Fixed-odds betting
Fixed-odds betting is a form of wagering against odds offered by a bookmaker, an individual, or on a bet exchange.
Calculating fixed odds
It is customary with fixed-odds gambling to know the odds at the time of the placement of the wager (the "live price"), although this category also includes wagers whose price is determined only when the race or game starts (the "starting prices"). It is ideal for a bookmaker to price/mark up a book such that the net outcome will always be in his favour, i.e. the sum of the probabilities quoted for all possible outcomes will be in excess of 100%. The excess over 100% (or overround) represents profit to the bookmaker in the event of a balanced/even book. In the more usual case of an imbalanced book, the bookmaker may have to pay out more winnings than what is staked, or he may earn more than mathematically expected. An imbalanced book may arise since there is no way for a bookmaker either to know the true probabilities for the outcome of competitions left to human effort or to predict the bets that will be attracted from others by fixed odds compiled on the basis of his own personal view and knowledge.
With the advent of Internet and bet exchange betting, the possibility of fixed-odds arbitrage actions and Dutch books against bookmakers and exchanges has expanded significantly. Betting exchanges in particular act like a stock exchange, allowing the odds to be set in the course of trading between individual bettors, usually leading to quoted odds that are reasonably close to the "true odds."
In making a bet where your expected value is positive, you are said to be getting "the best of it". For example, if you were to bet $1 at 10 to 1 odds (you could win $10) on the outcome of a coin flip, you would be getting "the best of it" and you should always make the bet (assuming you are rational and risk-neutral with linear utility curves and have no susceptibility to such fallacies as loss aversion). However if someone offered you odds of 10 to 1 that a card chosen at random from a regular 52 card deck would be the ace of spades, then you would be getting "the worst of it" because the chance is only 1 in 52 that the ace will be chosen. It is mathematically disadvantageous to make a bet where you are getting "the worst of it."
When making a bet where you must put more at stake than you stand to win, you are laying the odds or laying the bet. So, for example, if you bet $1000 that it will rain tomorrow, and if you win you will only win $200 but if you lose you will lose your entire $1000, then you are laying a bet. It is possible that you could be getting "the best of it" or "the worst of it" when you lay a bet; the fact that you are laying a bet does not necessarily mean you are getting "the worst of it". A lay bet is a bet that something won't happen, so if you lay $50 on a horse then you are betting the horse won't win.
Providers for fixed odd betting would include ChoiceOdds, Ladbrokes, Paddy Power, and William Hill plc.
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Favourite-longshot bias
In gambling and economics, the favourite-longshot bias is an observed phenomenon where on average, bettors tend to overvalue "long shots" and undervalue favourites. That is, in a horse race where one horse is given odds of 2-to-1, and another 100-to-1, the true odds might for example be 1.5-to-1 and 300-to-1 respectively. Betting on the "long shot" is therefore a much worse proposition than betting on the favourite. Various theories exist to explain why people willingly bet on such losing propositions, such as risk-loving behavior, or simply inaccurate estimation as presented by Sobel and Raines.[1]
References
- ^ 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
References
- http://bpp.wharton.upenn.edu/jwolfers/Papers/Favorite_Longshot_Bias.pdf
- http://favourite-longshot-bias.behaviouralfinance.net/
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Dutching
In gambling, Dutching is sharing the risk of losing across a number or runners by backing more than one selection in a race or event. The process calculates the correct stake to place on each selection so that the return is the same if any of them wins. This is not to be confused with what constitutes a Dutch book which is when a bookmaker goes overbroke (the opposite to overround).
It is thought the strategy behind Dutching was originally conceived and employed by Arthur Flegenheimer (aka Dutch Schultz) alongside various rackets he had running at the racetrack. The system has since taken his name.
The strategy can pay dividends when gamblers successfully reduce the potential winners of an event to a select few from the field or when information about runners not expected to perform well does not reach the market (so as to affect the odds) making backing the rest of the field profitable.
Dutching calculators that perform the mathematics behind the system are freely available on the internet.
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Daily double
A daily double is a wager offered by horse and dog racing tracks. Bettors wager on the winners of two races, pre-designated by the track for a particular race day. While the Daily Racing Form's glossary defines a Daily Double as two consecutive races, [1] this is a loose rule. Many tracks' Daily Doubles are not consecutive. Because of the increased difficulty of picking two straight winners, winning daily double bets often pay off at high odds. [2]
The daily double was the first so-called "exotic" wager offered by North American racetracks. Introduced in 1931 at Ottawa's Connaught Park Racetrack,[3][4] the wager was typically offered only for the first two races of each day's program as an enticement for spectators to arrive early for the entire program. As with all other American racing wagers, the "double" is conducted in parimutuel fashion, but with the number of betting interests in the daily double pool equal to the product of the number of entries in each race. For example, if there are ten entries in the first race and eight in the second, there will be eighty betting interests, one for each combination of two potential winners. This results in higher payoffs than those found in straight betting for win, place, or show.
For many years the daily double was the only exotic wager offered. Later the exacta was also offered on select races during each program. The wagers were offered only a few times each day largely because of the limitations of electro-mechanical totalisator systems. When computer technology took over, more exotic wagers were introduced, such as the trifecta, superfecta and pick 6. The higher payouts for these wagers tended to diminish interest in the "old fashioned" daily double, but it is still offered at all tracks, sometimes more than once during a program. A "late double" is frequently offered on the day's final two races; some tracks offer a "rolling double" - a daily double starting on each race on the program except the last race.
The "Pick 3" and "Pick 4" wagers are derived from the daily double. These wagers require bettors to pick the winners of three or four consecutive races. These are also often offered on a rolling basis — a rolling pick 3 on races one through three, another on races two through four, and so on throughout the day.
Occasional doubles are offered on important races contested on separate days. The most prominent example is the "Oaks-Derby Double" offered by Churchill Downs, where bettors pick the winners of the Kentucky Oaks and the Kentucky Derby. The Oaks is run the day before the Derby, which is always run on the first Saturday of May.
Notes
- ^ Daily Racing Form Glossary of Terms
- ^ Saratoga Racetrack Horse Racing Glossary
- ^ Snider, Steve (December 30, 1979). "If You Think This Decade is Something, Try ...". The Palm Beach Daily Post: p. E7.
- ^ "Innovation for 'Double' Tickets". Montreal Gazette: p. 19. May 20, 1932.
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An alternative mathematical analysis for the Martingale betting system
The previous analysis calculates expected value, but we can ask another question: what is the chance that one can play a casino game using the Martingale strategy, and avoid the losing streak long enough to double one's bankroll.
As before, this depends on the likelihood of losing 6 roulette spins in a row assuming we are betting red/black or even/odd. Many gamblers believe that the chances of losing 6 in a row are remote, and that with a patient adherence to the strategy they will slowly increase their bankroll.
In reality, the odds of a streak of 6 losses in a row are much higher than the many people intuitively believe. Psychological studies have shown that since people know that the odds of losing 6 times in a row out of 6 plays are low, they incorrectly assume that in a longer string of plays the odds are also very low. When people are asked to invent data representing 200 coin tosses, they often do not add streaks of more than 5 because they believe that these streaks are very unlikely.[1] This intuitive belief is sometimes referred to as the representativeness heuristic.
The odds of losing a single spin at roulette are q = 20/38 = 52.6316%. If you play a total of 6 spins, the odds of losing 6 times are q6 = 2.1256%, as stated above. However if you play more and more spins, the odds of losing 6 times in a row begin to increase rapidly.
- In 73 spins, there is a 50.3% chance that you will at some point have lost at least 6 spins in a row. (The chance of still being solvent after the first six spins is 0.978744, and the chance of becoming bankrupt at each subsequent spin is (1-0.526316)x0.021256 = 0.010069, where the first term is the chance that you won the (n-6)th spin - if you had lost the (n-6)th spin, you would have become bankrupt on the (n-1)th spin. Thus over 73 spins the probability of remaining solvent is 0.978744 x (1-0.010069)^67 = 0.49683, and thus the chance of becoming bankrupt is 1-0.49683 = 50.3%.)
- Similarly, in 150 spins, there is a 77.2% chance that you will lose at least 6 spins in a row at some point.
- And in 250 spins, there is a 91.1% chance that you will lose at least 6 spins in a row at some point.
To double the initial bankroll of 6,300 with initial bets of 100 would require a minimum of 63 spins (in the unlikely event you win every time), and a maximum of 378 spins (in the even more unlikely event that you win every single round on the sixth spin). Each round will last an average of approximately 2 spins, so, 63 rounds can be expected to take about 126 spins on average. Computer simulations show that the required number will almost never exceed 150 spins. Thus many gamblers believe that they can play the Martingale strategy with very little chance of failure long enough to double their bankroll. However, the odds of losing 6 in a row are 77.2% over 150 spins, as above.
We can replace the roulette game in the analysis with either the pass line at craps, where the odds of losing are lower q=(251:244, or 251/495)=50.7071%, or a coin toss game where the odds of losing are 50.0%. We should note that games like coin toss with no house edge are not played in a commercial casino and thus represent a limiting case.
- In 150 turns, there is a 73.5% chance that you will lose 6 times in a row on the pass line.
- In 150 turns, there is a 70.7% chance that you will lose 6 times in a row at coin tossing.
In larger casinos, the maximum table limit is higher, so you can double 7, 8, or 9 times without exceeding the limit. However, in order to end up with twice your initial bankroll, you must play even longer. The calculations produce the same results. The probabilities are overwhelming that you will reach the bust streak before you can even double your bankroll.
The conclusion is that players using Martingale strategy pose no threat to a casino. The odds are high that the player will go bust before he is able even to double his money.
Table limits are not specifically designed to prevent players from using Martingale strategy. The table limits exist so that the casino is not gambling more money than they can afford to lose. (E.g., a casino that takes in an average of $1000 a day on a roulette table might not accept a $7000 bet on black at that table; that bet would have a 18/38 chance of negating an entire week's profits.)
References
- ^ (wizardofodds.com/askthewizard/images/streaks.pdf)
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Introducing Live Betting
As opposed to conventional online sports betting, live betting is a system in which the odds change during matches according to the score. Here is a quick example from the NBA: if you are watching a Lakers-Clippers game, the betting odds before the game would obviously favor the Lakers, but if the clippers open a big lead at halftime, the odds may change accordingly, to reflect the fact that Clippers chances of winning have increased significantly. The same is true to football and other sports as well. Live betting can be a whole lot of fun, but you should be sure to read about the betting system on any site you bet at, and make sure you understand the rules before placing a wager.
Arbitrage using bookmakers
This type of arbitrage takes advantage of different odds offered by different bookmakers. Assume the following situation:
We consider an event with 2 possible outcomes (e.g. a tennis match - either Federer wins or Henman wins), the idea can be generalized to events with more outcomes, but we use this as an example.
The 2 bookmakers have different ideas of who has the best chances of winning. They offer the following Fixed-odds gambling on the outcomes of the event
| Bookmaker 1 | Bookmaker2 | |
| Outcome 1 | 1.25 | 1.43 |
| Outcome 2 | 3.9 | 2.85 |
For an individual bookmaker, the sum of the inverse of all outcomes of an event will always be greater than 1. 1.25 − 1 + 3.9 − 1 = 1.056 and 1.43 − 1 + 2.85 − 1 = 1.051
The fraction above 1, is the bookmakers return rate, the amount the bookmaker earns on offering bets at some event. Bookmaker 1 will in this example expect to earn 5.6% on bets on the tennis game. Usually these gaps will be in the order 8 - 12%.
The idea is to find odds at different bookmakers, where the sum of the inverse of all the outcomes are below 1. Meaning that the bookmakers disagree on the chances of the outcomes. This discrepancy can be used to obtain a profit.
For instance if one places a bet on outcome 1 at bookmaker 2 and outcome 2 at bookmaker 1:
1.43 − 1 + 3.9 − 1 = 0.956
Placing a bet of 100$ on outcome 1 with bookmaker 2 and a bet of $100 * 1.43 / 3.9 = 36.67 on outcome 2 at bookmaker 1 would ensure the bettor a profit.
In case outcome 1 comes out, one could collect r1 = $100 * 1.43 = $143 from bookmaker 2. In case outcome 2 comes out, one could collect r2 = $36.67 * 3.9 = $143 from bookmaker 1. One would have invested $136.67, but have collected $143, a profit of $6.33 (%4.6) no matter the outcome of the event.
So for 2 odds o1 and o2, where o1-1+ o2-1 < 1. If one wishes to place stake s1 at outcome 1, then one should place s2 = s1 * o1 / o2 at outcome 2, to even out the odds, and receive the same return no matter the outcome of the event.
Or in other words, if there are two outcomes, a 2/1 and a 3/1, by covering the 2/1 with $500 and the 3/1 with $333, one is guaranteed to win $1000 at a cost of $833, giving a 20% profit. More often profits exists around the 4% mark or less.
Reducing the risk of human error is vital being that the mathematical formula is sound and only external factors add "risk". Numerous online arbitrage calculator tools exist to help bettors get the math right. For example, the Arb Cruncher sports betting calculator handles calculations for both book arbitrage (back/back or lay/lay) and back/lay arbitrage opportunities on an intra-exchange or inter-exchange basis, and is free.
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United Kingdom gambling industry
Traditionally, bookmakers have been located at the racecourse, but improved TV coverage and modernisation of the law have allowed betting in shops and casinos in most countries. In the UK, on-track bookies still mark up the odds on boards beside the race course and use tic-tac or mobile telephones to communicate the odds between their staff and to other bookies, but, with the modernisation of United Kingdom Bookmaking laws, online and high street gambling are at an all-time high, with a so-called Super Casino having been planned for construction in Manchester prior to the government announcing that this plan had been scrapped on 26 February 2008.
In 1961, Harold Macmillan's Conservative Government legalised betting shops and tough measures were enacted to ensure that bookmakers remained honest. A large and respectable industry has grown since. At one time there were over 15,000 betting shops in the UK. Now, through consolidation, they have been reduced to about 8,500. Currently there are four major "high street" bookmakers in the United Kingdom: William Hill, Ladbrokes, Coral, and state-owned ToteSport, with Sky Bet, Bet24, Betfred, Victor Chandler, Stan James, Sportingbet, Mansion and Bet365, rapidly emerging, in terms of turnover and event sponsorship.
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Odds
Odds for different outcomes in a single bet are presented either in European format (decimal odds), UK format (fractional odds), or American format (moneyline odds). European format (decimal odds) are favoured in continental Europe, Canada, and Australia. They are the ratio of the full payout to the stake, in a decimal format. Decimal odds of 2.00 are an even bet. UK format (fractional odds) are favoured by British bookmakers. They are the ratio of the amount won to the stake. Fractional odds of 1/1 are an even bet. US format odds are favoured in the United States. They are the amount won on a 100 stake when positive and the stake needed to win 100 when negative. US odds of 100 are an even bet.
| Decimal | Fractional | US |
| 1.50 | 1/2 | -200 |
| 2.00 | 1/1 | +100 |
| 2.50 | 3/2 | +150 |
| 3.00 | 2/1 | +200 |
| x | To | Do this |
|---|---|---|
| Decimal | Fractional | x-1 , then convert to fraction |
| Decimal | US | 100*(x-1) if x>=2; -100/(x-1) if x<2 |
| Fractional | Decimal | divide fraction, then x+1 |
| Fractional | US | divide fraction, then 100*x if x>=1; -100/x if x<1 |
| US | Decimal | (x/100)+1 if x>0; (-100/x)+1 if x<0 |
| US | Fractional | x/100, then convert to fraction if x>0; -100/x, then convert to fraction if x<0 |
In Asia betting markets, other frequently used formats for expressing odds include Hong Kong, Malay, and Indonesian-style odds formats. Odds are also quite often expressed in terms of implied probability, which corresponds to the probability with which the event in question would need to occur for the bet to be a breakeven proposition (on the average).
Many online tools also exist for automated conversion between these odds formats.
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Operational procedures of the bookmakers
By adjusting the odds in his favor or by having a point spread, the bookmaker will aim to guarantee a profit by achieving a 'balanced book', either by getting an equal number of bets for each outcome, or (when he is offering odds) by getting the amounts wagered on each outcome to reflect the odds. When a large bet comes in, a bookmaker can also try to lay off the risk by buying bets from other bookmakers. The bookmaker does not generally attempt to make money from the bets themselves, but rather profiting from the event regardless of the outcome. Their working methods are similar to that of an actuary, who does a similar balancing of financial outcomes of events for the assurance and insurance industries.
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Bookmakers
Bookmakers on a greyhound race course, Reading, UK
A bookmaker, or bookie, is an organization or a person that takes bets on sporting and other events at agreed upon odds.
Range of events
Most bookmakers in the United States bet merely on college and professional sports, though in the United Kingdom and Ireland they offer a wider range of bets, including each-way betting on golf, football and tennis, and especially horse racing and greyhound racing. They also specialize in novelty events such as betting that there will be a white Christmas, the outcome of political elections and reality television contests.
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Betting strategy
A betting strategy or betting system is a structured approach to gambling intended to counter the inherent bias held by the house in casino and card games and by bookmakers in horseracing and sports betting. A successful strategy should increase the odds of winning in order to produce long term profits from a pursuit which under normal circumstances will only ever result in a long term loss.
All betting systems are predicated on statistical analysis, seeking to exploit the rare circumstances when the odds are in the favour of the player. Though the basis of all risk is fundamentally the same, betting systems vary in relation to the rules and circumstances of each particular game. The most established betting systems include:
- Card games - Card counting
- Roulette - Martingale
- Horse racing - Hedging, Arbitrage
- Sports - Handicapping[citation needed]
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