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  4. Expected Value (EV)
Back to Gambling Math & Concepts
intermediate
8 min readGambling Math & ConceptsBonusBellLast updated:February 22, 20262 of 9
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BonusBell Editorial Team

The BonusBell editorial team researches and reviews online gambling platforms across all 50 US states. Every ranking and recommendation is backed by hands-on testing, regulatory verification, and transparent methodology. Our editorial standards require primary sources for every tax rate, launch date, and bonus figure; every article carries a fact-checked date; and corrections are issued publicly when operators or regulators change the facts.

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Where to Play

Top-rated platforms reviewed by our editorial team

FanDuel Sportsbook

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9.6

Best for: overall experience and ease of use

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DraftKings Sportsbook

Best for Promotions & Odds Boosts

9.5

Best for: daily promotions and prop betting

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BetMGM Sportsbook

Best for Odds Quality

9.2

Best for: sharp odds and casino crossover

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Frequently Asked Questions

What does expected value mean in betting?

Expected value (EV) is the average amount you expect to win or lose per bet if you placed the same wager thousands of times. Positive EV (+EV) means the bet is profitable long-term. It is calculated as (probability of winning times profit) minus (probability of losing times stake).

How do I find positive expected value bets?

Compare your estimated probability of an outcome to the implied probability from the odds. If you believe a team has a 55% chance to win but the odds imply only 45%, that is a +EV bet. Sharp lines and statistical models help you estimate true probabilities.

Can I lose money on positive EV bets?

Absolutely, in the short term. EV only guarantees results over a large sample size. You can lose 10 +EV bets in a row. The key is proper bankroll management so you survive variance long enough for your edge to materialize.

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intermediate
8 min read

Expected Value (EV)

The single most important concept for making smart gambling decisions.

BonusBell Team

Expected Value (EV) is the mathematical average of what you'll win or lose on a bet over the long run. It's the single most important concept for understanding gambling— and the foundation for every smart betting decision.

Expected Value Formula
EV = (Win × Pwin) - (Loss × Plose)
Win Amount
× Probability
Loss Amount
× Probability

What Is Expected Value?

EV answers the question: "If I made this bet a million times, how much would I win or lose per bet on average?"

EV Formula
(Win Amount × Win Probability) - (Loss Amount × Loss Probability)=EV

This calculates the weighted average outcome of a bet.

Example: Coin Flip Bet

Someone offers you a bet: flip a fair coin. Heads you win $11, tails you lose $10.

Coin Flip EV
($11 × 0.50) - ($10 × 0.50)=+$0.50

On average, you win $0.50 per flip. This is a +EV bet—you should take it every time.

Strategy Insight

Any bet with positive expected value (+EV) is worth making in the long run. Professional gamblers and advantage players only make +EV bets.

EV in Casino Games

In casino games, EV is almost always negative—that's the house edge.

Roulette: Betting on Red
($10 × 18/38) - ($10 × 20/38)=-$0.53

On a $10 bet on red in American roulette, you lose $0.53 on average. The house edge is 5.26%.

Good to Know

Negative EV doesn't mean you'll lose every time. Short-term results vary wildly. But over thousands of bets, your results will converge toward the expected value.

Finding +EV Opportunities

While most gambling is -EV, there are exceptions:

✓ Promotions and Bonuses

Some bonuses with low wagering requirements can be +EV when played optimally.

✓ Poker vs. Weak Players

Poker is player vs. player. Skilled players have +EV against weaker opponents.

✓ Sports Betting (with Edge)

Finding mispriced lines can create +EV opportunities, but it's extremely difficult.

✓ Card Counting

When the deck is rich in high cards, blackjack becomes +EV (and casinos will ban you).

EV vs. Variance

Understanding the difference is crucial:

  • EV tells you what to expect in the long run
  • Variance tells you how much results will swing in the short run

A -EV game with high variance can produce winning sessions. You might win on slots (high variance) but lose on blackjack (low variance) in a single night— even though blackjack has better EV.

Warning

Winning streaks don't change EV. If you're up $500 in a -EV game, continuing to play still has negative expected value. Walk away while you are ahead.

Applying EV to Decisions

Use EV thinking beyond gambling:

  • Should I pay for that extended warranty? (Usually -EV)
  • Should I buy lottery tickets? (Extremely -EV)
  • Should I insure my blackjack hand? (Almost always -EV)

Strategy Insight

When someone offers you a bet or proposition, always ask: "What's the expected value here?" If you can't calculate it, assume it favors the other party.

Return to Player (RTP) by Game

Higher is better for the player

Try It: Expected Value Calculator
($11 × 50%) − ($10 × 50%) = $0.50
Expected Value
+0.50
ROI per Bet
5.0%
Verdict
+EV Bet!

Good to Know

Calculate Your Edge

Use our Bonus Value Calculator to find the true EV of any bonus offer. Got a free bet? The Free Bet Converter shows you the estimated conversion value.

Sources & References

  1. Expected value formula — standard probability theory: EV = Σ(outcome × probability). Independently verifiable from any statistics textbook.
  2. Roulette EV calculation — mathematical derivation using standard probability and verified house edge figures (American roulette: −5.26% EV per dollar wagered).
  3. Nevada Gaming Control Board. Nevada Gaming Abstract. Published annually at gaming.nv.gov. Referenced for reported casino game win percentages used in RTP context.
  4. National Council on Problem Gambling (NCPG). Resources at ncpgambling.org. Long-term negative EV is a factor cited in responsible gambling education; all wagering carries financial risk.

Mathematical claims are independently verifiable derivations. BonusBell platform analysis reflects data from 220+ tracked platforms as of February 2026.

Key Takeaways

  • 1EV is the average outcome of a bet over many repetitions
  • 2+EV bets are profitable long-term; -EV bets cost you money
  • 3Most casino games are -EV by design (the house edge)
  • 4Variance causes short-term swings, but can't overcome long-term EV
  • 5+EV opportunities exist in promotions, poker, and finding mispriced lines