Category: Questions

Craps is, of course, a casino game in which players bet on the outcome of a roll, or a series of rolls, of a pair of dice. The name ‘craps’ is believed to be an Anglicisation of the French word ‘crapaud’, meaning ‘toad’ which, in turn, is derived from how a precursor of craps, called ‘hazard’, was played by people crouched on floors or pavements in seventeenth century France. However, the origins of hazard are believed to be much older. The invention of the game is credited to William of Tyre, during the siege of the castle of Hazarth – after which the games was probably named – in the early twelfth century.

Fast forward five hundred years or so and craps was a simplification of hazard created in France in the late sixteenth century. In the early nineteenth century, the game was introduced to New Orleans by French-American nobleman Bernard de Marigny who, as an errant young man, spent time frequenting the gambling houses of London. In the early years of the twentieth century, John H. Winn, a.k.a. ‘the Father of Modern-Day Craps’, remedied an obvious flaw in the game, by allowing ‘pass’ and ‘don’t pass’ options. His innovation revolutionised craps and encouraged its spread throughout French Louisiana and along the Mississippi River. Fast forward again, to the early Thirties, and the legalisation of gambling in Nevada further increased the popularity of craps and it has remained a rollicking, social game on the tables of Las Vegas ever since.

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In Texas hold’em poker, ‘floating the flop’ is an intermediate, or advanced, bluffing technique used to defend against the continuation bet, or ‘c-bet’, which can, itself, be a bluffing technique. Aggressive players frequently follow a pre-flop raise with a bet on the flop – that is, a continuation bet – regardless of whether or not they hit the flop, but floating the flop allows player to turn a continuation bet on a weak, non-made hand against his opponent.

Floating the float is best done when in position – that is, when you are the last player to act in a hand – in a heads-up pot, against a tight-aggressive opponent, who frequently raises pre-flop and continuation bets. The idea is that you lead your opponent to believe that you have a legitimate hand, by calling pre-flop and calling his or her continuation bet on the flop, with a view to forcing him or her to check on the turn card.

If your opponent shows any sign of weakness, by checking to you, you are in perfect position to take the pot by betting heavily on the turn, at three-quarters of the pot size, to make it too expensive for him or her to continue. Otherwise, if your opponent bets heavily on the turn, you can fold safe in the knowledge that you probably have an inferior hand in any case or, if he or she bets weakly on the turn, perhaps re-raise, although this is a dangerous tactic, especially against an unfamiliar opponent.

An ace-high straight flush, or royal flush, consisting of ace, king, queen, jack and ten, all of the same suit, is the most valuable and, consequently, the most sought after, hand in Texas hold ‘em poker. However, the royal flush is, indeed, a rare bird and occurs in Texas hold ‘em poker once in every 40,000 hands, on average.

Each hand in Texas hold ‘em poker consists of a combination of five cards, from the two, known as hole cards, dealt face down to each player at the start of the hand, and the five, known as community cards, dealt face up in the centre of the table. Regardless of any other factors, the overall odds of achieving a royal flush in a seven-card game of this type are 30,940/1.

However, the community cards are dealt in three stages, the first of which consists of a series of three cards, collectively known as the flop. Consequently, ‘flopping’ a royal flush requires a player to be dealt two suited cards, ten or better – the odds against which are 32.2/1, in the first place – followed by a flop consisting of three specific cards, so the odds of doing so are much higher than forming a royal flush on the fourth, or fifth, card.

Indeed, it is possible to form 2,598,960 hands from a deck of 52 cards, but a royal flush can only be formed in one of four ways – clubs, diamonds, hearts or spades – so the odds of ‘flopping’ a royal flush are 2,598,960/4 or 649,739/1. In other words, according to one estimate, your chances of doing so are only marginally better than winning an Olympic gold medal during your lifetime.

All fair, modern slot machines rely on a Random Number Generator (RNG) that is hardware-based and, as such, generates random numbers by sampling naturally occurring electromagnetic noise. Random numbers are not derived by means of a repeatable algorithm, or set of rules, so even if the starting point, or any other number, in a sequence is known, the sequence cannot be reproduced at a later date.

The outcome of each spin of the reels of a slot machine is determined by the RNG, which generates thousands of random numbers per second. Consequently, while the outcome may be winning or losing, depending on the exact millisecond when the reels are activated, the player cannot predict what will happen, one way or the other, and each spin is an independent, truly random event. Indeed, it is the combination of fair, random numbers and other mathematical considerations, such as the weighting of the virtual reels, pay table and so on, that provide a casino with its house edge on slot machines.

By contrast, a so-called Pseudo Random Number Generator (PRNG) is software-based and relies on mathematical algorithms to mimic randomness based on a 32-bit integer, known as a ‘seed value’. However, PNRG algorithms can be reverse-engineered, such that the exact sequence of pseudo-random numbers for each seed value can be predicted. In the past, this vulnerability has been exploited by unscrupulous individuals, who have illicitly profited by hundreds of thousands, or millions, of pounds from slot machines at casinos worldwide. Consequently, the PNRG is a thing of the past as far as slot machines are concerned.