Looking for ways to boost your strategy when playing casino table games or online slots? It’s time to get clued up on expected value.

Read on to discover how to find the expected value of each play, what it is and how it can potentially improve your chances of winning when playing casino online games. Discover how it applies to various types of casino games, including blackjack, poker, slots and roulette.

What Is Expected Value in Gambling

Expected value, also known as EV, is a concept derived from the world of probability and statistics. It represents the average amount a player can expect to win or lose on a bet in the long run. In short, it tells you how much you can expect to win or lose on average when repeating a particular bet.

The math is quite straightforward — simply multiply the potential outcomes of the bet by their respective probabilities and sum them up (also taking the game’s house edge into consideration.) If the result is positive, it suggests a favorable bet. On the other hand, if you get a negative value, the bet is considered unfavorable.

For example, when playing blackjack, suppose you’re dealt a hand with a total value of 16 (e.g., 10 and 6.) The dealer’s up card is a 9. Now, you face the decision of whether to hit or stand.

You need to consider the probabilities and outcomes associated with each possible decision to calculate EV. 

Hit

There are several possible outcomes if you decide to hit. You could improve your hand, go bust or end up with the same value. Consider the following outcomes and their probabilities:

• Improve: There are four aces and three cards with a value of five that could improve your hand without going bust. So, there are a total of seven favorable cards remaining in the deck.
• Bust: Any card with a value greater than 5 will cause you to go bust. Since there are 36 cards with values greater than five (10, jack, queen and king,) the probability of busting is 36/52.
• Same value: If you draw any other card (2, 3, 4, 6, 7, 8, 9) your hand value will remain at 16.

Stand

There are only two possible outcomes if you decide to stand:

• Win: If the dealer busts or ends up with a lower hand value than yours, you win.
• Lose: If the dealer has a higher hand value than yours, you lose.

So, to calculate the expected value, multiply each outcome by its respective probability, sum them up and then subtract the probability of losing (since that represents a negative outcome.) Assume the following payout structure: +1 for a win, 0 for a push (tie) and -1 for a loss.

EV = (Probability of Winning × Payout for Winning) + (Probability of Push × Payout for Push) + (Probability of Losing × Payout for Losing)

EV = (Probability of Winning × 1) + (Probability of Push × 0) + (Probability of Losing × (-1))

Now, plug in the numbers:

EV = (Probability of Winning × 1) + (0 × 0) + (Probability of Losing × (-1))

EV = (Probability of Winning – Probability of Losing)

To calculate the probability of winning, you also need to consider the probabilities of the dealer’s possible outcomes based on their up card (in this case, a 9.)

By consulting a blackjack strategy chart or using simulation tools, you can estimate that the probability of winning in this situation is around 28%. Don’t forget to subtract the house edge. This example uses a conservative house edge of 1%, leaving you with a 27% probability of winning.

Therefore, the EV can be calculated as follows:

EV = (0.27 – 0.72)

EV = -0.45

In this case, the EV of hitting is negative (-0.45,) indicating that hitting would result in a lower average outcome compared to standing. The bottom line is it would be more advantageous to stand rather than hit in this specific situation.

Remember, EV provides insights into long-term averages and doesn’t guarantee immediate results. That said, it definitely serves as a useful tool for making informed decisions and optimizing your strategy over time.

Did the numbers leave your head spinning? Worry not. There are plenty of expected value calculators online to help you out.

Understanding the Relationship With the House Edge

The house edge is the casino’s built-in advantage on every bet. It’s the reason why casinos can stay in business and continue offering those flashy experiences everybody loves. The house edge is expressed as a percentage, representing the average amount the casino expects to win from each bet in the long run.

The relationship between EV and the house edge is pretty straightforward. When calculating the EV of a bet, subtract the house edge percentage from 100%. This adjustment reflects the proportion of the total wagered amount that the player can expect to win back on average.

Expected Value in Popular Casino Games

You now have a decent idea of how EV works. Here’s how it applies to popular casino games.

Blackjack

As seen above, factors like the dealer’s up card, the number of decks used and the specific rules of the table impact EV in blackjack. Understanding the probabilities of card combinations and applying optimal strategies can give you an edge over the casino.

Roulette

Each roulette bet has a specific probability of winning and its associated payout. By calculating the EV for each bet, you can make more informed choices. For instance, betting on a single number has a low probability but offers a high payout, while betting on red or black has a higher probability but a lower payout. Evaluating the EV can help you select bets that align with your risk appetite and potential rewards.

Slot Machines

While the outcome of each spin is purely random when playing slots, understanding the concept of EV can still be helpful. Different slot machines have varying paytables, indicating the payouts for different winning combinations. By comparing the potential payouts with the probabilities of hitting those combinations, you can estimate the EV and choose machines that offer better long-term returns.

Poker

Poker, a game of skill, strategy and calculated risks, calls for a deeper understanding of EV. In this game, you evaluate the EV of your decisions based on the information available. Assessing the strength of your hand, the pot odds and other factors can help you make solid betting decisions. By consistently making positive EV plays, you can increase your chances of long-term success in poker.

Play Casino Games at Borgata Online

Put your newfound EV knowledge to the test — play online games at a casino with Borgata Online. You’ll find all the action you could ever hope for in the form of jackpot slots, live dealer casino games, casino table games, variety games and more.

Register when you’re ready to explore our full offering.Don’t forget to explore the Borgata Online blog further — from why casino tables are green to a look at different cultural perspectives on gambling, there’s something of interest for everyone.