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Gambling is the wagering of something of value on a random event with the intent of winning something else of value, where instances of strategy are discounted. Gambling thus requires three elements to be present: consideration, risk (chance), and a prize. The outcome of the wager is often immediate, such as a single roll of dice, a spin of a roulette wheel, or a horse crossing the finish line, but longer time frames are also common, allowing wagers on the outcome of a future sports contest or even an entire sports season.
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 an event has occurred more frequently than expected, it is less likely to happen again in the future. 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.
Fixed-odds betting is a form of gambling where individuals place bets on the outcome of an event, such as sports matches or horse races, at predetermined odds. In fixed-odds betting, the odds are fixed and determined at the time of placing the bet. These odds reflect the likelihood of a particular outcome occurring. If the bettor's prediction is correct, they receive a payout based on the fixed odds. This means that the potential winnings are known at the time of placing the bet, regardless of any changes in the odds leading up to the event.
In probability theory, odds provide a measure of the likelihood of a particular outcome. When specific events are equally likely, odds are calculated as the ratio of the number of events that produce that outcome to the number that do not. Odds are commonly used in gambling and statistics.
Prospect theory is a theory of behavioral economics, judgment and decision making that was developed by Daniel Kahneman and Amos Tversky in 1979. The theory was cited in the decision to award Kahneman the 2002 Nobel Memorial Prize in Economics.
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.
Prediction markets, also known as betting markets, information markets, decision markets, idea futures or event derivatives, are open markets that enable the prediction of specific outcomes using financial incentives. They are exchange-traded markets established for trading bets in the outcome of various events. The market prices can indicate what the crowd thinks the probability of the event is. A typical prediction market contract is set up to trade between 0 and 100%. The most common form of a prediction market is a binary option market, which will expire at the price of 0 or 100%. Prediction markets can be thought of as belonging to the more general concept of crowdsourcing which is specially designed to aggregate information on particular topics of interest. The main purposes of prediction markets are eliciting aggregating beliefs over an unknown future outcome. Traders with different beliefs trade on contracts whose payoffs are related to the unknown future outcome and the market prices of the contracts are considered as the aggregated belief.
In a thought experiment proposed by the Italian probabilist Bruno de Finetti in order to justify Bayesian probability, an array of wagers is coherent precisely if it does not expose the wagerer to certain loss regardless of the outcomes of events on which they are wagering, even if their opponent makes the most judicious choices.
Subjectivism is the doctrine that "our own mental activity is the only unquestionable fact of our experience", instead of shared or communal, and that there is no external or objective truth.
In gambling, economics, and the philosophy of probability, a Dutch book or lock is a set of odds and bets that ensures a guaranteed profit. It is generally used as a thought experiment to motivate Von Neumann–Morgenstern axioms or the axioms of probability by showing they are equivalent to philosophical coherence or Pareto efficiency.
In decision theory, the Ellsberg paradox is a paradox in which people's decisions are inconsistent with subjective expected utility theory. John Maynard Keynes published a version of the paradox in 1921. Daniel Ellsberg popularized the paradox in his 1961 paper, "Risk, Ambiguity, and the Savage Axioms". It is generally taken to be evidence of ambiguity aversion, in which a person tends to prefer choices with quantifiable risks over those with unknown, incalculable risks.
In probability theory, the Kelly criterion is a formula for sizing a bet. The Kelly bet size is found by maximizing the expected value of the logarithm of wealth, which is equivalent to maximizing the expected geometric growth rate. Assuming that the expected returns are known, the Kelly criterion leads to higher wealth than any other strategy in the long run. J. L. Kelly Jr, a researcher at Bell Labs, described the criterion in 1956.
Probabilistic forecasting summarizes what is known about, or opinions about, future events. In contrast to single-valued forecasts, probabilistic forecasts assign a probability to each of a number of different outcomes, and the complete set of probabilities represents a probability forecast. Thus, probabilistic forecasting is a type of probabilistic classification.
A parlay, accumulator, combo bet, or multi is a single bet that links together two or more individual wagers, usually seen in sports betting. Winning the parlay is dependent on all of those wagers winning together. If any of the bets in the parlay lose, the entire parlay loses. If any of the plays in the parlay ties, or "pushes", the parlay reverts to a lower number of wagers with the payout odds reducing accordingly. Parlay bets are high-risk, high-reward; linking the possibilities drastically reduces the chance of the bet paying off overall. The benefit of the parlay is that there are much higher pay-offs, although as usual, casinos and bookkeepers offering parlays often exploit the poor calculation of gamblers by not increasing the pay-out as much as the odds truly demand, with the effect of the house edge increasing in parlays.
The Tote is a British gambling company founded in 1928. It is one of the world’s largest pool betting operators. Its product offering also includes sports betting and online casino. Business operations are led from its headquarters in Wigan.
Calibrated probability assessments are subjective probabilities assigned by individuals who have been trained to assess probabilities in a way that historically represents their uncertainty. For example, when a person has calibrated a situation and says they are "80% confident" in each of 100 predictions they made, they will get about 80% of them correct. Likewise, they will be right 90% of the time they say they are 90% certain, and so on.
In gambling parlance, making a book is the practice of laying bets on the various possible outcomes of a single event. The phrase originates from the practice of recording such wagers in a hard-bound ledger and gives the English language the term bookmaker for the person laying the bets and thus 'making the book'.
In probability theory, Proebsting's paradox is an argument that appears to show that the Kelly criterion can lead to ruin. Although it can be resolved mathematically, it raises some interesting issues about the practical application of Kelly, especially in investing. It was named and first discussed by Edward O. Thorp in 2008. The paradox was named for Todd Proebsting, its creator.
Probability has a dual aspect: on the one hand the likelihood of hypotheses given the evidence for them, and on the other hand the behavior of stochastic processes such as the throwing of dice or coins. The study of the former is historically older in, for example, the law of evidence, while the mathematical treatment of dice began with the work of Cardano, Pascal, Fermat and Christiaan Huygens between the 16th and 17th century.
The end-of-the-day betting effect is a cognitive bias reflected in the tendency for bettors to take gambles with higher risk and higher reward at the end of their betting session to try to make up for losses. William McGlothlin (1956) and Mukhtar Ali (1977) first discovered this effect after observing the shift in betting patterns at horserace tracks. Mcglothlin and Ali noticed that people are significantly more likely to prefer longshots to conservative bets on the last race of the day. They found that the movement towards longshots, and away from favorites, is so pronounced that some studies show that conservatively betting on the favorite to show in the last race is a profitable bet despite the track’s take.
References
- ↑ https://daily.jstor.org/betting-on-the-longshot/
- ↑ "We discount the chances of any party at 100/1 or bigger. The reverse of tweak 1 applies here. Almost all of these probably have effectively zero chance. Why don’t we just make them a bigger price? We don’t think we’ll take much extra money, certainly not enough to compensate us for the day we get it wrong." Matthew Shadwick, Ladbrokes, 2010-02-25. See Ladbrokes Election Forecast Feb 25th 2010
- ↑ Russell S. Sobel & S. Travis Raines, 2003. "An examination of the empirical derivatives of the favourite-longshot bias in racetrack betting," Applied Economics, Taylor and Francis Journals, vol. 35(4), pages 371-385, January
- ↑ Convert Betting Odds to Probabilities More Accurately and Efficiently than Shin and Power Methods
- ↑ Adjusting Bookmaker’s Odds to Allow for Overround
- ↑ On determining probability forecasts from betting odds
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