The Kelly Criterion is a mathematical formula that can be used to make the most of your bets, whether in gambling or investing. In this blog post, we provide you with all the necessary information to understand this concept. We'll go over the basic principles and origins and give you simple examples to see how you can apply the Kelly Criterion to your betting tactics.  The Math Behind It? Using the Kelly Criterion is a strategy that balances the risk of losing with the potential for profitability, guiding you to bet a portion of your funds that corresponds to the probability of winning. It was formulated in 1956 by John L. Kelly Jr., a researcher at Bell Labs. Kelly, originally focusing on long-distance telephone signal noise, unexpectedly created a system that found its most significant applications in sports betting and finance.  The core of the Kelly Criterion is its formula, which can be expressed as: f*= bp-qb f*represents the fraction of your bankroll to bet b is the net odds received on the bet (expressed as b:1) p is the probability of winning q is the probability of losing, which is 1-p Simply put, the formula can be expressed as the given odds multiplied by the probability of winning, subtracting the probability of a loss and that total divided by the odds.? Can Kelly Criterion Be Used in Casino Games? The essence of the Kelly Criterion betting is to wager a portion of your bankroll based on your edge in a given wager. However, in casino games, this becomes impractical due to the inherent house edge present in these games. Unlike skill-based betting, where the player can have an edge, online casino games are designed to give the house an advantage. This means that the return to player (RTP) is never 100%, leading to a situation where the Kelly Criterion would consistently suggest a negative betting percentage. Using the Formula in Sports Betting This approach is especially well-suited to making sports bets. If you manage to properly provide values needed for applying the Kelly Criterion formula, you should always get an optimal percentage of your bankroll needed for the bet to be profitable. Here are some examples of how you can use it in different sports.  Kelly Criterion in Football Betting When betting on football, the odds and probabilities can vary significantly depending on the matchup, league, and other factors such as team form, injuries, and historical performance. Let's consider a hypothetical scenario where you're betting on a team with odds of 3:1 (meaning b = 3) and you estimate the probability of your team winning at 50% (p = 0.5). The probability of losing (q) would be 50% (1-p = 0.5).  Plugging these values into the Kelly formula would look like this: f*= (30.5) - 0.53 = 1.5-0.53 = 0.333 This result suggests that you should bet approximately 33.3% of your bankroll on this football match to optimize your bankroll growth. Kelly in Basketball Betting Basketball betting, with its dynamic odds and frequent scoring, presents unique opportunities for applying the Kelly Criterion. Suppose you find a game where the odds are 2.5:1 ( b = 2.5) and you believe the probability of your chosen team winning is 55% (p = 0.55). Consequently, the probability of losing (q) is 45% (1 - p = 0.45). In application, it would look like this: f*= (2.50.55) - 0.452.5 = 1.375-0.452.5 = 0.37 This calculation indicates that you should allocate 37% of your bankroll to this bet. Applying the Formula in Tennis Betting Let's say you're betting on a tennis match. You have odds of 2:1 (so b=2), and you believe the probability of your chosen player winning is 60% (p=0.6). Therefore, the probability of losing (q) is 40% (1 - 0.6 = 0.4). If we use these numbers for the Kelly formula, we get: f*= (20.6) - 0.42 = 1.2-0.42 = 0.4 This result suggests that you should bet 40% of your bankroll on this match for optimal profit growth. Half, Third, and Quarter Kelly Adjusting the Kelly Criterion by betting a fraction of the recommended amount, like half (?), a third (?), or a quarter (?) Kelly, is a common strategy to manage further risks. These variations help in smoothing the volatility in your bankroll while still adhering to the principles of the Kelly Criterion. Here are a couple of reasons why bettors choose to employ this strategy.  Reduced volatility: By betting a fraction (like half) of what Kelly suggests, you reduce the fluctuations in your bankroll, leading to a more stable growth pattern. Less aggressive betting: This approach involves fewer initial bets and can be more suitable for those who are risk-averse or new to using the Kelly Criterion. Balance between growth and safety: Fractional Kelly strategies are the sweet spot between maximizing growth and protecting your bankroll from significant drops. What are Kelly Criterion Calculators?? For those looking to get serious about this strategy, Kelly Criterion calculators are a valuable tool. They simplify the process of determining the optimal bet size, eliminating the need for complex manual calculations. To use a Kelly Criterion betting calculator, you typically need to input the odds of the bet, your estimated probability of winning, and sometimes the total bankroll you are willing to bet. The calculator then uses the Kelly formula to determine the optimal bet size as a percentage of your bankroll. A key feature in many of these calculators is the Kelly multiplier. This is an adjustable factor that allows you to bet a fraction of the amount suggested by the pure Kelly Criterion, often used as a way to reduce risk. As mentioned above, this multiplier can be half, a third, or a quarter. For the full Kelly Criterion number, use a multiplier of 1.  Pros and Cons? The method is primarily aimed at enhancing the long-term growth of your betting bankroll, simultaneously working to reduce the risk of depleting all your betting funds. By using this criterion, bettors make informed decisions and align their betting strategies with the goal of long-term profitability while avoiding the pursuit of immediate, high-risk gains. There are several advantages to using the Kelly Criterion: Guides optimal bet sizing: This is crucial for maximizing the growth of your bankroll over an extended period. Emphasizes risk management: By recommending that only a portion of your bankroll should be placed on any given bet, it mitigates the likelihood of significant losses. Focus on long-term strategy: This makes it an ideal approach for disciplined bettors who are in it for sustainable gains rather than quick, risky wins. However, the Kelly Criterion is not without its drawbacks: Challenging to estimate winning probabilities accurately: Overestimation, for instance, can lead to overly aggressive betting and potential financial setbacks. Complex calculations: This is particularly the case in dynamic betting scenarios, and might demotivate some bettors. Understanding the percentages in Kelly Criterion betting is crucial for effective application. The formula's result, expressed as a percentage, indicates the recommended portion of your bankroll to wager. A positive value implies favorable odds and suggests that a bet is advisable. The higher the percentage, the stronger your edge is perceived, indicating a larger bet. Conversely, a negative or zero value signifies unfavorable odds, advising against placing the bet.  Minimize Your Betting Risk with Kelly Criterion Formula The Kelly Criterion betting approach stands as a beacon for bettors seeking a balanced method of managing their bankroll. This formula is not just about maximizing returns; it's equally focused on minimizing risk, ensuring you don't put your entire bankroll at stake. Its application in betting scenarios, especially in sports betting, is relatively straightforward, making it accessible even for those who are new to this concept.  So, if you're looking to optimize your betting strategy while keeping risks in check, consider implementing the Kelly Criterion to your next wager. It's a step toward more disciplined, calculated, and potentially profitable betting experiences.

If you ask 100 people which city has many casinos, the vast majority will say Las Vegas. The city has been a symbol of gambling ever since the first casinos started operating. However, the question remains—does it rank among the world's largest gambling cities? To answer this, we must consider the criteria for determining a city's status of being the "biggest." Are we evaluating the city's geographical area? Should we examine the annual financial throughput? Or perhaps, is the number of tourists visiting each year the key factor? In this article, we'll highlight the biggest gambling cities in the world based on their contribution to the gambling industry. 1. Macau, China Macau is the only city that might surpass Las Vegas as the top casino city in the world. Like Hong Kong, Macau is a special administrative region of China, operating differently from the mainland. Known as the Monte Carlo of the Orient, Macau's casinos generate substantial revenue. At first glance, Macau, with over 40 casinos, is no match for Las Vegas, especially considering the Strip alone. Yet, Macau is home to 7 of the world's 20 largest casinos, contributing over 50% to the city's economy, such as: Venetian Macao City of Dreams Resort Casino Ponte 16 MGM Grand Macao Sands Macao Starworld Hotel & Casino Wynn Macau Five of these are larger than any casino in Las Vegas. However, StarWorld Hotel & Casino and Wynn Macau are smaller than Las Vegas's biggest—the MGM Grand. While Las Vegas attracts plenty of gamblers, Macau focuses more on high rollers. This strategy has led to Macau surpassing Las Vegas in gambling revenue despite having fewer visitors yearly. 2. Las Vegas, USA When people think of Las Vegas, they immediately think of gambling. The famous metropolis is home to some of the world's largest gambling resorts, such as MGM Grand, Mandalay Bay, Caesars Palace, and Bellagio. Despite economic downturns, Las Vegas has stayed on top of the game and continues to cater to a wide range of visitors. Apart from gambling, tourists have options to visit The Fountains of Bellagio, Park Theater, and The Mob Museum. Las Vegas also stands out for being a large gambling city with over 150 casinos. The distribution of casinos in the main areas of Las Vegas is as follows: The Las Vegas Strip — 31 casinos. Boulder Strip — 32 casinos. Downtown Las Vegas — 12 casinos. North Las Vegas — 19 casinos. This raises the question—what defines a casino? For instance, does a local bar with a few video poker and slot machines count as one? The Nevada Gaming Commission states that establishments with over 15 slot machines or any with table games qualify for "unrestricted gaming licenses." This explains why so many places in Las Vegas are recognized as casinos and why there are so many of them in such a small area. 3. Monte Carlo, Monaco Monte Carlo is widely regarded as the ultimate luxury vacation spot, offering the finest gambling experience coupled with unparalleled glamor and sophistication. Nestled in Monaco, one of the world's smallest countries, this city is a magnet for some of the wealthiest individuals globally. The city boasts several famous casinos, but the crown jewel is undoubtedly the Monte Carlo Casino. This iconic establishment is not just a gambling venue; it's a symbol of style and opulence, making it a must-visit destination for anyone seeking the essence of high-end gambling and a luxurious lifestyle. The principality, famed for its casinos, does not levy personal income taxes on its residents, a policy that extends back to the 1860s. However, Monaco's gambling industry is heavily regulated and taxed by the government. The profits from its casinos, including the renowned Monte Carlo Casino, contribute substantially to Monaco's economy. This strategic taxation and regulation of gambling establishments allow Monaco to maintain its tax-friendly policies for residents while benefiting from the lucrative gambling sector. 4. Marina Bay, Singapore Singapore's economic growth has positioned it as a key player in Asia, and its developing gambling industry is now a notable source of revenue. Despite the relatively recent legalization of casinos, Singapore has quickly made a mark in the gambling world. The Marina Bay Sands, for instance, has rapidly become the largest gambling resort globally. This impressive complex boasts 2,500 rooms, a Universal Studios theme park, and multiple swimming pools, illustrating Singapore's commitment to integrating entertainment and luxury into its burgeoning gambling sector. Singapore's approach to taxes, particularly in the gambling sector, reflects its strategic economic planning. The city-state imposes a relatively high tax rate on its casinos. This tax structure is part of Singapore's broader fiscal policy, which balances competitive corporate and personal tax rates with higher levies in specific sectors like gambling. This balance helps maintain the country's overall economic health and contributes to funding public services, similar to the scenario in Monaco. 5. London, United Kingdom London, renowned as a top tourist destination worldwide, boasts a diverse array of attractions, including historical sites, art museums, and entertainment venues. The city offers a traditional British gambling experience, supported by the UK's sophisticated gambling laws. In London, over 20 casinos cater to a variety of preferences, yet the Empire Casino stands out as the most spectacular. Spanning 55,000 square feet, this British casino features world-class restaurants and bars and an exclusive VIP Dragon Lounge reserved for the most loyal and high-spending guests. 6. Paradise Island & Nassau, Bahamas Considering its proximity and beauty, the Bahamas is an ideal getaway for United States gamblers. This destination is perfect for those seeking a break from daily routines, offering relaxation and ample sunshine. Besides its stunning beaches, the Bahamas is also known for some of the world's most famous casinos, making it a haven for gambling enthusiasts. Key places to visit include Paradise Island and Nassau. This archipelagic state has a rich history in the gambling industry. It has previously hosted the prestigious PokerStars Caribbean Adventure, further cementing its status in the world of poker. 7. Atlantic City, New Jersey, USA Atlantic City is often seen as the less glamorous sibling of Las Vegas, partly due to its historical ties with organized crime. Yet, it remains a popular destination for East Coast Americans looking to gamble without traveling across the country. Despite losing some of its glitz and glamor, it still ranks high in terms of the sheer size of the casinos. Currently, there are nine casinos in Atlantic City, distributed somewhat unevenly throughout the area. In terms of square footage, these casinos are comparable to those in Las Vegas and Macau. For instance, the MGM Grand in Vegas, one of the largest, boasts 171,500 square feet of casino space, which is only slightly larger than some in New Jersey. Given the 27 million visitors Atlantic City receives annually, the casinos are substantial to accommodate this influx of guests. 8. Paris, France Paris, the city of lights, may not be the first place that comes to mind when we think about casinos, but it offers plenty of surprises with its lively gambling scene. The Casino Cercle Haussman, situated near the Opera Garnier at the city's heart, stands out as one of the best gambling spots in Paris. This casino features 25 tables for games like blackjack, punto banco, baccarat, and various types of poker. For a night of high stakes, you can visit the famous Club Barrière, which is located on one of the most exclusive avenues in the world—Champs-élysées. Spend your days exploring Paris's beautiful monuments and your nights experiencing the dazzle of its casinos. 9. Sydney, Australia In Sydney, travelers can effortlessly blend gambling with their road trips, even though the city is famed for cultural landmarks like The Opera House. Among Sydney's hidden gems is The Star, a resort complex featuring a hotel, spa, and casino. This destination attracts tens of thousands of tourists and gamblers annually, marking it as one of the most exciting travel spots. Owned by Star Entertainment, the complex includes two gaming floors. Exclusive areas like the Inner Sanctum are invitation-only and cater to international guests who frequently visit the establishment, adding an element of exclusivity to the gambling experience in Sydney. 10. San Jose, Costa Rica San Jose, the capital and largest city of Costa Rica, is also recognized as one of the world's top gambling cities. The city's casinos are famed for their diverse offerings and affordability. San Jose is home to several renowned theaters and museums with global acclaim, such as The National Theater of Costa Rica, The Melico Salazar Theater, and The Museum of Costa Rican Art. While gambling is a popular pastime here, sports betting also enjoys widespread popularity. For those who enjoy following sports matches or are keen on news about unique athletes, like the tallest soccer player, San Jose offers an engaging experience.

Blackjack is generally considered a game of skill rather than luck, although luck plays a role as well. Therefore, it's important to understand the rules of the game and learn all the strategies you can use to your advantage. One of those strategies is knowing when to split in blackjack, so let's go over the basics. What Does Splitting Mean in Blackjack? It's possible to split two cards of the same number in blackjack, such as fours and eights, and play them like a separate hand. You have to place the same bet on the new hand as the original bet you placed on the first hand. The following is a more detailed explanation of how to play each pair, but you can learn the basics in the following way: Aces and 8s should always be split Don't split 10s Split 4s if you can double on split hands When to Split in Blackjack? It's possible to split any pair of cards in blackjack. The question is, however, whether splitting every time is a good idea. The answer to this question is no. To determine if a split is possible, you need to know the dealer's card. Let's see when can you split in blackjack. If You Get a Pair of Aces It's easier to hit 21 when you have an ace because the deck has many 10-value cards. Therefore, if you get a pair of aces, you shouldn't second-guess your decision to split because any drawn card valued at 10 gives you 21. If You Get a Pair of Eights It's always a good idea to split a pair of eights because you risk busting if you stand or hit. In other words, if you stand, the dealer will likely beat you with a higher total. On the other hand, if you hit, you'll probably bust. However, if you decide to split, you have a high chance of getting a 10, bringing your new total to a hard 18. Furthermore, if you don't get a 10, you have a chance of getting an ace, which results in a total of 19. Finally, even if you get a nine, your total will be 17, which is again a better outcome. When Not to Split in Blackjack? You already have a good hand if you've got nines or tens. With a pair of nines, you have the best chance of beating the dealer. A marginally stronger hand can be made by splitting them if you hit an ace or ten. The same applies to tens. With 20, you have a great starting hand, and it's hard to improve upon if you split. However, you may split high pairs when the dealer's up card isn't good. If You Get a Pair of Fives Most players decide not to split a pair of fives regardless of the number of decks in a game. They know they have a better starting point if they have a 10 as opposed to two pairs with fives. Therefore, instead of splitting, you can either hit or double down. If You Get a Pair of Fours Basically, if you split two fours, there's a high chance of ending up with two 14s, which isn't good for you. The best strategy, in this case, is to hit and hope to get a 10, resulting in a total of 18, which is a far better outcome. The bottom line is that this is a decent hand. Splitting Depending on the Dealer The dealer can also split hands when certain up cards are shown. The following are three examples: Dealer: 2, 3, 4, 5, 6, 7 You: 2-2, 3-3, 7-7 Decision: split You have a better chance of getting a strong hand if you split these. However, take another card if the dealer shows an eight or higher. Dealer: 2, 3, 4, 5, 6 You: 6-6 Decision: split Even if the dealer busts, it's possible to win at blackjack. As a result, splitting 6s is a wise move. A dealer may have to hit again and lose if you draw a 10 to make 16. Dealer: 2, 3, 4, 5, 6, 8, 9 You: 9-9 Decision: split In general, nines are bad for splitting, but they can be good if the dealer gets a strong hand (18, 19) or busts (having to hit on 12, 13, 14, 15, or 16). Blackjack Splitting Rules The best way to learn blackjack split rules is to play at an online or land-based casino. Splitting is just one possible strategy, depending on the cards you're dealt. Keep the following rules in mind before playing: Splitting 10-value cards is only allowed in some casinos if they rank similarly. It's fine to split a 10-10 hand, but not a jack-queen hand. Doubling down and splitting hands may be limited after the first split. If you have a 10-value card on one or both of the aces or an ace on one or both of the tens, they're considered non-blackjack 21. You aren't allowed to hit more than once after splitting aces. Pros and Cons of Splitting in Blackjack Pros: Increases your chances of beating the dealer Splitting doubles your winnings It can turn a bad hand into a decent one It can turn a bad hand into a decent one Your initial hand is at an advantage as a result Cons: If you make the wrong move, you can lose twice as much as you bet Since you'll be doubling your bet, splitting requires a higher bankroll Luck plays a major role in the game FAQ When should you split cards in blackjack? It's always a good idea to split aces because there's a high chance of drawing a 10-value card and reaching a total of 21. Should you ever split 10s? Blackjack players are generally advised not to split 10s and to always stand on 20. This is because card counters sometimes split 10-rich decks. What are the best numbers to split in blackjack? It makes sense to split a pair of aces because there are a lot of 10-value cards in blackjack. A single ace receives a value of 1 if there is no splitting and a double ace gets a value of 11. With a nine, you can only get to 21 on your next card. Should you split 7s in blackjack? Knowing when to split in blackjack sometimes depends on the number of decks used. In multi-card games, it's generally advised to split a pair of 7s when the dealer has cards 2–7. In double-deck games, on the other hand, split a pair of 7s against the dealer's 2–8 if DAS and 2–7 if NDAS.

Dice control stirs up a lively debate in casino circles: skillful strategy or gambler's myth? This concept refers to the practice of throwing dice to influence the outcome of a roll in favor of specific numbers. In this article, we highlight the basics of the strategy, then we look into the controversy and see if there is any truth to controlling dice outcomes or if it is just wishful thinking.  How Dice Control Works Commonly used in the game of craps, the dice control technique goes beyond a simple toss. It consists of a strategic grip, a calculated arm movement, and a precise release, all of which are intended to reduce the dice's random spin and bounce upon landing. The goal is for the dice to hit the craps table in such a way that they roll gently against the back wall, all while maintaining the desired orientation to land on specific numbers more often. This practice stems from the desire to gain an advantage in casino games by using skill to overcome the laws of physics and probability. While skeptics question the reliability of dice control, given the game's inherent randomness, proponents argue that mastering these techniques can shift the odds slightly in a player's favor. Let’s look at what the arguments for and against dice control are next. Yay Sayers of Dice Manipulation The debate around dice control intertwines expert achievements with mathematical analysis. Dominic LoRiggio, known as “The Dominator,” illustrates the power behind controlled throws. His ability to consistently avoid rolling a seven over 70 times demonstrates skill beyond mere chance.  LoRiggio's move to educate both players and casino staff about dice control tactics may indicate its intrigue and acceptance, and some casinos' vigilance towards skilled rollers may reflect the success of this method. This narrative finds further support in a UNLV Gaming Institute study, which explores the minimal level of control needed to effectively counter the house advantage. The research proposes that even slight improvements—identified as just over 8%—in dice control could tip the odds in favor of the player. But is this enough to render the practice a legitimate gambling strategy? Those Who Doubt Dice Control Validity Critics of dice control present two main arguments. The first challenges the foundation of dice control, labeling it as a fundamentally flawed premise. Skeptics point out the absence of definitive proof that anyone can influence dice outcomes to a significant degree.  The second critique acknowledges the theoretical possibility of dice influence but questions its practicality, especially given casino regulations. In craps, for instance, the rule demanding that dice bounce off the back wall introduces a randomizing element that skeptics believe undermines any attempt at control.  Furthermore, the fact that most casinos do not explicitly forbid dice control raises eyebrows. It implies, from a skeptical standpoint, that the establishments may not view it as a genuine threat to their odds, potentially classifying it more as a hopeful strategy than a reliable technique. But what are casinos’ stances on dice control? We’ll look into that next. Is Dice Control Considered Illegal in Casinos? While there are no explicit laws against this practice, some casinos dislike it and impose restrictions. These regulations usually include the following: The dice must hit the back wall of the craps table. Players are restricted in how long they can hold the dice before rolling. Certain dice-throwing techniques are off-limits. In the few instances where dice control is explicitly prohibited as a form of cheating, casinos use advanced surveillance to detect any form of advantage play that crosses into forbidden territory, and violators risk being barred or facing legal action. Curious? Try out These Techniques and Tips For players eager to explore dice control, here are a few useful tips from experts: Focus on how you release the dice. Aim for a controlled, softer toss to influence its landing and alignment. Keep the dice level and unified throughout the throw. This reduces bounce and increases the likelihood of getting the desired result. Before the throw, orient the dice so your preferred numbers are strategically positioned. When practicing dice control skills, practice precision shooting and grip adjustment diligently. Set realistic expectations—dice control requires patience and consistent practice. Be aware of the potential risks, including the possibility of inconsistent outcomes despite your best efforts.  Odds are Both For and Against the Idea of Dice Control  Overall, the conversation around dice control spins from practiced throws to the hard bounce of skepticism. With some players swearing by their ability to sway the odds and critics waving the flag of chance, the topic remains a hotly debated one.  If the idea of possibly outsmarting the craps table calls to you, consider this your invitation to experiment with dice control yourself. Test the theories, practice the throws, and see where your judgment lands.