What’s the history of blackjack?

Blackjack is derived from the ancient game of ‘twenty-one’, which is believed to have existed in Spain, as ‘veintiuna’, in the seventeenth century and subsequently spread to France, as ‘vingt-un’, or ‘vingt-et-un’, the surrounding countries, including Britain, and eventually to America from the early eighteenth century onwards. Vingt-un, albeit occasionally pronounced, and written, as ‘Van John’, was played under its French name in Britain and America throughout the nineteenth century.

However, until 1931, when gambling was legalised in Nevada and the first gaming licence was awarded to the Northern Club on Fremont Street, Las Vegas, vingt-un was played in illicit casinos and speakeasies. In fact, blackjack wasn’t called actually ‘blackjack’ until the twentieth century; in the early days of legitimate gambling in Las Vegas, casinos offered a series of promotional bonus payments, one of which was 10/1 against a hand consisting of the ace of spades and the jack of spades or the jack of clubs or, in other words, a ‘black jack’. Of course, that bonus payment for ‘blackjack’ no longer exists – the best modern patrons can hope for is odds of 3/2 and, even then, only in a standard, six-deck game – but the name stuck.

Following the publication of basic blackjack strategy – a mathematically correct set of rules for playing any hand – in the Fifties, blackjack quickly rose to become the most popular casino game in Las Vegas. Subsequently, in the face of multi-deck shoes and apparently minor rule changes, not least cutting the payout on blackjack to 6/5 in all bar single-deck games, the popularity of blackjack has waned slightly. Even so, blackjack remains the second most popular card game on the Las Vegas Strip, after baccarat.

What are the odds against making four-of-a-kind in Texas hold’em poker?

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.

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