Anti-Martingale System: A system of position sizing that correlates the levels of investment with the risk and portfolio size. An anti-Martingale strategy involves halving your bets each time you.
- Martingale Roulette System Banned??? To further convince you of the legitimacy of their claims, they often tell you that the Martingale is banned from casinos and that you need to keep your winnings at around £150 per day to avoid detection and that you should play at several casinos to spread the winnings out.
- Oct 1, 2009 16 0 0. They are rediculously risky. I have seen a few trades done on fixed odds using martingale system but you have to have big.
- The Martingale strategy was originally developed as a gambling strategy in 18th century France. Since a gambler with infinitive wealth will certainly win, it was seen as a “sure thing” by many wealthy players. Some of them won such large amounts in a short period of time that a number of gambling joints banned the use of the system.
- A martingale is any of 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 it if the coin comes up tails.
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Frenchchess player Gilles Andruet, the son of former rally driverJean-Claude Andruet, was murdered on 22 August 1995. He was drugged before being beaten to death.
Background[edit]
In 1993, Gilles Andruet was using a martingale betting system that he had designed to win at blackjack. The system used Andruet's memory, his mathematical prowess, and the card-counting method devised by American player Ken Uston to its advantage.[1]
In his first year of using the martingale, Andruet won a lot of money and played increasingly often in casinos around the world, both out of enjoyment for the game and for the financial opportunities on offer. He drew attention to himself through his provocative personality and ended up on casinos’ radars. He was ultimately banned from casino blackjack, being referred to as the “Demon of the Game”. Unable to play blackjack, he switched to roulette. However, his exceptional memory and mathematical abilities did not give him an advantage in roulette, and he lost much more than he won. His friends tried in vain to dissuade him from playing. In order to sustain his lifestyle, he started consuming and selling drugs, including heroin and cannabis. This led to the large amount of money won at blackjack rapidly evaporating, and he entered into the vicious cycle of gambling addiction. He spent more money than he had, took out loans that he could not repay, was banned from holding a bank account (known as interdit bancaire – literally “bank-barred” – in France),[2] became homeless, and his lifestyle became increasingly chaotic and vulnerable.
On 4 August 1995, Andruet received a notary’s cheque of 398,000 francs as an advance on an aunt's inheritance. As he was banned from holding a bank account, he was unable to cash the cheque,[3] so he asked his casino acquaintances for help. Joseph Liany – a former businessman whom Andruet had met at the casino in Enghien-les-Bains, on the outskirts of Paris, and who was also a frequent gambler – offered Andruet help through his son Franck.[4][5] With Frank Liany as a guarantor and proxy,[3] Andruet was able to open a bank account at Moroccan bank Chaabi (a subsidiary of the Banque Populaire du Maroc), where he cashed his cheque.[6]
Murder[edit]
At around 11 p.m. on 21 August 1995, Gilles Andruet drove his car to a branch of the L’Entrecôte restaurant chain in Paris to meet Yolanda, a friend who worked as a waitress there. Three men were in the car with him.[7]
Gilles Andruet's body was discovered by a market trader in the early hours of 22 August 1995, wrapped in a white mattress protector and half submerged in the river Yvette in Saulx-les-Chartreux, in the Essonnedépartement south of Paris. Andruet had been drugged with morphine and Rohypnol – known as a date-rape drug – before repeatedly being hit with a baseball bat.[8] His car was abandoned a few miles away from where his body was found. There were multiple bloodstains in the car boot, while a photocopy of the inheritance cheque was found in the glove compartment. In 2001, mitochondrial DNA was found on a hair on the mattress protector in which Andruet's body had been wrapped. The DNA was a match to an undetermined person in the Liany family. On 25 August 1995, Franck Liany emptied Andruet's bank account.[6]
Suspects[edit]
Franck Liany was a waiter at Golf de l’Étoile, a sports club and bar-restaurant near the Arc de Triomphe in central Paris. Sacha Rhoul, the manager of the club, was his cousin: Liany's father and Rhoul's mother are siblings.[9][10]
One night in December 1995, Loïc Simon, a waiter at the sports club, openly complained of having received only 30,000 francs of the promised 50,000 from Joseph Liany for beating to death with a baseball bat a chess player who owed gambling debts to Liany.[11] On 14 August 1996, shortly after confessing to murdering Gilles Andruet, Simon committed suicide by hanging.[12][13][14] Yolanda, the waitress whom Andruet was meeting on the night of his death, gave a witness testimony confirming that Joseph Liany was one of the passengers in Andruet's car.[15] Following her statement, Yolanda suffered persistent anonymous phone calls in which death threats were made to her and her child. These calls continued even after she changed her telephone number and made it unlisted.[3][7]
Legal proceedings[edit]
First trial (2003)[edit]
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The first trial was held in November 2003. Sacha Rhoul was not called and did not attend. Rhoul's cousin, Franck Liany, was charged with receiving a murder weapon, while Rhoul's uncle, Joseph Liany, was charged with the murder of Gilles Andruet. Both defendants pleaded not guilty and blamed each other.[16] 18 witnesses were called, many of whom are believed to have been threatened – they displayed unusual memory lapses or submitted medical certificates excusing them from attending court.[17] Regardless, Franck Liany was found guilty of receiving a murder weapon and sentenced to 7 years’ imprisonment. Joseph Liany was found guilty of murder and sentenced to 15 years’ imprisonment. The latter's conviction rested on witness statements and mitochondrial DNA extracted from the hair found on the mattress protector. Only Joseph Liany appealed his conviction.[18]
Retrial of Joseph Liany (2006)[edit]
Joseph Liany appealed against his conviction and was granted a retrial in March 2006 at the Court of Assizes of the Val-de-Marne département. Sacha Rhoul was tried in absentia, found guilty and sentenced to 15 years’ imprisonment.[19] Despite this, it appeared that Rhoul was living freely in France at the time.[20]
Joseph Liany's defence relied solely on the fact that the mitochondrial DNA could also belong to Sacha Rhoul, Joseph's nephew. This was enough reasonable doubt to see Joseph Liany acquitted, to the despair of Jean-Claude Andruet, Gilles’ father.[18]
References[edit]
- ^'Echec et mort d'un surdoué'. LExpress.fr (in French). 1995-09-21. Retrieved 2018-09-21.
- ^'Le champion d'échecs avait été drogué et noyé'. ladepeche.fr (in French). Retrieved 2018-09-21.
- ^ abcmagazine, Le Point (2014-01-25). 'Le mystérieux meurtre de Gilles Andruet rejugé'. Le Point (in French). Retrieved 2018-09-21.
- ^'Le Franco-Marocain Sacha Rhoul acquitté du meurtre de Gilles Andruet' (in French). Retrieved 2018-09-21.
- ^'Gilles Andruet, la dérive d'un génie'. Le Parisien. 27 January 2014. Retrieved 21 September 2018.
- ^ ab'Sacha Rhoul acquitté du meurtre du joueur d'échecs Gilles Andruet'. Le Monde.fr (in French). Retrieved 2018-09-21.
- ^ ab'Affaire Andruet : témoin agressé et malaise à l'audience'. Libération.fr (in French). Retrieved 2018-09-21.
- ^'L'assassin présumé de G.Andruet extradé'. FIGARO. 2010-03-07. Retrieved 2018-09-21.
- ^Match, Paris. 'Affaire Andruet, le coupable arrêté' (in French). Retrieved 2018-09-21.
- ^'Saulx-les-Chartreux : Jean-Claude Andruet raconte la vie de son fils'. Le Parisien. 30 January 2014. Retrieved 21 September 2018.
- ^'Procès Andruet: Sacha Rhoul fait bonne figure'. FIGARO. 2014-01-30. Retrieved 2018-09-21.
- ^'Loïc Simon - Echecs 64'. echecs64.20minutes-blogs.fr (in French). Retrieved 2018-09-21.
- ^Thomas, Sébastien (15 November 2003). 'Le meurtrier condamné à quinze ans de prison'. Le Parisien. Retrieved 21 September 2018.
- ^'Une procédure judiciaire à rallonges'. Le Parisien. 27 January 2014. Retrieved 21 September 2018.
- ^Auguy, Stéphanie (11 November 2003). 'Le témoignage poignant de Jean-Claude Andruet'. Le Parisien. Retrieved 21 September 2018.
- ^'Procès Andruet: quinze ans de réclusion'. Libération.fr (in French). Retrieved 2018-09-21.
- ^Loisy, Florian (19 July 2016). 'Affaire Andruet : le meurtre du champion d'échecs reste impuni'. Le Parisien. Retrieved 21 September 2018.
- ^ ab'Affaire Andruet : un acquitté, un condamné… par contumace - Echecs 64'. echecs64.blog.20minutes.fr (in French). Retrieved 2018-09-21.
- ^'L'extradition de Rhoul relance l'affaire Andruet'. L'Obs (in French). Retrieved 2018-09-21.
- ^'Le Gambit Rhoul, variante Bamberski ? - Echecs 64'. echecs64.20minutes-blogs.fr (in French). Retrieved 2018-09-21.
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A martingale is any of 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 it if the coin 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. The martingale strategy has been applied to roulette as well, as the probability of hitting either red or black is close to 50%.
Since a gambler with infinite wealth will, almost surely, eventually flip heads, the martingale betting strategy was seen as a sure thing by those who advocated it. None of the gamblers possessed infinite wealth, and the exponential growth of the bets would eventually bankrupt 'unlucky' gamblers who chose to use the martingale. The gambler usually wins a small net reward, thus appearing to have a sound strategy. However, the gambler's expected value does indeed remain zero (or less than zero) because the small probability that the gambler will suffer a catastrophic loss exactly balances with the expected gain. In a casino, the expected value is negative, due to the house's edge. The likelihood of catastrophic loss may not even be very small. The bet size rises exponentially. This, combined with the fact that strings of consecutive losses actually occur more often than common intuition suggests, can bankrupt a gambler quickly.
Intuitive analysis[edit]
The fundamental reason why all martingale-type betting systems fail is that no amount of information about the results of past bets can be used to predict the results of a future bet with accuracy better than chance. In mathematical terminology, this corresponds to the assumption that the win-loss outcomes of each bet are independent and identically distributed random variables, an assumption which is valid in many realistic situations. It follows from this assumption that the expected value of a series of bets is equal to the sum, over all bets that could potentially occur in the series, of the expected value of a potential bet times the probability that the player will make that bet. In most casino games, the expected value of any individual bet is negative, so the sum of many negative numbers will also always be negative.
The martingale strategy fails even with unbounded stopping time, as long as there is a limit on earnings or on the bets (which is also true in practice).[1] It is only with unbounded wealth, bets and time that it could be argued that the martingale becomes a winning strategy.
Mathematical analysis[edit]
The impossibility of winning over the long run, given a limit of the size of bets or a limit in the size of one's bankroll or line of credit, is proven by the optional stopping theorem.[1]
Mathematical analysis of a single round[edit]
Let one round be defined as a sequence of consecutive losses followed by either a win, or bankruptcy of the gambler. After a win, the gambler 'resets' and is considered to have started a new round. A continuous sequence of martingale bets can thus be partitioned into a sequence of independent rounds. Following is an analysis of the expected value of one round.
Let q be the probability of losing (e.g. for American double-zero roulette, it is 20/38 for a bet on black or red). Let B be the amount of the initial bet. Let n be the finite number of bets the gambler can afford to lose.
The probability that the gambler will lose all n bets is qn. When all bets lose, the total loss is
The probability the gambler does not lose all n bets is 1 − qn. In all other cases, the gambler wins the initial bet (B.) Thus, the expected profit per round is
Whenever q > 1/2, the expression 1 − (2q)n < 0 for all n > 0. Thus, for all games where a gambler is more likely to lose than to win any given bet, that gambler is expected to lose money, on average, each round. Increasing the size of wager for each round per the martingale system only serves to increase the average loss.
Suppose a gambler has a 63 unit gambling bankroll. The gambler might bet 1 unit on the first spin. On each loss, the bet is doubled. Thus, taking k as the number of preceding consecutive losses, the player will always bet 2k units.
With a win on any given spin, the gambler will net 1 unit over the total amount wagered to that point. Once this win is achieved, the gambler restarts the system with a 1 unit bet.
With losses on all of the first six spins, the gambler loses a total of 63 units. This exhausts the bankroll and the martingale cannot be continued.
Martingale Betting System
In this example, the probability of losing the entire bankroll and being unable to continue the martingale is equal to the probability of 6 consecutive losses: (10/19)6 = 2.1256%. The probability of winning is equal to 1 minus the probability of losing 6 times: 1 − (10/19)6 = 97.8744%.
The expected amount won is (1 × 0.978744) = 0.978744.
The expected amount lost is (63 × 0.021256)= 1.339118.
Thus, the total expected value for each application of the betting system is (0.978744 − 1.339118) = −0.360374 .
The expected amount lost is (63 × 0.021256)= 1.339118.
Thus, the total expected value for each application of the betting system is (0.978744 − 1.339118) = −0.360374 .
In a unique circumstance, this strategy can make sense. Suppose the gambler possesses exactly 63 units but desperately needs a total of 64. Assuming q > 1/2 (it is a real casino) and he may only place bets at even odds, his best strategy is bold play: at each spin, he should bet the smallest amount such that if he wins he reaches his target immediately, and if he doesn't have enough for this, he should simply bet everything. Eventually he either goes bust or reaches his target. This strategy gives him a probability of 97.8744% of achieving the goal of winning one unit vs. a 2.1256% chance of losing all 63 units, and that is the best probability possible in this circumstance.[2] However, bold play is not always the optimal strategy for having the biggest possible chance to increase an initial capital to some desired higher amount. If the gambler can bet arbitrarily small amounts at arbitrarily long odds (but still with the same expected loss of 1/19 of the stake at each bet), and can only place one bet at each spin, then there are strategies with above 98% chance of attaining his goal, and these use very timid play unless the gambler is close to losing all his capital, in which case he does switch to extremely bold play.[3]
Alternative mathematical analysis[edit]
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 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.[4] This intuitive belief is sometimes referred to as the representativeness heuristic.
Anti-martingale[edit]
This is also known as the reverse martingale. In a classic martingale betting style, gamblers increase bets after each loss in hopes that an eventual win will recover all previous losses. The anti-martingale approach instead increases bets after wins, while reducing them after a loss. The perception is that the gambler will benefit from a winning streak or a 'hot hand', while reducing losses while 'cold' or otherwise having a losing streak. As the single bets are independent from each other (and from the gambler's expectations), the concept of winning 'streaks' is merely an example of gambler's fallacy, and the anti-martingale strategy fails to make any money. If on the other hand, real-life stock returns are serially correlated (for instance due to economic cycles and delayed reaction to news of larger market participants), 'streaks' of wins or losses do happen more often and are longer than those under a purely random process, the anti-martingale strategy could theoretically apply and can be used in trading systems (as trend-following or 'doubling up'). (But see also dollar cost averaging.)
See also[edit]
References[edit]
- ^ abMichael Mitzenmacher; Eli Upfal (2005), Probability and computing: randomized algorithms and probabilistic analysis, Cambridge University Press, p. 298, ISBN978-0-521-83540-4, archived from the original on October 13, 2015
- ^Lester E. Dubins; Leonard J. Savage (1965), How to gamble if you must: inequalities for stochastic processes, McGraw Hill
- ^Larry Shepp (2006), Bold play and the optimal policy for Vardi's casino, pp 150–156 in: Random Walk, Sequential Analysis and Related Topics, World Scientific
- ^Martin, Frank A. (February 2009). 'What were the Odds of Having Such a Terrible Streak at the Casino?'(PDF). WizardOfOdds.com. Retrieved 31 March 2012.
Martingale System Banned List
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