Kelly Betting Can Be Too Conservative

Kelly betting is a prescription for optimal resource allocation among a set of gambles which are typically repeated in an independent and identically distributed manner. In this setting, there is a large body of literature which includes arguments that the theory often leads to bets which are "too aggressive" with respect to various risk metrics. To remedy this problem, many papers include prescriptions for scaling down the bet size. Such schemes are referred to as Fractional Kelly Betting. In this paper, we take the opposite tack. That is, we show that in many cases, the theoretical Kelly-based results may lead to bets which are "too conservative" rather than too aggressive. To make this argument, we consider a random vector X with its assumed probability distribution and draw m samples to obtain an empirically-derived counterpart Xhat. Subsequently, we derive and compare the resulting Kelly bets for both X and Xhat with consideration of sample size m as part of the analysis. This leads to identification of many cases which have the following salient feature: The resulting bet size using the true theoretical distribution for X is much smaller than that for Xhat. If instead the bet is based on empirical data, "golden" opportunities are identified which are essentially rejected when the purely theoretical model is used. To formalize these ideas, we provide a result which we call the Restricted Betting Theorem. An extreme case of the theorem is obtained when X has unbounded support. In this situation, using X, the Kelly theory can lead to no betting at all.Comment: Accepted in 2016 IEEE 55th Conference on Decision and Control (CDC

Betting men’s ideas on iddaa (Turkey's official football betting game)

Football is a popular culture area that comes into our lives further day by day and has much more place in life as well. Football legitimates its dominance that achieves dominance all around the world, over Turkey, too. Society’s ideas on football changes into from football lovers point to football society. Sport spectators’ reasons of watching competitions vary. These are thought as amusement, social identity, discharges and materialistic expectation. On materialistic expectation, İddaa (betting game), Sport Toto (football pool), Sport Lotto (lotto) and Horse Racing are ale to be evaluated as to supply materialistic expectations. In this study, a questionnaire forms from 73 question which is 8 questions are on demographic information is applied on 1080 betting men in Elazığ province. Aim of the study is to determine betting men’s psychological and sociological expectations from betting game which is the most common way of supplying materialistic expectation at materialistic expectation ways at sports and their ideas on media and match fixing rumors. As a result, when general averages are calculated at the study in which 5 point likert scale is used, prominent factors are like below: %84.4 of participators are between 18-25 year-old age range, %83.8 of them earn their least income from betting game and %74’s of them state that they do not earn money from betting game. Whereas participators express “I agree.” on (X:4.15) portion on question of “Earning money easily plays important role on spreading this game of chance.”, they state that “Newspapers play important game on popularizing the game.” (X:4.23). Factor of “Government should tighten up control of age limit.” is shown as (X:3.93), “Governors support this games because government earn money from this games.” is followed by (X:4.23) factor. It is turned out that “Participators believe in that there is match fixing at some matches.” (X:3.96), “Believing in footballers fix some matches” (X:3.95), “Believing in referee fixes at some matches” (X:3.92), “Believing in club managers fix matches at some matches” (X:3.91) factors are followed by least differences

Probability and uncertainty in Keynes's The General Theory

Book description: John Maynard Keynes is undoubtedly the most influential Western economist of the twentieth century. His emphasis on the nature and role of uncertainty in economic thought is a dominant theme in his writings. This book brings together a wide array of experts on Keynes' thought such as Gay Tulip Meeks, Sheila Dow and John Davis who discuss, analyse and criticise such themes as Keynesian probability and uncertainty, the foundations of Keynes' economics and the relationship between Keynes' earlier and later thought. The Philosophy of Keynes' Economics is a readable and comprehensive book that will interest students and academics interested in the man and his thought

Testing for efficiency in the New Zealand horse racetrack betting market a thesis in partial fulfilment of the requirements for the degree of Master of Applied Economics at Massey University

Using a large sample of New Zealand pari-mutuel horse race betting data, this study tests for market efficiency. This involves testing for weak form efficiency and an anomaly known as the favourite longshot bias. Additionally, a test developed by Henery (1985) is used to examine the extent to which bettors discount their losses. Also, two utility' estimations are calculated using the first three moments surrounding the distribution. Each test is performed twice, firstly with the odds at the close of the tote and secondly with the odds quoted 30 minutes before the tote closes. A number of previous studies are reviewed. The data set is discussed along with its limitations. An extensive description of the research methodology' is presented, followed by the results, interpretations and discussion. Many former studies have found that racetrack betting is not weak form efficient, but instead there exists a negative risk-return trade-off in the market. This study, exhibiting the negative risk-return trade-off and the favourite longshot bias, is consistent with previous studies. Using opening odds, there is much evidence to suggest that the favourite longshot bias exists 30 minutes before the tote closes but is essentially eliminated in the final 30 minutes of betting. The estimation of Henery's test is consistent with his results that bettors discount approximately 2% of their losses as 'not typical'. The implications of this are also discussed. The estimation of bettor's utility' functions shows that bettors are risk lovers and, contrary' to one study, the inclusion of the third moment is insufficient to prove bettors are in fact risk averse

Catching Card Counters

The casino industry has been researched through a variety of disciplines including psychological gambling habits, technological advances, business strategies, and mathematical simulations. In the vast number of studies that have been conducted, there are few scholarly articles that focus on the specific aspect of card counting. The majority of games in the casino are designed to favor the “house”. This study focuses on the game of blackjack, in which players using a card counting strategy can tip the odds in their favor. A computer simulation was used to model the betting strategy of a card counter who would bet methodically. Conversely, the unpredictable betting strategy of a “normal” gambler was gathered through observations of over one thousands hands of blackjack. The comparison of the two led to deviations in behavior and betting habits. An understanding of these differences will provide a casino with additional information to catch card counters at the table

How to Determine the Probability of the Higgs Boson Detection

The Higgs boson is the most important, though yet undiscovered ingredient of the standard model of particle physics. Its detection is therefore one of the most important goals of high energy physics that can guide future research in theoretical physics. Enormous efforts have been undertaken to prove the existence of the Higgs boson, and the physics community is excitedly awaiting the restart of the Large Hadron Collider at CERN. But how sure can we be that the Higgs exits at all? The German philosopher Immanuel Kant recommended betting at such controversial questions, and Stephen Hawking announced a $100 bet against the Higgs. But seriously, online prediction markets, which are a generalized form of betting, do provide the best possible probability estimates for future events. It is proposed that the scientific community uses this platforms for evaluation. See also an online description www.Bet-On-The-Higgs.com.Comment: 4 pages PdfLaTeX, 2 figure

Wagers’ ideas on iddaa who accommodate betting game

Many researchers who work on individuals’ participation to sports as spectators have dealt with factors which affect participation to sports as four main perspectives such as attraction of competition, economic factors, socio-demographic factors and spectators’ choices. Target population of the study is dealers and Internet cafés which accommodate wagers DDAA in Turkey. Sample of the study is consisted of 146 dealers of DDAA and Internet cafés managers from Elazıg, Ankara, Malatya, Diyarbakır, Sivas, Kahramanmaras, Gaziantep, Antalya, Kayseri and Giresun provinces. As a result, it is stated that “Children play betting games even with their pocket money.” item is at medium level “Medium” with (X=3,09) degree, “This game will soon be the most played one.” item is at top level “Most” with (X=3,69) degree, “Letting people earn money easily makes an important role to become widespread on betting game.” item is top level “Most” with (X=4.12) degree and “Playing DDAA needs accumulation of knowledge and continuous follow up thus I think that gamers deserve money what they get from DDAA betting game.” It is ensued that most of the people who go Internet Cafés consist of teenagers. However habitués of Internet Cafés have to be above 15 years old legally, it is remarked that this rule is always broken

A betting interpretation for probabilities and Dempster-Shafer degrees of belief

There are at least two ways to interpret numerical degrees of belief in terms of betting: (1) you can offer to bet at the odds defined by the degrees of belief, or (2) you can judge that a strategy for taking advantage of such betting offers will not multiply the capital it risks by a large factor. Both interpretations can be applied to ordinary additive probabilities and used to justify updating by conditioning. Only the second can be applied to Dempster-Shafer degrees of belief and used to justify Dempster's rule of combination.Comment: 20 page