Expected Value

Lesson 7 of 12

Expected Value (EV) is one of the most important concepts in probability and gambling mathematics.

It describes the average outcome that can be expected over a very large number of trials.

In roulette, Expected Value helps explain why casinos maintain a long-term advantage.

What Is Expected Value?

Expected Value measures the average gain or loss per bet over time.

It does not predict the result of a single spin.

Instead, it describes what happens over thousands or millions of spins.

A Simple Example

Imagine a €1 straight-up bet on a single number in European Roulette.

Possible outcomes:

  • Win: Receive €35 profit

  • Lose: Lose €1

Probabilities:

  • Winning: 1/37

  • Losing: 36/37

Expected Value calculation:

EV = (1/37 × €35) + (36/37 × -€1)

EV = -€0.027

This means the average loss is approximately:

€0.027 per €1 wagered

or

2.70%

The Connection to the House Edge

The house edge in European Roulette is:

2.70%

This is not a coincidence.

The house edge is simply the negative Expected Value experienced by the player.

Player EV:

-2.70%

Casino EV:

+2.70%

Every bet in European Roulette contains this mathematical disadvantage.

Why the Zero Matters

Without the green zero, European Roulette would contain:

  • 18 red numbers

  • 18 black numbers

A total of 36 outcomes.

In that case, even-money bets would be perfectly fair.

The addition of the green zero creates the casino advantage.

This single pocket is responsible for the entire house edge.

Short-Term vs Long-Term Results

Expected Value does not guarantee immediate outcomes.

A player may:

  • Win €500 today

  • Lose €300 tomorrow

Short-term results can vary significantly.

Expected Value describes the long-term average.

Over many thousands of spins, results tend to move closer to the mathematical expectation.

Why Betting Systems Do Not Change EV

Many betting systems alter:

  • Stake size

  • Progression speed

  • Risk exposure

However, they do not change Expected Value.

Examples:

  • Martingale

  • Fibonacci

  • D'Alembert

  • Labouchere

  • Paroli

All operate within the same mathematical framework.

The expected value remains unchanged.

Expected Value and Intelligent Play

Understanding Expected Value helps players evaluate systems and claims objectively.

If a strategy cannot change probability or payouts, it cannot change Expected Value.

This is one of the most important principles in roulette analysis.

At Roulette Intelligence, we believe that understanding Expected Value is far more valuable than chasing unrealistic promises.

Key Facts

  • Expected Value measures long-term average outcomes

  • European Roulette EV: -2.70%

  • Casino EV: +2.70%

  • The green zero creates the house edge

  • Betting systems do not change Expected Value

Next Step

Continue with Variance to learn why short-term results often differ dramatically from long-term expectations.

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