, known in gambling circles as ‘The Run’.

Reputedly arriving in Las Vegas with just $50, Karas borrowed $10,000 from a fellow poker player, which he quickly turned into $30,000 playing a form of stud poker known as ‘Razz’. Turning his attention to nine-ball pool, Karas played an unidentified individual for progressively higher stakes, up to $40,000 a game, eventually winning $1.2 million. Karas subsequently relieved the same individual of a further $3 million playing poker at Binion’s Horseshoe and, in the coming months, built his bankroll to $7 million.

Karas continued to play poker, for eye-wateringly high stakes, against some of the best players in the world, including the likes of Stuart ‘Stu’ Ungar and David ‘Chip’ Reese. At the end of a six-month period, Karas had won over $17 million. At that point, Karas began shooting craps at Binion’s Horseshoe, for $100,000 a roll, and kept on winning, eventually amassing over $40 million.

After two-and-a-half years, Karas’ luck ran out; in 1995, he lost approximately $42 million, predominantly on craps and baccarat. Between 1988 and 2013, Karas was arrested five times for cheating at blackjack in Nevada and, as a result of ‘numerous transgressions’, was subsequently included on the Gaming Control Board (GCB) Excluded Person List maintained by the Nevada Gaming Commission.

Every casino game, including blackjack, has an integral mathematical edge, usually referred to as the ‘house edge’, over a player in the long term. In blackjack, the house edge for the standard, six-deck version is 0.64% but, by applying basic blackjack strategy, a player can reduce the house edge to the point where it is almost negligible. Regardless of some minor – albeit often strategically important – rule variations, blackjack is essentially a mathematical game, with a fixed set of rules, a fixed number of cards in the deck(s) and, hence, only a finite number of possible card combinations. Nevertheless, every playing decision has a direct influence on the outcome of a hand.

Basic blackjack strategy is a set of rules, determined mathematically, which allow a player to make correct playing decisions, thereby maximising winnings and minimising losses. Of course, the only information available to a blackjack player is the cards in his/her hand and the card that the dealer is showing, known as the ‘upcard’. However, by reference to a blackjack strategy chart, or matrix, which shows all possible card combinations, a player can take the action that gives him/her the best chance, mathematically, of winning any hand. To allow for rule variations, such as the option to ‘double down’ – that is, to double your original bet in exchange for a single card – after splitting two cards of the same value, some of the actions in basic blackjack strategy are dependent upon house rules.

The so-called gambler’s fallacy is a commonly-held, but mistaken, belief that in a game of chance, such as roulette, sequences of one binary outcome, such as the appearance of a red number, will be balanced by the opposite outcome, such as the appearance of a black number. Worse still, the longer the sequence, the stronger the belief becomes.

Of course, in reality, each spin of a roulette wheel is an independent, random event, which cannot be influenced, in any way, by past events. Indeed, the longest recorded sequence of one colour is 32, but even shorter sequences of one colour or the other can lead to a form of distorted thinking – technically known as ‘negative recency’ – that makes gamblers believe they have a higher-than-average chance of winning.

Notwithstanding the inherent house edge which, even in the European, single-zero version of roulette, stands at 2.7%, the probability of a red or a black number appearing on a single spin of the wheel is always approximately 50:50, regardless of previous results. The appearance of the green zero renders all ‘outside’ bets, including those on red or black, losers, so the actual probability of winning on red or black is 47.37%; the point is that that probability never changes, regardless of how counter-intuitive that may seem to the gambler. Of course, the gambler’s fallacy applies not just to roulette, but also to other games of chance, including blackjack, poker and slots, which operate on the same hard-and-fast laws of mathematical probability.

Exactly what happens if you’re caught cheating in a casino depends, to some extent, on the geographic location of the casino – and, hence, the local, regional or national laws in operation – and the seriousness of the cheating. However, in any event, if you’re suspected of cheating, you’re likely to be detained and questioned by casino staff. In Las Vegas, for example, suspected cheats can be detained, for a reasonable length of time, under reasonable conditions, if there is probable

Similarly, you can expect to be relieved, sooner or later, of any winnings obtained illegally, or improperly. In Las Vegas, it is legal for a casino to confiscate any such winnings and you could also be charged with a felony, the penalty for which is a fine of up to $10,000 and/or up to six years’ imprisonment. In Britain, the Gambling Act made cheating in casinos a criminal offence and, depending on the circumstances of the cheating, you could also be charged under the Fraud Act and/or the Identity Fraud Act. These pieces of legislation make securing convictions for cheating in casinos easier than was once the case and, if convicted, you could be looking at a lengthy custodial sentence, as well as having any winnings confiscated under the Proceeds of Crime Act.

If you’re caught cheating, a casino will probably record your details in a ‘Black Book’, officially known as the ‘List of Excluded Persons’, which, depending on the location, is shared with the local gaming commission and/or other licensed gaming establishments in the area. Once your name is on the list, you’re effectively blacklisted and banned from entering the casino(s) involved for life.