betting systems

Originally, martingale referred to a class of betting strategies popular in 18th century France. The simplest of these strategies was designed for a game in which the gambler wins his stake if a coin comes up heads and loses it if the coin comes up tails. The strategy had the gambler double his bet after every loss, so that the first win would recover all previous losses plus win a profit equal to the original stake. Since a gambler with infinite wealth will with probability 1 eventually flip heads, the Martingale betting strategy was seen as a sure thing by those who practised it. Unfortunately, none of these practitioners in fact possessed infinite wealth, and the exponential growth of the bets would eventually bankrupt those foolish enough to use the Martingale. Moreover, it has become impossible to implement in modern casinos, due to the betting limit at the tables. Because the betting limits reduce the casino's short term variance, the martingale system itself does not pose a threat to the casino, and many will encourage its use, knowing that they have the house advantage no matter when or how much is wagered.Suppose that someone applies the martingale betting system at an American roulette table, with 0 and 00 values; on average, a bet on either red or black will win 18 times out of 38. If the player's initial bankroll is $150 and the betting unit is $10, he can afford 4 losing bets in a row (of $10, $20, $40, and $80) before he runs out of money. If any of these 4 bets wins he wins $10 and wins back any past losses. The chance of losing 4 bets in a row (and therefore losing the complete $150) is (20/38)4 = 7.67%. The remaining 92.3% of the time, the player will win $10. We will call this one round (playing until you have lost 4 times or until you win, whichever comes first). If you play repeated rounds with this strategy then your average earnings will be (0.923·$10) − (0.0767·$150) = −$2.275 per round. Therefore, you lose an average of $2.275 each round. However, if the gambler possesses an infinite amount of money, the expected return is (18/38)*b per roll (where b is the initial bet). With an initial bet of $10, the expected return is thus $4.736 per roll..
[edit] Effect of varianceAs with any betting system, it is possible to have variance from the expected negative return by temporarily avoiding the inevitable losing streak. Furthermore, a straight string of losses is the only sequence of outcomes that results in a loss of money, so even when a player has lost the majority of their bets, they can still be ahead over-all, since they always win 1 unit when a bet wins, regardless of how many previous losses.[1]
[edit] Intuitive analysisSince expectation is linear, the expected value of a series of bets is just the sum of the expected value of each bet. Since in such games of chance the bets are independent, the expectation of all bets is going to be the same, regardless of whether you previously won or lost. In most casino games, the expected value of any individual bet is negative, so the sum of lots of negative numbers is also always going to be negative.
[edit] Mathematical analysisLet q be the probability of losing (e.g. for roulette it is 20/38). Let y be the amount of the commencing bet (e.g. $10 in the example above). Let x be the finite number of bets you can afford to lose.
The probability that you lose all x bets is qx. When you lose all your bets, the amount of money you lose is
In a classic martingale betting style, gamblers will increase their 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 in this manner the gambler will benefit from a winning streak or a "hot hand", while reducing losses while "cold" or otherwise having a losing streak. This general idea of increasing bets when conditions are believed to be favorable can improve the odds in games with a memory by using a strategy like card counting. But in a true random memoryless game there is no such thing as a winning streak or losing streak (these notions are gambler's fallacy) so this strategy can't improve the expected winnings in such situations.
One activity where money management based on an anti-martingale approach has a recognized value[2] is speculation and trading. Many financial markets have some cyclical component to them, and the approach of an individual speculator or trader may only be appropriate for one portion of that cycle. Using an anti-martingale risk management scheme will increase profits during time periods when a trading approach is working well, while automatically decreasing exposure during portions of the cycle where trading is unprofitable. This is believed to decrease the risk of ruin for trading.
Sports betting systems refers to a set of events that when combined for a particular game for a particular sport represents a profitable betting scenario. Since sports betting involves humans, there is no deterministic edge to the house or the gambler. Systems supposedly allow the gambler to have an edge.
Sportsbooks use systems in their analysis to set more accurate odds. Therefore the novice gambler may believe that using a system will always work, it is the general consensus that at some point, the oddsmakers will have adjusted for the system to make it no longer profitable. Very short-lived systems are called trends. Any single event that estimates a selection to have a higher likelihood of winning is called an angle as they are meant to be used in conjunction with other angles and trends to produce systems.
Systems can be deceiving. Any sample space can be constrained enough with meaningless criteria to create the illusion of a profitable betting system. For example, a coin can be flipped with heads being home teams and tails being road teams. Heads and tails each have a 50% probability of landing but if the amount of flips is limited to a small number, it is conceivable to create the illusion of predicting heads will come up 75% of the time.
That, in conjunction with the fact that sportsbooks adjust their odds according to the systems makes it difficult to follow systems indefinitely. The sportsbooks are slower to adjust the odds in some sports versus other sports depending on the number of games played and the amount of money they take in from bettors.
[edit] Determining systemsDetermining systems is a matter of using computer analysis tools and extracting all the possible games that meet a bettor's criteria. Then the bettor analyzes the results of those games to make a determination if one team is favored over the other.
Factors that are used into determining betting systems are a mix of psychological, motivational, biological, situational factors that, based on past performances, support one team over another. It is generally believed that more than one factor pointing towards a team is needed to have a successful betting system.