Roulette Double Down Method

admin 4/12/2022

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%.

The Paroli System. The Paroli System uses the Martingale strategy referenced above but in reverse. In other words, instead of doubling your bets when you use, you double-down when you win. So, if you bet $5 in Round 1 and you lose, you’d bet $5 in Round 2. If you win in Round 2, you’d bet $10 in Round 3.

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]

For more on the martingale system and the best sign up bonuses go here The Martin.
Many gamblers still swear by this method and use it in casino games such as roulette. But does the bet doubling strategy work in reality? This article takes a look at this gambler's strategy that, while sound in its mathematical accuracy is seriously flawed in its expectations.

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

{displaystyle sum _{i=1}^{n}Bcdot 2^{i-1}=B(2^{n}-1)}

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

{displaystyle (1-q^{n})cdot B-q^{n}cdot B(2^{n}-1)=B(1-(2q)^{n})}

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 2^k 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.

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.)

References[edit]

^ ^a^bMichael 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.

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Lightning Roulette is very similar to European Roulette but it adds some unique, innovative twists to make the game even more exciting. For example, the studios in which the games are held aren’t like what you’d expect from your typical Live Roulette session. It acts more like a TV game show with the dealer being the host.

The rules of the game are easy to understand. As usual, place a bet on an individual number, groups of numbers or groups of colors. Once the wheel is spun and bets are no longer allowed, the dealer pulls a lever and all the panels on the wheel are struck by lightning, randomly choosing 1 to 5 lucky numbers in the process.

Straight-up bets on the lucky numbers can win between 50x and 500x your wager amount, depending on how many are drawn. So, with this in mind, here are 4 Lightning Roulette strategies to help you get the most from your bets.

1. Basic Lightning Roulette Strategy

Since the big wins from lucky payouts can only be achieved through betting straight-up, one really basic roulette strategy to use is just betting on every number.

While this increases your overall risk, if the lucky numbers do land, you can be rewarded with a huge payout.

The increased risk factor means that, though it’s the most basic possible strategy out there, it’s not one that too many people consider.

Now, it’s important that you don’t double your bets on losing rounds to cover your losses. Since you’re covering the entire roulette wheel, losing just 2 or 3 rounds in a row will put a large dent in your bankroll with this strategy.

Best Roulette Method

For reference, this type of betting is used as part of the Martingale strategy on European Roulette games – it usually covers just betting on red or black rather than betting every number.

2. The Paroli System

The Paroli System uses the Martingale strategy referenced above but in reverse. In other words, instead of doubling your bets when you use, you double-down when you win. So, if you bet $5 in Round 1 and you lose, you’d bet $5 in Round 2. If you win in Round 2, you’d bet $10 in Round 3. If you win, you’d bet $20 in the next, but if you lose, you’d go back down to $5.

This Lightning Roulette betting strategy assumes you will go on a hot streak and aims to capitalize big when that happens. In this particular game, you also have the massive roulette payout multipliers as an advantage too. Of course, you must stick to betting straight-up to be eligible for the big multipliers.

3. La Bouchere Strategy

As you will note by its name, this particular strategy comes from France, the birthplace of roulette, and works at its best with virtual chips in live dealer games.

But before going any further, this strategy does not make use of the lucky numbers.

Now, in order to get the maximum from La Bouchere, you must divide your chips in a particular method, which is as follows.

Firstly, spread your chips out in either one or two lines. Not all only casinos allow you to actually do this so you need to find one that will. Then use the first and last numbers in those lines to help determine how much to stake. In an ideal world, you will have a line of numbers that look something like 6, 8, 4, 2 and 2.

If the first number is 6 and the last number is 2, you would add 6 and 2 together to make a wager worth 8 virtual chips. Then choose the next first number, which is assumed to be 8 in this example. You would then add 8 to the 2 on the other side, meaning you would make another bet of 10 virtual chips on that line.

This strategy aims to ensure you will have made an even number of bets by the time you finish your session.

The important thing to note here is that you should be looking to make bets that give you as close to a 50% chance of winning as possible. The more you can get it even, the more likely you can come out of the game in profit. And, since you’ll be making “50/50” bets, you can always keep playing until you make a profit. After all, a small win is better than a big loss.

4. Betting With Bonuses

The final Lightning Roulette strategy you’re not aware of uses bonuses as part of your bankroll to increase your profits quickly.

It’s a simple idea but still goes under the radar. All you have to do is find a list of the real money roulette games with Lightning Roulette in their libraries and ensure you can get a bonus to play it.

There are plenty of casinos available now that will give you a bonus just for registering or making a deposit. There are even some that give you weekly or monthly rewards for playing regularly.

So, by having multiple ways to claim bonus funds, you can play through several rounds of Lightning Roulette and make some money without playing with your own.

The only catch is that casinos don’t give this money to you without wanting something in return. Every bonus you claim will have some rules determining how you can withdraw your winnings. For example, some casinos make you wager 35x your deposit amount before you can withdraw. It’s even higher in others, but this is stop cheaters and people taking the money and running.

Make sure that you always read the terms and conditions on the bonus before claiming and use those that make it simple to withdraw.