Category: Questions

Every casino game, without exception, has an integral mathematical edge over the player. This edge, commonly known as the ‘house edge’, ensures that the casino will always win in the long-term and maintain an operating profit. That said, the house edge varies, quite widely, from one casino game to another and, fairly obviously, the games with the lowest house edge give the player the best chance of winning.

It is not without good reason that casinos, in Las Vegas and elsewhere, offer six-deck blackjack – that is, blackjack played with cards dealt from a multiple-deck shoe, containing 310 cards at the start of the shoe – as standard; six decks of cards increase the house edge by 0.42% against the basic blackjack strategy player when compared with a single deck of cards. Of course, the house edge for six-deck, or even eight-deck, blackjack still compares very favourably with that for other, less demanding games, such as keno or slots. However, if you can find a single-deck blackjack game with a suitable minimum bet, you can take advantage of a house edge of just 0.58%, or possibly lower, with basic playing strategy.

Similar comments apply to craps, insofar as the many rules of the game are off-putting to newcomers, with the added complication of a wide house edge spread. Some so-called ‘sucker’ bets, such as ‘Proposition 2 or 12’, ‘Proposition 3 or 11’ and ‘Any 7’ offer a house edge well into double-figures, percentage-wise, and should be avoided. At the other end of the scale, though, craps does offer some of the lowest house edge bets available, including pass/come at 1.41% and don’t pass/don’t come at 1.36%.

Baccarat is a gambling game at cards, played by a banker, or dealer, and two patrons who lay stakes against the banker. Regardless of the number of patrons, just two hands – designated the ‘player’ hand and ‘banker’ hand – of two or three cards each are dealt and the object of the game is to bet on the hand that adds up closer to nine. The three possible outcomes are a player win, a banker win and a tie, and patrons can bet on any of these eventualities, but not on a player win and a banker win simultaneously. In the event of a tie, stakes laid on player win and banker win are returned.

For the purposes of calculating the value of each hand, tens and face, or picture, cards have a value of zero, aces have a value of one and cards between two and nine have their face values. Of course, this allows a hand to add up to more than nine but, in that event, the value of the hand is the second digit.

The player hand is concluded before the banker hand. If the player hand has a total between zero and five, unless the bank hand has a total of eight or nine, known as a ‘natural’, the player hand draws a third card. The player hand stands on total values of six and seven and, for obvious reasons, on eight and nine. A natural eight or nine for either hand wins outright, with no further cards drawn, unless the natural eight or nine is tied, or beaten, by the opposing hand. By contrast, while the banker hand always draws another card on values between zero and two and always stands on values between seven and nine, the response to values between three and six depends on the value of the third card in the player hand.

‘The Man Who Broke the Bank at Monte Carlo’ was a popular British music hall song in the late nineteenth century but, by that stage, half a dozen players had, quite literally, set the bells ringing in the Casino de Monte-Carlo by winning more than the 100,000 franc cash reserve – otherwise known as the ‘bank’ – set aside to cover liabilities on each roulette.

The first man to famously do so was Joseph Jagger, a mechanically-minded, but down-on-his-luck, piece worker from Yorkshire in the North of England. In 1873, working in cahoots with unscrupulous casino staff, Jagger recorded the results of every spin of each roulette wheel at the Casino de Monte-Carlo for a period of weeks. Subsequently, having discovered that one of the wheels displayed a distinct bias towards some numbers rather than others, he began to bet on the frequently-occurring numbers. Over a period of several days, he won 2,000,000 francs, or the equivalent of £7.5 million in modern terms.

Less than two decades later, in 1891, Charles Wells, a known petty criminal born in Hertfordshire in the East of England, but educated at Clermont-Ferrand University in central France, broke the bank at Monte Carlo not once, but several times. Surprisingly, perhaps, given his dubious background, each time he did so by pure good fortune, without resorting to any form of skullduggery, subterfuge, or out-and-out cheating. One the first occasion, when he won 1,000,000 francs, he reportedly won twenty-three of thirty consecutive spins of the roulette wheel and, on his return to Monte Carlo later the same year, he managed to win another 1,000,000 francs from a series of random bets.

Texas hold’em poker is the most popular ‘community card’ variant of the game, featuring two cards, known as ‘hole cards’, dealt to each player and five more on the board. In other words, each player has the choice of seven cards from which to build the best five-card hand. Of course, a four-of-a-kind hand must include four cards of the same rank – from one of the thirteen ranks available – along with a single card, or ‘singleton’, of some other rank.

Overall, the probability of four-of-a-kind in seven cards is 0.168%, which represents odds of 594/1. In other words, a Texas hold’em player can expect to make four-of-a-kind, or ‘quads’, once every six hundred hands or so, on average. However, while four-of-a-kind is not an unbeatable hand – it ranks behind a straight flush of any description and, in the case of kings or lower, behind four-of-a-kind of higher rank – it is worth waiting for. Indeed, the probability of losing a hand with four-of-a-kind is 0.00001%, or 100,000/1 against.

If a player has paired hole cards, the probability of which is 5.88% or, in terms of odds, 16/1, the probability of ‘flopping’ four-of-a-kind is 0.245% or, in terms of odds, 400/1, although the probability of hitting four-of-a-kind by the fifth, and final, community card, known as the ‘river card’ increases to 2%, representing odds of 50/1. By contrast, a player without paired hole cards has just a 0.001%, or 1,000/1, chance of flopping four-of-a-kind.