What Is Expected Value (EV) in Betting and Why It Matters

Defining and Calculating Expected Value

Expected Value is the sum of all possible outcomes, each multiplied by its probability of occurring. It tells you, on average, how much you stand to win or lose per bet.

The $\text{EV}$ Formula

For a simple bet with two outcomes (win or lose), the formula is:

The Sign is Everything

The result of the $\text{EV}$ calculation dictates whether a bet is mathematically worthwhile:

• Positive Expected Value ($\text{+EV}$): This means you are expected to profit on average over time. Sharp bettors only look for $\text{+EV}$ opportunities.
• Negative Expected Value ($\text{-EV}$): This means you are expected to lose money on average over time. Most casino games and bad sports bets fall into this category.
• Zero Expected Value ($\text{0 EV}$): This is a perfectly fair bet where you are expected to break even over time (no profit, no loss).

Calculation Example: Finding the Edge

Imagine a bookmaker offers you $\text{+110}$ odds on a fair coin toss (which has a true $50\%$ chance of hitting Heads). You bet $100:

1. Probability: $50\%$ chance to win, $50\%$ chance to lose.
2. Payout: Win $\text{\$110}$ profit; Lose $\text{\$100}$ stake.

This is a $\text{+EV}$ bet. You expect to earn an average of $5 per $\text{\$100}$ wagered over the long run. By contrast, if the book offered standard $\text{-110}$ odds on the same $50/50$ bet, the $\text{EV}$ would be approximately $\text{-\$4.50}$, confirming that standard odds are a losing proposition over time.

Why $\text{EV}$ is the Cornerstone of Betting Success

Expected value is arguably the most important metric in long-term betting strategy.

The Only Way to Beat the House

Sportsbooks build a vig (house edge) into their odds, making most wagers slightly $\text{-EV}$ by default. Since even the best bettors rarely win more than $55\%$ of the time, the only way to overcome the house’s edge and achieve profitability is to consistently identify and place bets that you believe have a positive Expected Value.

Professionals Bet Numbers, Not Teams

A recreational bettor often wagers based on hunches, fandom, or the excitement of the game. A professional bettor (a “sharp”) treats betting like a business and focuses solely on the numbers.

Pros are constantly comparing their own estimated probabilities (derived from models or research) to the odds offered by the sportsbook. They hunt for discrepancies where the book has underpriced an outcome, creating a value bet. This laser focus on the $\text{EV}$ of the line, not just who they think will win, is the fundamental advantage sharps hold.

$\text{EV}$ Across Different Betting Domains

The $\text{EV}$ concept applies universally, but its application differs based on the game.

Expected Value in Sports Betting

In sports, a value bet is one where your estimated true probability of an outcome is higher than the implied probabilityof the bookmaker’s odds.

For instance, an underdog is listed at $\text{+130}$ odds, which implies they have about a $43.5\%$ chance to win. If your deep analysis suggests the team actually has a $50\%$ chance to win, placing a $\text{\$100}$ bet yields:

Because the odds overpay relative to your assessment of the true probability, the bet is $\text{+EV}$. Consistently finding even small $\text{+EV}$ opportunities is how sports bettors generate profit over the long haul.

Expected Value in Casino Games

In contrast to sports betting, virtually all casino games are designed to have a long-term negative Expected Value for the player, representing the house edge.

This mathematical reality is why “the house always wins” over thousands of hands or spins. For a recreational player, the negative $\text{EV}$ is simply the cost of entertainment.

Expected Value in Poker

Poker is a game of skill where players bet against each other, and $\text{EV}$ is used to evaluate every decision. Good poker players strive to make $\text{+EV}$ decisions with every call, raise, or fold.

• Example: If you have a $20\%$ chance to hit a winning hand on the river, and the pot offers you better than $4$-to-$1$odds (i.e., you only have to put in less than $20\%$ of the pot to make the call), the decision to call is $\text{+EV}$.

In poker, making the correct $\text{+EV}$ play consistently will win you money, even if you lose the pot due to variance (short-term bad luck) on a single hand.

$\text{EV}$ Misconceptions and Responsible Betting

Understanding what $\text{EV}$ is not is just as important as knowing what it is.

Common Misconceptions

$\text{EV}$ and Responsible Gambling

Knowing the Expected Value of a bet is crucial for responsible gambling:

1. Setting Realistic Expectations: Realize that $\text{-EV}$ games (like the lottery or most casino offerings) will result in long-term losses. If you play them, budget for the expense of entertainment.
2. Avoiding Loss Chasing: The $\text{EV}$ of a game remains constant regardless of past results (the “wheel has no memory”). Chasing losses under the illusion that you are “due” for a win is the definition of betting against the math.
3. Informed Choice: $\text{EV}$ allows you to make an informed choice. You can choose a better game (like European vs. American Roulette) or avoid a bad bet because you recognize that the math is heavily stacked against you.

In every betting scenario, $\text{EV}$ is your compass. It is the tool that directs you toward value and steers you away from mathematically unsound decisions.