Expected Value Calculator

Why Expected Value Matters

Expected value (EV) is one of the most powerful concepts in decision-making. It transforms uncertainty into a single number you can use to make rational choices. I use it constantly in investing, business decisions, and even everyday life.

Here's why EV matters: it tells you what happens on average if you repeat a decision many times. A single bet might go either way, but over 100 or 1,000 trials, your actual results will converge to the expected value.

This is professional gamblers, successful investors, and smart business leaders all think in terms of expected value. They don't focus on whether they won or lost the last hand—they focus on whether they made positive EV decisions.

I use expected value to:

• Evaluate investment opportunities: "This startup has a 10% chance of 100x return, 40% chance of 5x, and 50% chance of total loss. What's the EV?"
• Make business decisions: "Launching this product costs $50K. There's a 30% chance it generates $200K, 70% chance it flops. Is it worth it?"
• Analyze gambling scenarios: "This casino game has a 48.6% chance to win $100, 51.4% chance to lose $100. What's my expected loss per bet?"
• Decide whether to take risks: "Should I quit my job to start a business? What are the outcomes and probabilities?"

How to Calculate Expected Value: The Complete Formula

The math behind expected value is straightforward. You multiply each possible outcome by its probability, then sum all the results.

Here's a real example: You're considering a bet where you win $100 with 50% probability, or lose $50 with 50% probability.

• Outcome 1: Win $100 × 50% = +$50
• Outcome 2: Lose $50 × 50% = -$25
• Expected Value: $50 + (-$25) = +$25

The EV is +$25, which means on average, you'll profit $25 every time you take this bet. Over 100 bets, you'd expect to make $2,500. This is a positive EV scenario you should take.

My calculator handles all of this automatically. Just enter your outcomes and probabilities, and it calculates the EV instantly.

Expected Value in Real Life: Examples

Expected value isn't just for gamblers and mathematicians. It applies to countless real-world situations. Let me walk you through some examples.

Example 1: Job Offer Decision

You have two job offers. Job A pays $100K guaranteed. Job B has a commission structure where there's a 50% chance you earn $150K, 50% chance you earn $80K.

• Job A EV: $100K × 100% = $100,000
• Job B EV: ($150K × 50%) + ($80K × 50%) = $75K + $40K = $115,000

Job B has a higher expected value ($115K vs $100K), but it's riskier. The EV tells you that over many years, Job B would pay more on average. Whether that's worth the risk depends on your risk tolerance and financial situation.

Example 2: Launching a Product

You're a business owner considering launching a new product. It costs $50,000 to develop. Market research suggests:

• 30% chance of high demand: $200,000 profit
• 40% chance of moderate demand: $50,000 profit
• 30% chance of failure: $0 profit (lose the $50K investment)

The expected value is $65,000, which is positive. On average, this product launch would generate $65K profit. The fact that you might lose $50K 30% of the time is scary, but the EV says go for it.

Example 3: Insurance Decision

Should you buy insurance? Let's say your $10,000 car has a 5% chance of being totaled in an accident this year. Insurance costs $600.

• No insurance EV: (95% × $10K) + (5% × $0) - $600 = $9,500 - $600 = $8,900 (expected value of car after paying insurance)
• With insurance EV: $10K - $600 = $9,400 (guaranteed car value minus premium)

Wait, this shows insurance has negative EV ($9,400 vs $8,900 expected value without it). That's how insurance companies make profit. But most people still buy it because they can't afford the 5% worst-case scenario of losing $10K. This is where risk tolerance matters more than pure EV.

Expected Value in Gambling and Games

Casinos are built on expected value. Every game they offer has negative EV for players—that's how they stay in business. Understanding this changed how I think about gambling.

Let's look at a simple coin toss game. You bet $100 on heads. If you win, you get $200 back (your $100 plus $100 profit). If you lose, you get nothing.

This is a fair game with EV of $0. Over time, you'd break even. But casinos don't offer fair games. They take a cut called the "house edge."

In American roulette, betting on red (18 winning numbers, 20 losing numbers including 0 and 00):

For every $100 bet on red, you expect to lose $5.26. That's the house edge. You might get lucky and win a few times, but over thousands of spins, you'll lose exactly 5.26% of everything you bet.

Professional poker players succeed because they can make positive EV decisions by reading opponents and understanding pot odds. Amateurs play by "feel." Pros play by EV.

My calculator helps you analyze any gambling scenario. Just enter the possible outcomes and their probabilities to see if a bet is worth taking.

Expected Value in Investing

Smart investors think in expected value. Every stock purchase, every real estate deal, every angel investment has multiple possible outcomes. EV helps you make rational decisions.

When I evaluate a stock, I consider scenarios:

• Bull case (30%): Company crushes earnings, stock doubles (+$100)
• Base case (50%): Steady growth, stock up 20% (+$20)
• Bear case (20%): Economy crashes, stock down 40% (-$40)

The expected value is +$32 per share. This tells me the stock is undervalued if the current price is less than $32 below my fair value estimate.

Venture capitalists use EV constantly. They might invest in 10 startups knowing 8 will fail, 1 will return 5x, and 1 might return 100x. The portfolio has positive EV even though most individual investments fail.

The key insight: You don't need to win every time. You just need positive EV. A single investment with negative expected value is a mistake. A portfolio of 100 negative EV investments is a disaster. But a portfolio of 100 positive EV investments is likely to succeed—because the law of large numbers makes expected value become actual value.

When Expected Value Misleads: The Limits

Expected value is powerful, but it's not perfect. There are situations where EV alone doesn't tell the whole story.

1. One-Time Decisions

EV assumes you can repeat a decision many times. But you only get married once. You can't "average out" a marriage over 1,000 trials. For one-time decisions, consider other factors beyond EV.

2. Ruin Risk

A bet might have positive EV but a tiny chance of bankrupting you. If you can't survive the worst case, don't take the bet—no matter how good the EV looks. This is why professional traders limit position sizing.

3. Probability Uncertainty

EV is only as good as your probability estimates. If you think there's a 90% chance of success when it's really 10%, your EV calculation will be completely wrong. Be conservative with probabilities you're uncertain about.

4. Non-Monetary Outcomes

Some outcomes can't be easily quantified in dollars. Happiness, reputation, time, relationships—these matter too. A job with higher salary EV might make you miserable. Consider the whole picture.

5. Black Swan Events

EV calculations often miss rare, extreme events. The 2008 financial crisis was a "black swan"—something models said was virtually impossible but happened anyway. Always ask: "What am I missing?" and "What if the worst case is worse than I imagined?"

Expected Value vs. Most Likely Outcome

This is a crucial distinction that trips people up constantly. Expected value is NOT the same as the most likely outcome.

Let me give you an example. You're offered this bet:

• 99% chance: Win $1
• 1% chance: Lose $1,000

The most likely outcome is winning $1 (99% chance). But the expected value is -$9.01, which is terrible! Even though you'll probably win this single bet, the 1% chance of losing $1,000 makes the overall EV deeply negative.

This is why lottery tickets have negative EV. You'll probably win nothing (most likely outcome), but even if you occasionally win small amounts, the tiny probability of hitting the jackpot doesn't compensate for all the losing tickets. The EV of a lottery ticket is always negative.

When making decisions, ask yourself two questions:

1. What's the most likely outcome? (What will probably happen?)
2. What's the expected value? (What happens on average over many trials?)

Sometimes they align. Sometimes they don't. Smart decision-makers consider both.

My Rules for Using Expected Value

After years of using EV for investing, business, and life decisions, I've developed some rules:

• Always calculate EV before risky decisions: Don't rely on gut feelings. Do the math. Positive EV doesn't guarantee success, but negative EV guarantees long-term failure.
• Be conservative with probabilities: If you're unsure about probabilities, assume the worst. Better to be pleasantly surprised than disappointed.
• Consider ruin risk separately: No matter how good the EV looks, don't risk more than you can afford to lose. A positive EV bet that bankrupts you is a mistake.
• Think long-term, not short-term: EV shows what happens over many trials. A single positive EV bet might lose. But over 100 bets, you'll likely come out ahead.
• Combine EV with other factors: Money isn't everything. Consider time, happiness, relationships, and personal values. EV is one tool, not the whole toolkit.
• Update probabilities with new information: As you learn more, recalculate. Don't be married to outdated assumptions.
• Distinguish between EV and most likely outcome: Just because something is likely doesn't mean it has good EV. Just because EV is good doesn't mean success is likely.
• Use EV for investing, not gambling: Casinos always have the edge. Unless you're a professional advantage player, gambling has negative EV by design. Focus on positive EV activities like education, career growth, and smart investing.