Anti Martingale Blackjack

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 if it 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.

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Since a gambler will almost surely eventually flip heads, the martingale betting strategy is certain to make money for the gambler provided they have infinite wealth and there is no limit on money earned in a single bet. However, no gambler possess infinite wealth, and the exponential growth of the bets can bankrupt unlucky gamblers who chose to use the martingale, causing a catastrophic loss. Despite the fact that the gambler usually wins a small net reward, thus appearing to have a sound strategy, the gambler's expected value remains 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. Additionally, as the likelihood of a string of consecutive losses occurs more often than common intuition suggests, martingale strategies can bankrupt a gambler quickly.

The martingale strategy has also been applied to roulette, as the probability of hitting either red or black is close to 50%.

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]

However, without these limits, the martingale betting strategy is certain to make money for the gambler because the chance of at least one coin flip coming up heads approaches one as the number of coin flips approaches infinity.

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

${\displaystyle \sum _{i=1}^{n}B\cdot 2^{i-1}=B(2^n-1)}$

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 10/19 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.

Martingale System Blackjack

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]

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, also known as the reverse martingale, 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.)

Anti Martingale Blackjack

See also[edit]

Martingale Blackjack Simulator

References[edit]

1. ^ ^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
2. ^Lester E. Dubins; Leonard J. Savage (1965), How to gamble if you must: inequalities for stochastic processes, McGraw Hill
3. ^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
4. ^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.

The Martingale system of staking is a betting strategy which requires you to double your bet on a losing wager. It’s one of the simplest and most famous staking plans in the world of gambling. Also, it requires even odds bets – which seems perfect for playing online blackjack. However, there is a lot more to this blackjack strategy worth discussing.

How does Martingale Work in Blackjack?

For the sake of the beginners among us, let’s start with the basics. We’ll go over a simple step-by-step process you’ll need if you want to know how to use Martingale in blackjack.

1. Start with the minimum stake and play blackjack as you would normally.
2. If you win, just repeat the previous step.
3. If you lose, double the previous stake and play again. If you keep losing, you’ll have to double up each time.
4. As soon as you win another hand, go back to the initial stake.

The main idea of Martingale betting is to prevent any kind of loss. It’s simple, really – at odds of 1:1, doubling your stake will make up any losses made previously. That’s why this strategy only works with even odds bets – you need roughly 50% chances for Martingale.

The main disadvantage of this strategy should be fairly obvious. A short losing streak will result in the stake growing exponentially. If you don’t have to bankroll to support this kind of bet, you could end up losing everything. Two things have been done to mitigate this disadvantage.

Firstly, that’s why we start with the minimum bet. If you have the cash to support more, go for it by all means. Just be aware that just 5 losing hands will multiply your stake by 32. Additionally, that’s why the stake resets back to the minimum each time you win.

Can Martingale Beat Blackjack?

This is a tricky question to answer. Sometimes, beginners get the impression that Martingale betting is a sure-fire way to beat the casinos. This is simply a myth, and the reason is the main driving force behind all gambling – statistics.

In a perfect scenario, the Martingale could guarantee success. In this case, the perfect scenario would involve a casino with 0% house edge and unlimited time and money. Since all of those are impossible, the Martingale does not guarantee that you will win in blackjack.

Here’s the gist. Martingale relies on the fact that every bet has a 50% chance to win and 1:1 betting odds. Because of how the house edge works, though, the chance to win is never strictly 50%. It’s pretty close in blackjack compared to other casino games, but “close enough” doesn’t cut it in the long run.

Although you’re protecting yourself from a loss, the more you play, the closer the winnings will be to your losses. Now you might think that not losing is the next best thing to winning, right? Well, yes. However, there is always a small chance of losing too many consecutive hands. At some point, your bankroll is going to run dry. At that moment, you’ve spent a bunch of games not losing or winning, and then you suddenly lose it all.

Should I Use Martingale in Blackjack?

What we wrote above doesn’t necessarily mean you should always stay away, though.

Top online casinos offer a less than 1% house edge on blackjack, for example. That way, you can keep betting using Martingale for quite a while and maintain the same bankroll. It’s a lot of effort for negligible returns, of course, but it could be used to practice blackjack.

Secondly, you could also combine it with other strategies such as card counting. Despite its shortcomings, martingale can be used for proper bankroll management. This is one of the most important things to keep in mind when gambling.

Anti Martingale Blackjack Trainer

Hopefully, we’ve cleared up any questions about using Martingale for blackjack.