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What is Expected Value in Gambling? A Simple Explanation with Examples

Whether you’re spinning the reels of a slot machine or placing chips on a roulette wheel, understanding the concept of expected value (EV) is crucial to making informed decisions in gambling. In this article, we’ll break down the basics of expected value in gambling, explain related terms like RTP, house edge, volatility, and variance, and walk you through a simple EV calculation with an easy example.

What is Expected Value? (EV Explained)

Expected Value is the average amount of money you can expect to win or lose per bet over the long run. It’s a mathematical way of expressing your average return from playing a particular casino game repeatedly. In simple terms, it answers the question:

"On average, how much will I win or lose every time I play?"

EV is usually expressed as a monetary amount or sometimes as a percentage. Knowing your EV helps set realistic expectations. For example, if a game has an EV of -5 cents per $1 bet, it means over 100 bets of $1 each, you will lose about $5 on average.

The Formula for Expected Value

The mathematical formula to calculate expected value is:

Outcome Probability (p) Payoff (winnings or losses) Contribution to EV = p × payoff Outcome 1 p1 payoff1 p1 × payoff1 Outcome 2 p2 payoff2 p2 × payoff2 ... etc. ... ... ... Expected Value (EV) Σ (p × payoff)

In other words, multiply each possible outcome by the probability it occurs, then add everything together.

RTP: Return to Player Meaning and Its Limits

Return to Player (RTP) is closely related to expected value but is typically expressed as a percentage. It represents, on average, how much of all the money wagered will be paid back to players over a long period.

For instance, a slot with an RTP of 96% means that for every $100 wagered, $96 is returned to players over thousands or millions of spins. The remaining $4 represents the casino’s profit, also called the house edge.

Important: RTP is a theoretical long-term average measured over an extremely large number of plays — typically hundreds of thousands or millions of spins. It can never guarantee what will happen in your feet2inches.com session of 50 or 100 spins, only what usually happens over the long haul.

House Edge vs Payout Percentage – What's the Difference?

The house edge is the casino’s advantage expressed as a percentage of each bet it expects to keep over time. It is complementary to the payout percentage or RTP.

  • House edge = 1 − RTP
  • If RTP is 96%, house edge = 4%.

Think of it this way: if you play 100 spins of a $1 slot with a 4% house edge, you can expect to lose about 4 dollars on average over the long term.

Example Table of RTP and House Edge

Game RTP (%) House Edge (%) European Roulette 97.3 2.7 Blackjack (Basic Strategy) 99.5 0.5 Slot Machine (Average) 95 5

Basic Probability in Casino Games

Understanding expected value requires a grasp of probability fundamentals because EV depends on the chance of various outcomes happening.

Probability measures how likely an event is to happen and is expressed as a number between 0 (impossible) and 1 (certain). For example:

  • A fair coin landing heads = 0.5 (50 out of 100 flips)
  • A single number pocket on European roulette (0-36) = 1/37 ≈ 0.027 (about 2.7 out of 100 spins)

All possible outcome probabilities in a game add up to exactly 1 (or 100%). Knowing these allows you to weight your payoffs correctly when calculating expected value.

Simple Probability Example: Rolling a Die

Suppose you get paid 5 times your bet if you roll a six on a fair six-sided die and lose your bet otherwise. What is the expected value?

  1. Probability of rolling a 6 = 1/6 ≈ 0.167
  2. Probability of other outcomes = 5/6 ≈ 0.833
  3. If you bet $1:
    • Win = +$5
    • Lose = −$1

EV = (0.167 × $5) + (0.833 × −$1) = $0.835 − $0.833 = $0.002

This means on average, you win 0.2 cents every roll — a very slight positive expected value.

Volatility and Variance: What They Mean for Your EV

While expected value tells you the average return over many bets, it doesn’t say anything about how your results might fluctuate session to session. This is where volatility or variance come in.

  • Volatility describes the size and frequency of wins and losses.
  • High volatility games have big wins but less often (e.g., jackpot slots).
  • Low volatility games pay smaller wins more often (e.g., low variance slots or table games like blackjack).

Two games can have the same expected value but very different playing experiences because of volatility. For example, a slot with 95% RTP could have wildly different variance levels, meaning your bankroll swings during play could be very different though the average long term loss (the EV) is the same.

Putting It All Together: Expected Value Calculation Example

Let’s revisit a real-world gambling example with a simple slot machine scenario to see how expected value is calculated and explained.

Scenario: Basic Slot Machine

  • Cost per spin: $1
  • Possible outcomes:
    • Jackpot (win $500): 1 in 10,000 spins
    • Small win ($2): 1 in 10 spins
    • Lose everything: all other spins

Step 1: Calculate probabilities

  • Jackpot probability = 1/10,000 = 0.0001
  • Small win probability = 1/10 = 0.1
  • Lose probability = 1 − (0.0001 + 0.1) = 0.8999

Step 2: Calculate payoffs relative to bet

  • Jackpot payoff = +$500 − $1 (bet) = +$499
  • Small win payoff = +$2 − $1 = +$1
  • Lose payoff = −$1

Step 3: Calculate the expected value

EV = (0.0001 × 499) + (0.1 × 1) + (0.8999 × −1)

EV = 0.0499 + 0.1 − 0.8999 = −0.75

This means the expected value is −75 cents per spin. On average, you lose 75 cents every $1 spin over the long run.

What Does This Mean for Your Average Return?

Your average return per spin in the above example is $1 − $0.75 = $0.25, or 25%. This is the RTP — extremely low compared to the typical RTP of slots, which often ranges from 90% to 98%. Real slots are designed to give much better average returns but still keep the house profitable.

Brief Bankroll Note 📝

When dealing with expected value, always keep in mind actual bankroll management. Since EV is a long-run average, short-term play can vary greatly. Your bankroll should be large enough to withstand swings caused by volatility — especially on high variance games.

Summary: EV Explained in a Nutshell

  • Expected Value (EV) tells you the average win or loss per bet over time.
  • RTP is the expected value expressed as a percentage of your wager returned over time.
  • House edge is the casino’s expected profit percentage, the flip side of RTP.
  • Probability is the likelihood of different outcomes occurring and is needed to calculate EV.
  • Volatility affects how much your results swing around that EV, not the EV itself.
  • Use EV calculations to make informed choices, but remember variance means results vary in the short term.

Next time you sit down at a casino game or slot, think about what the expected value tells you about your chances. It’s the best mathematical insight you have into “what you can expect” from any game.