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Everything You Need to Know About Expected Value Calculations in Online Gambling

Written by: Eddie Griffin

Published: Mon Dec 30, 2024, 12:29 am ET

Read Time: 8 minutes

Expected Value (EV) is a fundamental mathematical concept that lies at the heart of gambling mathematics and probability theory.

For casino players, understanding EV is crucial as it helps quantify the long-term mathematical expectation of any betting situation, whether at a land-based casino or one of the best online casinos. This guide will explore EV in detail, its practical applications in casino games, and how it relates to other important gambling concepts such as house edge and Return to Player (RTP).

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What is Expected Value?

Expected Value is the average outcome of a random event when repeated many times. In gambling terms, it represents the average amount you can expect to win or lose per bet over the long run, whether you are playing roulette, blackjack, baccarat, or other popular casino games.

A positive expected value (+EV) means you can expect to profit over time, while a negative expected value (-EV) indicates you'll lose money in the long run.

What Is the Formula for Expected Value?

The basic formula for calculating expected value is:

EV = (Probability of Winning × Amount Won) + (Probability of Losing × Amount Lost)

For scenarios with multiple possible outcomes, the formula expands to:

EV = ∑(Probability of Outcome × Value of Outcome)

Where ∑ represents the sum of all possible outcomes.

Example Calculation

Let's consider a simple coin flip bet where you win $110 on heads (probability 0.5) and lose $100 on tails (probability 0.5).

The calculation would be: EV = (0.5 × $110) + (0.5 × -$100), which simplifies to $55 + (-$50) = $5.

In this case, the positive EV of $5 means you would expect to profit $5 per bet on average over many bets.

Expected Value in Popular Casino Games

Roulette

American roulette provides a clear example of negative EV. For a single number bet with a 35:1 payout, the probability of winning is 1/38 (2.63%) and the probability of losing is 37/38 (97.37%).

This results in an EV calculation of (1/38 × 35) + (37/38 × -1) = -0.0526 or -5.26%. This negative EV represents the house edge in American roulette. European roulette, with only one zero, has a better EV of -2.7%.

Blackjack

Blackjack's EV varies based on multiple factors including house rules (such as number of decks and dealer hitting soft 17), player strategy (comparing basic strategy versus suboptimal play), and whether card counting is employed, which can actually create positive EV situations in some cases.

When played with basic strategy, blackjack typically has an EV of -0.5% to -1%, making it one of the best casino games for players.

Slots

Modern slot machines use Return to Player (RTP) percentage to express long-term expected value. If a slot machine has an RTP of 96%, this translates to an EV of -4%.

This means that for every $100 wagered, the expected return is $96, with the remaining $4 representing the house edge.

What Is the Relationship Between Expected Value, House Edge, and RTP?

These three concepts are intimately connected and can be expressed in relation to each other. The house edge is simply the negative of EV when expressed as a percentage. RTP can be calculated as 100% plus the EV, or alternatively as 100% minus the house edge.

For example, if a game has -5% EV, then the house edge is 5% and the RTP is 95%.

To better connect these three concepts, we recommend checking out our content on the other two concepts. In addition to our in-depth look at RTP, we have similar rundowns of the house edge in blackjack, the house edge in roulette, and the house edge in baccarat.

Factors Affecting Expected Value

Variance vs. Expected Value

While EV predicts long-term results, short-term outcomes can vary significantly due to variance, also known as volatility.

Games with low variance, such as baccarat, tend to play closer to EV in shorter sessions. Conversely, high variance games like slots can deviate significantly from EV in the short term.

Impact of Online Casino Bonuses

Online casino bonuses can substantially modify the base EV of games. Welcome bonuses, such as a 100% match up to $500 with 40x wagering requirements, add temporary value to bets during the wagering period, and the best online casino bonuses, such as the $8000 welcome package at Lucky Red Casino, the $20,000 welcome package at OnlineCasinoGames, and the $9000 welcome package at Wild Casino, can be especially impactful.

That said, game contribution percentages must be considered when it comes to casino bonuses. For example, all slots play–perhaps other than progressive jackpot slots, which are excluded from bonus play at many sites–often counts for rollover requirements, but only a percentage of table games, video poker, and specialty games like keno might count for playthrough purposes, depending on the site.

Cashback rewards, which are considered some of the best online casino rewards, effectively improve EV by their percentage rate – a 0.1% cashback program improves EV by that amount. Online casino VIP and loyalty programs that feature redeemable points function in a similar manner.

Practical Applications of EV in Gambling

Understanding EV helps inform proper bankroll management by determining appropriate bet sizing, required bankroll for given risk tolerance, expected loss rate per hour of play, and realistic win/loss expectations.

This knowledge also assists in game selection, helping players choose between lower house edge games for longer play, high RTP slots for bonus wagering, and favorable rule variations in table games.

When evaluating promotions, EV calculations are essential. The true value of a casino offer can be determined by calculating Bonus EV (Bonus Amount minus Wagering Requirement multiplied by House Edge) while considering the time value of money and any game restrictions.

Common EV Misconceptions

Several common misconceptions exist regarding expected value in gambling. The "due for a win" fallacy incorrectly assumes that past results affect future EV, when in reality each bet stands independent and the law of large numbers doesn't guarantee short-term results.

Similarly, the belief that betting systems can beat EV is incorrect – no betting system can change the base EV of a game, and progressive systems only modify variance without overcoming negative EV in the long term.

Players also sometimes mistakenly believe that hot or cold streaks matter, when these statistical clusters are normal and don't indicate changes in the underlying EV.

Expected Value: Online Casinos vs Land-Based Casinos

The fundamental mathematics of expected value remains constant whether you're playing in a physical casino or online, but several factors create meaningful differences between the two environments.

Online casinos such as DuckyLuck Casino and HighRoller Casino typically offer better RTPs and lower minimum bets due to their reduced overhead costs. For example, online slots commonly feature RTPs of 96-97%, while land-based slot machines average 88-93%.

Similarly, online blackjack often allows minimum bets of $1-$5, compared to $15-$25 in physical casinos, making it easier to extend playing time with the same bankroll despite identical expected value percentages.

The pace of play also significantly impacts realized expected value. Online games generally move faster than their physical counterparts, potentially increasing hourly losses despite better RTPs.

A land-based blackjack table might deal 60 hands per hour, while online players could see 200 or more hands in the same time period.

Jacks or Better video poker at a land-based establishment may be quicker than a lot of other casino games, but it can't compare to playing Jacks or Better at Lucky Red Casino or other top gambling sites, as several turns can take place in the course of a minute in an online game. This faster pace means that even with a more favorable house edge, online players might experience larger total losses over a given time period.

Another key difference lies in the competition level for player-versus-player games. Online poker, for instance, typically features more skilled opposition than low-stakes land-based games, potentially reducing expected value for average players.

However, real money online casinos often compensate with more generous bonus structures and loyalty programs, which can temporarily improve or even reverse negative expected value for strategic players.

Conclusion

Expected Value serves as the mathematical foundation of casino gambling, providing players with a framework for making informed game choices, setting realistic expectations, evaluating promotions effectively, and managing their bankroll appropriately.

While casino games generally have negative EV, understanding these principles helps players minimize losses through game selection, maximize value from promotions, and make rational decisions based on mathematics rather than emotion.

Remember that while EV predicts long-term results, individual sessions can vary significantly due to variance. Use EV as a tool for understanding and decision-making, but always gamble responsibly and within your means.

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Expected Value FAQ

Can you ever get positive expected value in casino games?

While most casino games have negative EV by design, certain situations in blackjack can create positive EV through card counting. Professional poker players can also achieve positive EV by outplaying their opponents despite the house rake.

How does variance affect expected value caluclations?

Variance represents the short-term deviations from expected value that occur in gambling. While EV predicts long-term results accurately, individual sessions can vary significantly from the mathematical expectation due to normal statistical fluctuations.

Why do slot machines with higher RTP still seem to lose more money?

Slot machines with higher RTP often feature higher volatility and faster gameplay speed. Players typically make many more bets per hour on slots compared to table games, which multiplies the effect of the negative expected value.

Does changing bet size affect expected value?

The expected value percentage remains the same regardless of bet size in casino games. A game with -5% EV will lose the same percentage whether you bet $1 or $100 per hand.

How do casino bonuses impact expected value?

Casino bonuses can temporarily improve or even reverse the negative expected value of games. The true EV depends on the bonus amount, wagering requirements, and the house edge of eligible games.

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