Depending on which variation of roulette a player has chosen (European or American), there are either 37 or 38 pockets on a roulette wheel. This is exactly why a large number of players would like to place their bets on as many numbers as possible.
Some players think that covering every pocket at the wheel or betting an equal amount on Red or Black would help them, but the truth is that they would not be able to win. This is exactly why most players are looking for some betting system that would help them generate a profit without risking too much.
All right I saved the best betting system for last but I have to tell you that you won’t find this option at most roulette games. That’s sad because it really helps the savvy player hang in the game. On the even-money bets of red/black, odd/even, and high/low some casinos will only take half your bet on these should the 0 or 00 hits. Apr 25, 2013 Real world stats: How (not) to win at roulette. With this strategy, I would not use RED/BLACK but columns, lines etc. Also, I would use a roulette software to keep track of the statistics as the results progresses. The problem with roulette is that you can’t use a counting strategy as all roulette statistical events are.
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The 3/2 roulette betting system is exactly what would help them in such cases. It is considered as a healthy compromise that provides players with the chance to cover as many pockets of the wheel as they can without sacrificing too much. This is exactly why the 3/2 roulette betting system is considered relatively more flexible when compared to other roulette systems, not to mention the fact that it allows players to keep their bet sizes constant.
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How Does the 3/2 System Work?
In fact, there are two opposite ways that could be used to play the 3/2 betting system. The first way is for the player to bet two units on the second column of numbers and also bet three units on Red section. The second way is to bet two units on the third column of numbers as well as three units on Black section.
No matter which way a person would choose, they would be given the chance to bet a 3/2 ratio on both a colour and a column. Choosing between the two betting options is all the system requires, but the player should make a decision how much they would like to wager. The fact that the 3/2 betting system allows customers to cover the majority of numbers on the roulette table is actually a great advantage in comparison to other systems, since it greatly increases the chances of a player to win.
The only objective of the 3/2 betting system is to allow player's wagers to cover as many pockets of the roulette wheel as possible. This is the way how the number of outcomes that could generate a winning is increased, which means players have better odds against the roulette by covering about 70% of the wheel.
Ascot Betting System
Oscar's Grind Betting System
3/2 Betting System
Shotwell Betting System
Pivot Betting System
In fact, the 3/2 betting system provides players with serious benefit, as customers are given the chance to cover a large part of the wheel by making two normal bets at a ratio 3/2. In case a player has decided to choose the American roulette variation, which is with greater house edge due to the extra 00 pocket, each of the bets made with the 3/2 betting system has a 5.26% house edge on its own. So, by using the system, players would be provided by more action, including winnings and losses, but they would not be given an actual statistical advantage, as roulette is, after all, a game of luck.
Players are actually dealing with simple outside bets, which is why some casino customers prefer to combine 3/2 betting system with another roulette betting system, which could turn out to be a successful move.
The 2 to 1 Columns Plus Red Strategy
The 2 to 1 Columns Plus Red Strategy resembles the 3/2 betting strategy a lot. However, players are required to place bet of an equal stake on the first two columns and on the outside red-coloured numbers. There are more red colour results in the third column of the roulette table layout that has not been covered and which is exactly why the strategy does work.
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Players are also recommended to spin the roulette wheel multiple times (at least ten times) with the same wager. Such actions increase player's chances of winning with each spin to about 87% thanks to the large number of red colour results included in the third column that has been left uncovered. The truth is that the 2 to 1 Columns plus Red strategy brings very low risks for the player but it is quite time-consuming.
The 2 to 1 Columns plus Red betting strategy has a series of advantages that make it one of the most popular ones among other roulette strategies. It offers a high probability of winning on every single spin, which means that really big losses are practically eliminated as an option. In addition, the strategy brings relatively low risks, especially to other roulette betting systems such as the Martingale, for example.
In addition, the 2 to 1 Columns plus Red provides players with the chance to enjoy playing for quite some time eliminating the high risk of making large losses, primarily due to the fact that the odd are in the player's favour with every spin.
Unfortunately, this betting system has two major disadvantages. First, it could be quite time-consuming, and second, usually, it would not help players generate large winnings quickly.
The Red and Black Betting Systems
The Red and Black roulette betting strategies are considered quite simple, actually, but they are still quite effective ones. These two betting systems would be useful especially to players who do not have large money balances at their disposal, unlike other strategies such as the Martingale, which requires the player to double the stakes that they have already lost.
The Red Betting System
The Red system originates from the 1960s. The system is based on the concept that there are a total of eight red numbers and only four black numbers situated in the third column of the roulette table layout.
The system is considered a simple, but efficient enough in order to help players generate a winning and limit their losses. This system requires from players to place a one-unit bet on the third column and a two-unit bet on the colour black.
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In fact the Red betting system does not help players gain any real edge over the house. Still, the system could be set up by using a negative betting progression, but some gaming experts would not recommend players to do that.
The Black Betting System
The Black system is much like the Red Betting System. It is based on the concept that there are eight black numbers and only four red numbers located in the second column of the roulette table layout.
So, instead of betting on the third column and colour black as they should be when using the Red Betting System, now players are recommended to place their wagers on the second column and on the colour red. In other words, it is exactly the opposite of the Red system, but just like the latter does not offer a real advantage to the casino players.
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 lots of negative numbers is also always going to 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.
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 .
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.
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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]
How To Win At Roulette
- ^ 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.