Betting Systems - FAQ

You've omitted two important details: the size of your bets and which game you’re playing. I'll assume your bets are consistently $1 on the Player in baccarat. baccarat The chance of the player winning, excluding any ties, stands at 49.3212%.

Let a_iLet’s define the probability: if the player has $i, what are the chances he will achieve $1,200 before depleting his funds? Denote p as the probability of winning any given wager, equal to 49.3212%.

a₀= 0

a₁= p*a₂
a₂= p*a₃+ (1-p)*a₁
a₃= p*a₄+ (1-p)*a₂

.

a₁₁₉₇= p*a₁₁₉₈+ (1-p)*a₁₁₉₆
a₁₁₉₈= p*a₁₁₉₉+ (1-p)*a₁₁₉₇
a₁₁₉₉= p*a₁₂₀₀+ (1-p)*a₁₁₉₈
a₁₂₀₀= 1

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Divide the left side into two parts:

p*a₁+ (1-p)*a₁= p*a₂
p*a₂+ (1-p)*a₂= p*a₃+ (1-p)*a₁
p*a₃+ (1-p)*a₃= p*a₄+ (1-p)*a₂
.
.
.
p*a₁₁₉₇+ (1-p)*a₁₁₉₇= p*a₁₁₉₈+ (1-p)*a₁₁₉₆
p*a₁₁₉₈+ (1-p)*a₁₁₉₈= p*a₁₁₉₉+ (1-p)*a₁₁₉₇
p*a₁₁₉₉+ (1-p)*a₁₁₉₉= p*a₁₂₀₀+ (1-p)*a₁₁₉₈

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Reorganize the equation such that (1-p) terms are to the left and p terms to the right:

(1-p)*(a₁) = p*(a₂- a₁)
(1-p)*(a₂- a₁) = p*(a₃- a₂)
(1-p)*(a₃- a₂) = p*(a₄- a₃)
.
.
.
(1-p)*(a₁₁₉₇- a₁₁₉₆) = p*(a₁₁₉₈- a₁₁₉₇)
Next multiply both sides by 1/p:₁₁₉₈(1-p)/p*(a₁₁₉₇) = (a₁₁₉₉- a₁₁₉₈)

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(1-p)/p*(a

- a₁) = (a₂- a₁)
(1-p)/p*(a₂- a₁) = (a₃- a₂)
(1-p)/p*(a₃- a₂) = (a₄- a₃)
.
.
.
(1-p)/p*(a₁₁₉₇- a₁₁₉₆) = (a₁₁₉₈- a₁₁₉₇)
Next telescope sums:₁₁₉₈(a₁₁₉₇- a₁₁₉₉) = (1-p)/p*(a₁₁₉₈)

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+ (1-p)*a

= p*a₂+ (1-p)*a₁p*a₁)
+ (1-p)*a₃= p*a₂+ (1-p)*a²(1-p)*(a₁)
) = p*(a₄- a₃(1-p)*(a³- a₁)
.
.
.
) = p*(a₁₁₉₉- a₁₁₉₈(1-p)*(a¹¹⁹⁸- a₁)
) = p*(a₁₂₀₀- a₁₁₉₉(1-p)*(a¹¹⁹⁹- a₁)

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) = p*(a

- a₁₂₀₀Next multiply both sides by 1/p:₁(1-p)/p*(a₁) = (a²- a³(1-p)/p*(a¹¹⁹⁹)

- a₁) = (a²- a³(1-p)/p*(a¹¹⁹⁹)

- a₁) = (a²- a³(1-p)/p*(a¹¹⁹⁹)

- a₁) = (a¹²⁰⁰- a

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(1-p)/p*(a₁- a₁₀₀₀:

) = (a₂- a₁Next telescope sums:₁)
(a₃- a₂) = (1-p)/p*(a²+ (1-p)*a₁)
= p*a₄+ (1-p)*a₃p*a³+ (1-p)*a₁)
.
.
.
= p*a₉₉₉+ (1-p)*a₁₈(1-p)*(a⁹⁹⁹⁸) = p*(a₁)
- a₁₀₀₀(1-p)*(a₁₉- a⁹⁹⁹⁹) = p*(a₁)

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- a

(1-p)*(a₁₀₀₀- a₁) = p*(a₁- a²(1-p)*(a³- a⁹⁹⁹)
) = p*(a₁₀₀₀- a₁Next multiply both sides by 1/p:¹⁰⁰⁰(1-p)/p*(a
) = (a₁₀₀₀- a¹²⁰⁰(1-p)/p*(a¹⁰⁰⁰- a
) = (a₁₀₀₀- a¹⁰⁰⁰(1-p)/p*(a¹²⁰⁰ - 1) = 0.004378132.

Over a sufficient period, players are likely to find their luck evening out in games of chance, leading to a gradual decline in their bankroll. However, larger bets would substantially enhance the odds of winning. Below are the chances of winning 20% before facing a total loss at various betting amounts.

$5: 0.336507
$10: 0.564184
$25: 0.731927
$50: 0.785049
$100: 0.809914

If you're interested in the mathematical intricacies of this issue, please refer to my - a ) = (a

(1-p)/p*(a

In your situation, if we assume you’re playing a game with negative expected value, the optimal bet size to maximize your chances of reaching your profit goal would be $50. Conversely, in a game with a positive expected value, you should bet the smallest amount possible. This is because the more you play, the more the house edge can wear you down, or conversely, you can erode the casino's advantage if you hold the edge.

Ultimately, this approach to managing money will neither be beneficial nor detrimental in the long term. While cutting your losses and calling it a day could prevent missing a potential recovery, leaving the table with a modest win may inhibit turning it into something larger. Of course, outcomes can also worsen. In general, consider that prior rounds don’t influence future ones, and every session is a fresh start. To enhance your chances, the key is reducing the house edge as much as possible. I support the practice of money management, but it doesn't impact the house edge itself.

There are numerous systems available, and their practical efficacy is questionable.

- a

As I’ve mentioned often, all betting systems tend to yield the same shortcomings in the long haul.

No, the number of hands played doesn't alter the house edge. The anticipated loss correlates directly with the house edge, average bet size, and total number of bets placed.

You got it! In fact, the strategy claimed a 7.94% edge. I'll adjust that and propose an 8.00% edge. Here’s the 'Wizard's 8.0% Advantage System'—here’s how to utilize it.

1. This strategy can be applied to any game with even money payouts, including roulette, although craps is highly recommended because of its lower house edge.
2. The player only engages in even money bets. In roulette, any even money wager is acceptable, and players can adjust their bets at any time (remember that past outcomes do not influence future results).
3. The player should be comfortable with a betting scope of 1 to 1000 units.
4. ) = (1-p)/p*(a
5. After each wager, the player will calculate 8.1% (an additional 0.1% acts as a margin of safety) of all previous bets. If their net winnings are below this figure, they will bet either the difference or a maximum of 1000 units. If their net win exceeds that threshold, they will stake just one unit.
6. (a

In a simulated roulette experiment I conducted 10,000 times, the player successfully achieved the 8.0% target in 4236 instances and failed in 5764 cases. Thus, during a live session, it’s quite likely the player might report a success story. In a game of craps, using the same strategy for betting on the pass line led to 6648 victories and 3352 defeats, translating to a success rate of 66.48%. In the roulette simulations, with a betting range from 1 to 10,000 units, the wins totaled 8,036 against 1,964 losses. In each of these instances where the system fell short over 7,500 spins, the losses were significant, exceeding 8.0% on average.

Of course, this system has the same limitations as others. My main point is that while it’s relatively simple to devise a strategy that often succeeds, the losses can be severe when they occur. Over the long term, the losses will outstrip the wins, resulting in a reduced bankroll.

I appreciate your kind words! It must have taken quite a bit of time to absorb everything on my site. Here’s the distinction: you’re conflating betting systems, which are ineffective, with genuine strategies that provide players a competitive edge. Two examples of games that can be consistently beaten when played with favorable rules and the right strategies are blackjack and video poker. I view a 'system' as a futile method of following trends in games with a built-in house advantage; on the other hand, a 'strategy' involves approaches like card counting in blackjack, which is mathematically validated. Video poker can be outmatched by finding the optimal pay tables and adhering to a reliable strategy regarding which cards to keep and which to discard.

Thank you! It’s true, I’ve mentioned that with a system offering a mere 1% advantage, transforming $1000 into $1,000,000 by leveraging that edge could be plausible. The same principle applies to video poker, though accumulating that sum would take considerably longer. The 0.77% edge (found in full pay deuces wild) is a quarter-level game. If we assume you can play 1000 hands per hour—an impressive speed few achieve—and play optimally, it would yield an average of $9.63 per hour. To reach $1,000,000 would ultimately demand 11.86 years of continuous play. Moreover, starting with just $1000 is quite undercapitalized for quarter-level video poker games, leading to a significant risk of losing everything. Achieving $1,000,000 would be quicker in table games where you can wager larger amounts.

I couldn't express it better myself.

Absolutely not! Betting systems won’t help you overcome the house advantage; in fact, they won't even make a noticeable difference to it. Their only effect is to change the level of volatility in the game. If you're someone who enjoys a game full of swings and excitement, then it's safe to say your chosen system is doing its job. Just remember not to rely on it for consistent wins.

I’ve said this countless times: there isn’t a specific number that defines when ‘long run’ begins. However, the more remarkable your results, the fewer attempts are necessary to demonstrate they're not random. In your situation, achieving a success rate of 54.5% across 2391 games is roughly a 1 in 200,000 chance. Therefore, I would argue that this record deserves serious consideration. Here’s how I reached that conclusion:

) = ((1-p)/p)
*(a
(a
The calculation for standard deviations from the expected outcome is: (107.5 + 0.5) / 24.45 = 4.4174.
The probability of achieving 4.4174 standard deviations or greater is: normsdist(-4.4174) which equals 0.000005, translating to 1 in 200,000.

To conduct a direct testing of your system, I would charge $2000 as that reflects the value of my time for the evaluation. Offering $20,000 for passing the challenge is virtually costless for me since the likelihood of winning is statistically negligible.

Personally, I don’t find Parrondo’s paradox that captivating, but since many people have asked me about it, I’ll share my insights. The essence of the paradox is that by shifting between two specific losing games, a player can end up with an edge.

For instance, in Game 1, the odds of winning $1 are 49% while losing $1 is 51%. In Game 2, if the player’s bankroll is divisible by 3, their chances of winning $1 drop to 9%, while the chances of losing $1 rise to 91%. Conversely, if the bankroll isn't divisible by 3, they have a 74% chance to win $1 and a 26% chance to lose $1.

Clearly, Game 1 has an expected outcome of 49% * 1 + 51% * -1 = -2%.

In Game 2, computing a simple weighted average for the two scenarios isn't feasible. That's because a win shifts the player's bankroll to a remainder of 1, often oscillating between remainders of 0 and 2. Essentially, this results in the player predominantly engaging with the 9% winning chance version. Overall, when playing Game 2 alone, the expected value comes out to -1.74%.

However, by alternating between two rounds of Game 1 and two rounds of Game 2, we disrupt that alternating cycle. This means the player gets to engage more with the 75% winning chance game while reducing exposure to the 9% game. There are countless ways to combine the two strategies. A tactic that alternates 2 rounds of Game 1 and 2 rounds of Game 2 and repeats can lead to an expected value of 0.48%.

I should stress that this has no practical advantage in a casino environment. No casino game modifies its rules based on how the player's bankroll is configured. Nevertheless, I suspect it’s only a matter of time before someone introduces a betting system based on Parrondo's principle, alternating between roulette and craps, which will undoubtedly turn out to be just as ineffective as all other betting systems.

I frequently receive variations of this type of inquiry. The reality is I've developed hundreds of simulations myself, primarily using C++ to suit my purposes. Most people seem to be looking for tools to assess betting strategies. Unfortunately, I don't have access to any program that allows users to input a betting strategy and evaluate it. If a tool like that existed, it would likely reinforce my assertion that all betting systems ultimately fail.

I have to disagree with you, particularly regarding your reasoning. Under your scenario, yes, most players would leave Vegas as winners. However, some individuals could lose their initial wager and just sink deeper into debt with continued play, ultimately depleting their bankrolls. If we maintain the same game and strategy, the house advantage remains constant, irrespective of any money management approaches. Simply put, betting systems can't beat the house edge; they don't even come close. To circle back to your point, if everyone quit gambling once they were up, the volume of gambling would significantly decrease. Although the house edge would still apply, it would be enforced on a lower amount, negatively impacting the casinos.

Certainly! Over an extended period of gameplay, 99.9% of those who rely on systems will incur losses, while only 0.1% will walk away believing it was skill when, in reality, it was nothing but pure luck.

You're on point. In the long term, betting strategies and the reasons behind bets become irrelevant. With a finite bankroll, the probability of experiencing ruin is high. Yet, there’s a ceiling on potential losses while the potential gains are nearly limitless. Eventually, everything balances out, and casinos generally profit close to their predictions based on bets placed and the house edge.

I’ve discussed this previously, and I don’t agree with your theory. As I've repeatedly stated, every betting system is doomed to fail. If a casino had zero house edge, it wouldn't have a long-term gain or loss. Let's say every player aimed to win $1,000,000 or bust in the attempt. While most would ultimately lose, the few who succeeded in winning $1,000,000 would balance it out.

I attempted to create an account on that platform, but they block users from the U.S. I’ve heard the minimum bet is £2 and the maximum is £50. Even in a zero house edge setup like no-zero roulette, there still isn’t a betting strategy that can achieve or lower that 0% figure. Ultimately, the more one bets in such a format, the more the actual house take will gravitate toward 0%.

I often field questions along these lines. If you're engaging in a game with a negative expectation—which is nearly always the situation—the best strategy to protect your finances is to avoid playing altogether. But if you're going to play for fun, there’s no definitive quitting point. The more you play, the greater your expected loss from your current bankroll. As I’ve mentioned frequently, a good moment to step away is when you’re no longer having fun.

Indeed, while there's no betting system that can alter the house advantage, individuals can employ these systems to enhance their chances of meeting their trip goals. Player A aims to keep risk at a minimum; therefore, placing flat bets would be the optimal choice for him. Conversely, Player B seeks a higher likelihood of winning during his trips, so he should consider increasing his bets following a loss. However, this approach entails the risk of a sizeable loss. You didn't ask this, but for a player wishing to either incur minor losses or have the chance for a substantial win, pressing bets after a win can be effective. While this strategy generally results in losses, it has the potential for larger payouts every so often.

I appreciate your kind words. I believe I may have addressed this topic previously, but even in the absence of a house edge, no betting system can guarantee long-term success.

You're welcome. Your history professor is mistaken. The 'little win' approach is not a new concept. While it commonly results in minor wins, the potential for substantial losses often wipes out those gains. To directly respond to your inquiry, interpreting 'better odds' can vary in meaning. If you’re referring to which method yields the highest average balance, it really doesn’t matter. The expected loss remains constant, whether you place one single bet of $1,000,000 or a million individual bets of $1 each, assuming you use basic strategy and have enough reserve funds to double or split. However, if you’re considering which option provides a greater probability of ending up with a profit, a single bet is statistically much more favorable. Making one million bets of $1 results in an anticipated loss of $2,850, with a standard deviation of $1,142, only giving a 0.6% chance of breaking even. By contrast, placing one bet of $1,000,000 gives you a 42.4% chance of winning, an 8.5% chance of a push, and a 49.1% chance of incurring a loss.

Thanks for your question. I receive similar inquiries often. Generally, I tend to disregard them, but since you’ve been so complimentary, I will respond this time. As I've mentioned repeatedly throughout my site, all betting systems are fundamentally flawed. There is no definitive point at which one should stop betting. While I have no objection to setting win or loss limits as a quitting factor, the expected value doesn't improve or decline compared to playing without any restrictions. Moreover, I've heard that there are systems capable of simulating what you’re looking for. Lastly, regarding Blackjack, your decision to hit or stand should not be influenced by the size of your wager. The correct decision for a $1 bet should also apply to a wager of a million dollars. 1 = a This question seems to delve into a theoretical business inquiry. If you were to develop a betting system that actually produced positive results and considered marketing it, how would you approach pricing this product? I want to clarify that I'm not suggesting, implying, or arguing anything; I'm merely seeking your business advice on how to price this.

You mentioned that prolonged gaming will cause our losses to move closer to the negative expected value represented by the house edge. So, doesn’t it stand to reason that if we played with perfect logic, we'd always place our entire bankroll on one single wager to avoid this gradual loss? This is similar to the advice given by Bluejay.

However, if enjoyment factors into your gambling experience, then making smaller bets over a more extended timeframe can yield more satisfaction. If your only goal is to minimize your anticipated losses, the best approach may simply be to refrain from playing altogether.

The segment on the Discovery Channel’s 'Hustling the House' focused on the optimal method for expanding $30 into $1,000. Andy Bloch asserted, \"If you have $30 and aim to convert it into $1,000, roulette is your only option.\" Andy elaborated on why betting the entire $30 on a single number offers better chances compared to repeatedly betting on even-money options.

After considerable experimentation, I crafted my own 'Hail Mary' roulette strategy, which adjusts the odds for turning $30 into $1,000 to 2.8074%.

Here's the Wizard’s 'Hail Mary' strategy for roulette:

This strategy assumes all bets are in $1 increments. Always round down in your calculations.

If 2*b >= g, then place a bet of (g-b) on any even-money option.

= 1 / (1 + ((1-p)/p) + ((1-p)/p)
+ ((1-p)/p)
+ .. + ((1-p)/p)

1. Otherwise, if 3*b >= g, then wager (g-b)/2 on any column.
2. Additionally, if 6*b >= g, then stake (g-b)/5 on any six numbers.
3. If 9*b >= g, then bet (g-b)/8 on any four-number corner.
4. If 12*b >= g, then wager (g-b)/11 on any three-number street.
5. If 18*b >= g, then bet (g-b)/17 on any split of two numbers.
6. Finally, if none of the above apply, place (g-b)/35 on a single number.
7. In essence, always strive to meet your goal with just one bet, if feasible, without going over your target. If multiple options exist for this, choose the one with the highest winning probability.

You may wonder about other games. The narrator from the Discovery Channel claimed, \"Everyone agrees that roulette is the fastest route to wealth in the casino.\" However, I disagree. Even when constrained to common games and regulations, I believe craps offers better opportunities, particularly when betting on the don’t pass and laying odds.

By following my Hail Mary technique for craps (detailed below), the probability of turning $30 into $1,000 is elevated to 2.9244%. This is based on the assumption that players can lay 6x odds regardless of the current point (which is applicable when 3x-4x-5x odds are allowed). This probability exceeds my roulette Hail Mary strategy by 0.117% and surpasses Andy Bloch’s strategy by 0.2928%.

Andy might counter that my calculations rest on the assumption of a minimum $1 bet, which can be hard to find in live dealer games in Vegas. Anticipating potential skepticism, I also analyzed both instances under the premise of a $5 minimum betting requirement, with increments of $5. With this setup, the probability using my Hail Mary strategy is 2.753% for roulette and 2.891% for craps—both exceeding Andy Bloch's 2.632% success rate.

I'm not questioning the idea of achieving success in gambling through various systems long-term, as we all know that's not feasible. However, could these systems potentially enhance the experience of losing? Take for instance Player A, who enjoys going to the casino and would rather come away with minor wins or losses each time, albeit slightly losing more than winning. On the other hand, Player B seeks a setup where he can win a little on four out of five visits but is willing to endure a significant loss on just one occasion.

Both players will ultimately lose money over time, but is there a betting method that could help each individual meet their preferences?

Indeed. Betting systems won't alter the house's advantage, but they can assist in achieving specific trip objectives. Player A, who wants to keep risks minimal, should opt for a flat betting approach. Conversely, Player B, who leans towards a higher chance of winning during his trips, would benefit from increasing his bets after experiencing a loss. This strategy carries a higher risk of significant losses. Additionally, while you didn't inquire about it, a player aiming for modest losses or significant wins after a win should increase their bets following a successful round. This tactic tends to lose more often, yet it can occasionally lead to substantial gains.

I'm a dedicated follower of your newsletter and continue to appreciate your website. Recently, I encountered an online casino that features a version of roulette where the wheel lacks any zeros, featuring just numbers 1-36, while all traditional roulette regulations still apply. Do you perceive any tactical advantages here? I understand your skepticism towards betting systems, but in this case, there’s no embedded house edge. Surely, there must be a viable money management strategy compatible with these table limits. Your insights would be invaluable.

a
= ((1-p)/p - 1) / (((1-p)/p)
- 1)

1. Now that we know a
2. I appreciate your kind feedback. I believe I might have addressed this in the past, but to clarify, even a zero house edge doesn't imply that a betting system can secure victory over the long haul.

Thank you for the wealth of knowledge available on your site. I am currently serving in the Air Force and preparing to conduct a seminar on responsible gambling.

During class, my history teacher at NMSU insisted that the sole method to win at Blackjack is to make small bets periodically and leave with minor profits, like $25. This rationale doesn't align with my understanding; I believe it's inaccurate. My inquiry is this: assuming I have a lifetime gambling budget of $1,000,000, am I statistically better off wagering the entire sum on one Blackjack hand versus betting smaller amounts? Are the odds the same in both scenarios? Your website is fantastic, and please keep up the great work. Thank you for your assistance! we can find a .