Recently updated on August 10th, 2023 at 09:17 pm
Strategies for Playing Games of Chance
Table of Contents
Curious about payout ratios and the role of variance in games of chance?
This guide will provide a comprehensive overview of payout ratios and variance. By understanding these principles, you can apply them to virtually any game of chance, enhancing your gameplay experience.
While many turn to this guide for insights on casino games, the strategies outlined can also be helpful for non-gambling games. Understanding these principles is crucial whether you’re betting real money or just playing for fun. For those who gamble, grasping these concepts can minimize losses, thereby optimizing winning potential.
Dive in to learn how the house edge operates and how variance influences probability. You’ll find these strategies particularly relevant to games such as:
The Casino Always Has a Winning Edge
There is a house edge in every game at both land-based and online casinos. Casinos entertain players with the potential to win big while they earn profits from this house edge. These establishments are businesses, and like all businesses, they aim to make a profit.
How is the House Edge Determined (RTP)?
Casinos present the ratio of winning versus losing in various ways:
- RTP Percentage (Return to Player Percentage): This represents the percentage of the staked amount the player can expect to receive back over time. For example, an RTP of 97% implies a house edge of 3%.
- Casino House Edge Percentage: This denotes the percentage the casino is expected to win from each game. For instance, Blackjack has a house edge of around 0.5%, meaning the RTP is 99.5%.
- A Ratio of Winning: Commonly seen in sports betting odds, some casino games use a winning ratio, such as 3 to 1. However, remember that the payout is always different from the odds of winning. In European Roulette, you have a 1 in 37 chance of landing on a single number, but the payout is only 35 to 1.
Mathematics underpins these odds. Casinos ensure that, when setting these odds, the edge is in their favor.
What Is Variance?
Variance, or volatility, dictates how outcomes can deviate from what’s statistically expected over a short period. Consider the classic coin flip. Theoretically, a coin has equal odds of landing on heads or tails. However, in practice, you might see tails land ten times consecutively, even though the odds of this happening are low. Over 50 coin flips, instead of the expected 25 heads and 25 tails, variance could result in an uneven result, say 32 heads to 18 tails.
Upswings Versus Downswings
Even after another 100 coin flips, the outcome may again favor tails. The point is that while casino games have a house edge benefiting the casino, variance can momentarily work in the player’s favor, leading to casino losses. If you were to bet on these coin flips, you’d experience upswings and downswings in wins and losses.
Introducing a Betting System to Counter Variance
Adding strategy can make even a simple game like flipping a coin more captivating. Suppose players take turns calling heads or tails before each flip. More strategic or mathematically-inclined players might employ a betting system or strategy to counteract the variance inherent in this 50/50 probability game.
Casino Players Often Use Betting Systems
Seasoned casino players often employ betting systems to counteract variance versus the house edge. In the game of heads or tails above there is no casino. That said, imagine the person that owns the coin is the host. He or she agrees to return 190% of your bet for every coin flip you win. However, takes 100% of every loss. Every $1 you bet, you win $1 back plus $0.90 on top.
Strictly speaking, you are losing out in the long run because the host of the coin has set a house edge of 10%. You may agree to do this because you have a betting system in mind that could work in the long run over the session.
We will cover betting systems and their importance in a lot more detail in later sections below.
Understanding the House Edge/RTP in Roulette
Let’s take a closer look at roulette. When placing a ‘straight bet’ (a bet on a single number), you have a 1 in 37 chance of winning, given there are 37 numbers on a European roulette board (0-36). The casino offers odds of 35 to 1.
If you win, you’ll receive 35 times your wager and your original bet. For instance, a $1 bet would yield a $36 return, translating to a $35 profit. Here, the house edge is 2.7%, with an RTP of 97.3%.
For bets on odds/even, red/black, or high/low, if the ball settles on 0, it’s a loss for you. The corresponding RTP is calculated as 2 x 18 ÷ 37 = 0.973 or 97.3%. Subtracting this from 100% gives a house edge of 2.7%, not 2.5%, as mentioned.
However, roulette isn’t uniform across casinos. American Roulette, for instance, features both ‘0’ and ’00’, bringing the total numbers to 38 and altering the RTP to 94.7% and a house edge of 5.3%. European Roulette, with just a single ‘0’, offers better odds for the player.
Determining the RTP/House Edge for Slot Machines
Slot machines operate on similar principles. Each reel is configured with a specified number of symbols, and the probability of symbol combinations aligns to favor the casino. This probability is represented as the RTP (Return to Player) While most land-based slots offer an RTP of 89% to 94%, online slots average around 96%.
Games like blackjack, baccarat, keno, craps, and poker are all designed with the foundational principle of ensuring a favorable ratio of winnings to payouts for the casino.
Demystifying the House Edge/RTP in Blackjack
Blackjack is slightly more complex (also see the rules of how blackjac) due to its multiple play styles—generally, the house edge hovers around 0.5%, translating to an RTP of 99.5%.
However, the game’s odds can be influenced by numerous factors:
- Dealer’s action on 17 (hits or stands)
- Number of decks in use (from 1 to 8)
- Rules associated with splitting or doubling down
- Availability of bonus side bets
Speaking of bonus side bets, they’re notably in the casino’s favor. So to optimize your potential winnings in blackjack, it’s best not to use these bets.
The Importance of Basic Strategy
While blackjack’s 0.5% house edge seems appealing, achieving this figure requires adherence to the basic blackjack strategy—a compilation of mathematically determined decisions based on your hand and the dealer’s visible card. You elevate your winning odds by systematically deciding when to hit, stand, double down, or split. However, remember, variance still plays a role.
The Allure and Pitfalls of Blackjack’s Bonus Side Bets
Diving straight in, let’s address Blackjack’s bonus side bets. These bets are usually heavily tilted in the casino’s favor, often more so than the base game itself. For those keen on optimizing their potential returns in blackjack, it’s advisable to steer clear of these side bets.
Harnessing the Power of Basic Strategy
While blackjack may flaunt a seemingly attractive house edge of just 0.5%, this figure is only attainable when employing the basic strategy. This strategy comprises a set of mathematical rules guiding players on how to respond based on their hand and the dealer’s upturned card.
In essence, the basic strategy offers a roadmap, indicating when to hit, stand, double down, split, etc., all grounded in mathematically validated probabilities that aim to enhance your chances of securing a win. Nevertheless, it’s vital to remember that variance can still influence outcomes in the game.
Understanding Game Payouts and Betting Systems
When engaging in games of chance, it’s vital to comprehend the concept of Return to Player (RTP) or House Edge. For instance, Blackjack’s 0.5% house edge is applied to each hand played, and Roulette’s 2.7% house edge on a straight bet is for each wheel spin. However, this doesn’t equate to the casino’s profit over an entire gaming session.
Neglecting to use an efficient betting system (like forgoing basic strategy in Blackjack) can escalate the house edge, diminishing the player’s RTP. Sound judgment and recognizing opportunities are vital to a player’s success.
Betting systems serve a purpose: they mitigate errors made by those unfamiliar with the game’s nuances. At a minimum, utilizing a betting system allows you to play to the house edge rather than unwittingly increasing it.
Countering Variance with Betting Systems
While it might seem straightforward, one can’t overlook the influence of variance on the house edge or RTP. So this is where betting systems come into play, designed to counterbalance game variance.
Astute players distinguish between the RTP for each deal, roll, or spin and their overarching betting system. Essentially:
- RTP or House Edge is applied to each individual game against the house.
- Betting systems account for variance across an entire betting session.
Considerations When Using Betting Systems
Players might select games with low house edges or simply opt for their favorites, applying a system as they go. However, important considerations include:
- Anticipating the game’s variance potential.
- Implementing bet sizing strategies.
- Recognizing when to exit.
The Importance of Bet Sizing
Effective bet sizing is paramount in chance-based games. Its essence is in leveraging variance — anticipating both upswings and downswings. In any chosen system, bet sizing remains a strategic pillar, influenced both by experience and common sense.
For instance, discerning slot players might adjust their bet sizes based on perceived payout patterns. Or, in Roulette, after observing a series of black outcomes, a player might double down on red, banking on probability and variance.
Some systems have built-in bet sizing patterns, adjusting bets based on previous results. Familiar systems include the Martingale, Fibonacci, and Labouchere roulette systems.
Optimal Betting Systems
It’s crucial to differentiate between feasible and now-obsolete betting systems. For instance, while card counting in Blackjack was once a profitable system, it has largely been nullified by casinos’ countermeasures.
In essence, there are two principal optimal betting strategies:
- Those are elevating your RTP above 100%.
- Those are minimizing potential losses.
The first might lead to confrontation with casinos, while the second hinges on discipline — adhering to the system and understanding bet sizing adjustments during winning or losing streaks.
A Case Study: The Rise and Fall of Blackjack Card Counting
Card counting in Blackjack once tipped the scales from an RTP of 99.5% to over 102%. And this was possible because decks weren’t frequently shuffled, allowing players to adjust their bets based on the deck’s composition. However, casinos adapted by shuffling more frequently, nullifying card counting’s advantage.
Despite this, basic mathematical strategy in Blackjack remains a solid approach. Over time, by adhering to this strategy, a player can closely approach the game’s theoretical RTP.
Bankroll Management: Betting Wisely
The essence of any betting strategy is understanding the game’s RTP, gauging one’s tolerance for loss, and setting a playtime limit. Contrary to some beliefs, a streak of losses isn’t necessarily a sign to increase bets. A disciplined approach suggests:
- Starting with low bets and increasing them during favorable streaks.
- Reducing bets during consistent losses.
Players can better manage their funds and optimize their gaming experience by comprehending the interplay between variance and volatility.
Variance/Volatility in Games of Chance
Volatility can typically be categorized in two ways, though some people use three:
- High-Volatility Games
- Low-Volatility Games
- Mid-Volatility Games (for those who differentiate three types)
Bet sizing is crucial in these games. As highlighted in the previous section about variance, every game has its upswings and downswings. Taking the coin flip as an example, a game of ‘heads’ or ‘tails’ shows that variance sometimes defies probability. Over time, however, probability will balance the results.
Given that the odds are 50/50, the coin flip can be considered a mid-volatility game.
Consider a game with a Return to Player (RTP) of 98%. If it’s a slot game, it might offer large wins during bonus rounds but smaller returns from regular reel combinations. These bonus rounds might be infrequent but are not impossible to attain.
Theoretically, if you bet $10,000 over a month, you should expect a return of at least $9,800 due to the 98% RTP. However, variance can create fluctuations:
- Month 1: You wager $10,000 and lose it all.
- Month 2: You bet another $10,000 and end up with $14,600, a profit of $4,600.
- Month 3: You stake another $10,000 and end with $14,800, a profit of $4,800.
Mathematically, this is calculated as (100 ÷ $30,000 x $29,400) = 98% RTP.
In this scenario, you recover $9,400 of your losses from Month 1 in the subsequent months. Despite staking $30,000 over three months, you end up with $29,400. That reflects the 98% RTP on a high-volatility slot, characterized by significant downswings followed by rapid upswings.
Many might be discouraged after the first month, but those familiar with variance and volatility might persevere, recalling the coin flip example.
These games frequently return smaller amounts, reducing the risk to your bankroll compared to high-volatility games.
To illustrate, blackjack played using basic strategy, is a low-volatility game. Typically:
- 3% of hands will be won
- 48% result in a loss or a push
- 7% have other outcomes (mainly splits)
What’s the likelihood of losing five consecutive hands?
Using probability: 0.48^5 = 0.012 or 1.2%, which is approximately a 1.2% chance.
Here’s a reference table for Blackjack probabilities:
|Lose 1 hand||52.6% Chance|
|Lost 2 Hands in a row||27.7% Chance|
|Lose 3 Hands in a row||14.6% Chance|
|Lost 4 Hands in a row||7.7% Chance|
|Lose 5 Hands in a row||4% Chance|
|Lost 6 Hands in a row||2.1% Chance|
|Lose 7 Hands in a row||1.1% Chance|
|Lost 8 Hands in a row||0.59% Chance|
|Lose 9 Hands in a row||0.31% Chance|
In blackjack, a win typically doubles your stake. A losing streak of 3 or 4 hands at $5 per hand (resulting in a loss of about $20) is unlikely, occurring just 7.7% of the time. However, should you lose nine hands consecutively—a rare 0.31% chance—you’ve only lost $45. With the variance in mind, a recovery phase will eventually follow, allowing you to recoup a significant portion of losses.
Did You Recognize How Variance/Volatility Influences RTP?
Understanding the distinction between RTP (or house edge) and actual outcomes is essential. For instance, betting on a single Roulette number gives a 1 in 37 chance of winning. Yet, 50 spins might pass without your chosen number appearing. Probability isn’t a guarantee in the short term; variance will always influence results.
RTP reflects the proportion of money returned over the long term, not the frequency of wins. A player might engage with a 96% RTP slot, bet $100, and either lose half or win an extra 50% in a particular session. Over an extended period, the 96% RTP should balance out. However, achieving this balance can take some players years, even decades.
RTP is not fixed. By understanding concepts like variance, probability, volatility, and the RTP/house edge, and by employing strategies such as the basic Blackjack strategy, appropriate bankroll management, and bet sizing, you can minimize long-term losses and even come out ahead.
Here’s a recap of these concepts:
- RTP/house edge
- Strategic play
- Bankroll management
- Bet sizing
Remember to always play responsible.