The gambler's fallacy, also known as the Monte Carlo fallacy or the fallacy of the maturity of chances, is the incorrect belief that, if a particular event occurs more frequently than normal during the past, it is less likely to happen in the future, when it has otherwise been established that the probability of such events does not depend on what has happened in the past. Such events, having the quality of historical independence, are referred to as statistically independent. The fallacy is commonly associated with gambling, where it may be believed, for example, that the next dice roll is more than usually likely to be six because there have recently been fewer than the expected number of sixes.
In poker, the probability of each type of 5-card hand can be computed by calculating the proportion of hands of that type among all possible hands.
Piquet is an early 16th-century plain-trick card game for two players that became France's national game. David Parlett calls it a "classic game of relatively great antiquity... still one of the most skill-rewarding card games for two" but one which is now only played by "aficionados and connoisseurs."
A martingale is a class of betting strategies that originated from and were popular in 18th-century France. The simplest of these strategies was designed for a game in which the gambler wins the stake if a coin comes up heads and loses if it comes up tails. The strategy had the gambler double the bet after every loss, so that the first win would recover all previous losses plus win a profit equal to the original stake. Thus the strategy is an instantiation of the St. Petersburg paradox.
Coin flipping, coin tossing, or heads or tails is the practice of throwing a coin in the air and checking which side is showing when it lands, in order to choose between two alternatives, heads or tails, sometimes used to resolve a dispute between two parties. It is a form of sortition which inherently has two possible outcomes. The party who calls the side that is facing up when the coin lands wins.
Matching pennies is the name for a simple game used in game theory. It is played between two players, Even and Odd. Each player has a penny and must secretly turn the penny to heads or tails. The players then reveal their choices simultaneously. If the pennies match, then Even keeps both pennies, so wins one from Odd. If the pennies do not match Odd keeps both pennies, so receives one from Even.
In mathematics, a subset of a Polish space is universally measurable if it is measurable with respect to every complete probability measure on that measures all Borel subsets of . In particular, a universally measurable set of reals is necessarily Lebesgue measurable.
German Whist is a variation on classic whist for two players. Also called Chinese Whist, it is probably of British origin.
In contract bridge, the principle of restricted choice states that "The play of a card which may have been selected as a choice of equal plays increases the chance that the player started with a holding in which his choice was restricted." Crucially, it helps play "in situations which used to be thought of as guesswork."
Clabber is a four-player trick-taking card game played in southwestern Indiana near Evansville. Clabber is a member of the Jack-Nine family of trick-taking card games that are popular in Europe. The game is a four player variation similar to that of klaberjass. The game also plays similar to Euchre, with a few differences being that points are not awarded based on the number of tricks taken, but rather on the actual point value of cards in those tricks. Clabber also doesn't use a left Bower, as does Euchre; other differences are that players don't use Bidding, instead, the trump makers must score at least eighty-two points to keep from "going set", where they don't score any of their points. Additional points can also be scored for a combination of cards in a hand, which would assist in "making it", or, not going set.
The Monty Hall problem is a brain teaser, in the form of a probability puzzle, loosely based on the American television game show Let's Make a Deal and named after its original host, Monty Hall. The problem was originally posed in a letter by Steve Selvin to the American Statistician in 1975. It became famous as a question from reader Craig F. Whitaker's letter quoted in Marilyn vos Savant's "Ask Marilyn" column in Parade magazine in 1990:
Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?
The mathematics of gambling are a collection of probability applications encountered in games of chance and can be included in game theory. From a mathematical point of view, the games of chance are experiments generating various types of aleatory events, the probability of which can be calculated by using the properties of probability on a finite space of events.
The ludic fallacy, proposed by Nassim Nicholas Taleb in his book The Black Swan (2007), is "the misuse of games to model real-life situations". Taleb explains the fallacy as "basing studies of chance on the narrow world of games and dice". The adjective ludic originates from the Latin noun ludus, meaning "play, game, sport, pastime".
Miwin's Dice are a set of nontransitive dice invented in 1975 by the physicist Michael Winkelmann. They consist of three different dice with faces bearing numbers from one to nine; opposite faces sum to nine, ten or eleven. The numbers on each die give the sum of 30 and have an arithmetic mean of five.
In common usage, randomness is the apparent or actual lack of pattern or predictability in information. A random sequence of events, symbols or steps often has no order and does not follow an intelligible pattern or combination. Individual random events are, by definition, unpredictable, but if the probability distribution is known, the frequency of different outcomes over repeated events is predictable. For example, when throwing two dice, the outcome of any particular roll is unpredictable, but a sum of 7 will tend to occur twice as often as 4. In this view, randomness is not haphazardness; it is a measure of uncertainty of an outcome. Randomness applies to concepts of chance, probability, and information entropy.
In the card game bridge, the law or principle of vacant places is a simple method for estimating the probable location of any particular card in the four hands. It can be used both to aid in a decision at the table and to derive the entire suit division probability table.
The "hot hand" is a phenomenon, previously considered a cognitive social bias, that a person who experiences a successful outcome has a greater chance of success in further attempts. The concept is often applied to sports and skill-based tasks in general and originates from basketball, where a shooter is more likely to score if their previous attempts were successful; i.e., while having the "hot hand.” While previous success at a task can indeed change the psychological attitude and subsequent success rate of a player, researchers for many years did not find evidence for a "hot hand" in practice, dismissing it as fallacious. However, later research questioned whether the belief is indeed a fallacy. Some recent studies using modern statistical analysis have observed evidence for the "hot hand" in some sporting activities; however, other recent studies have not observed evidence of the "hot hand". Moreover, evidence suggests that only a small subset of players may show a "hot hand" and, among those who do, the magnitude of the "hot hand" tends to be small.
In the mathematics of shuffling playing cards, the Gilbert–Shannon–Reeds model is a probability distribution on riffle shuffle permutations that has been reported to be a good match for experimentally observed outcomes of human shuffling, and that forms the basis for a recommendation that a deck of cards should be riffled seven times in order to thoroughly randomize it. It is named after the work of Edgar Gilbert, Claude Shannon, and J. Reeds, reported in a 1955 technical report by Gilbert and in a 1981 unpublished manuscript of Reeds.
Frustration is a solitaire game with roots in the 1700s, and is similar to but opposite of Hit or Miss. It relies purely on luck rather than on skill, and has been both mathematically analyzed and discussed in popular media. This is an example of a derangement problem in combinatorial mathematics, which can be understood using a combinatorial tool called a rook polynomial. The probability of winning the game has been determined exactly, and is approximately 1.6233%. The same technique can be applied to variations of the game that use different numbers of suits, and different numbers of cards per suit.
Lorum or Lórum is an old, Hungarian, compendium card game for 4 players. Although it is the ancestor of the French game, Barbu, it is still played today. It uses a German-suited pack of 32 cards and comprises 8 individual contracts, each with different rules, each of which is played four times so that a session consists of a total of 32 individual games and lasts about 1½ hours.
