Most people bet based on a gut feeling or a “hot streak.” But bettors who calculate tend to make money. These bettors rely on expected value, or EV. Expected value tells you how much you can expect to win or lose on a bet. It tells you whether a bet is worth making in the long run.
Think of it like this: if you flipped a fair coin and someone offered to pay you $1.10 every time it landed on heads, but you only lost $1.00 every time it landed on tails, this is a great deal. You would take this bet all day. This is a positive expected value. The formula looks like this:
EV = (Probability of Winning × Amount Won) – (Probability of Losing × Amount Lost)
A Simple Example to Make It Click
Let’s say a sportsbook offers you odds of +110 on a coin flip. That means you bet $100 to win $110.
| Outcome | Probability | Amount |
| Win | 50% (0.5) | +$110 |
| Lose | 50% (0.5) | -$100 |
EV = (0.5 × $110) – (0.5 × $100) = $55 – $50 = +$5
You can expect to gain $5 on average every time you make this bet. Now flip the scenario. Same coin flip, but now the odds are -120. You risk $120 to win $100.
EV = (0.5 × $100) – (0.5 × $120) = $50 – $60 = -$10
Why the House Always Has the Edge
Sportsbooks and casinos are not charities. Every game or market they offer is carefully designed to have a negative expected value for the bettor. This built-in edge is called the vig (short for vigorish) or the juice. Here’s how it works in a typical sports bet where both teams are evenly matched:
| Side | Odds Offered | Implied Probability |
| Team A | -110 | 52.4% |
| Team B | -110 | 52.4% |
| Total | 104.8% |
A true 50/50 event should add up to 100% probability. The extra 4.8% is the sportsbook’s profit margin baked right into the odds. This margin is what keeps the lights on at every casino and betting company in the world. According to the American Gaming Association, U.S. sportsbooks collected over $10.9 billion in revenue in 2023. This money came directly from bettors placing negative EV bets over and over again.
How to Calculate the Implied Probability of Any Bet
Before you can figure out whether a bet has positive or negative EV, you need to calculate the implied probability from the odds, and your own estimated probability of the outcome happening. Here’s how to convert common American odds to implied probability:
For negative odds (e.g., -150): Implied Probability = 150 ÷ (150 + 100) = 60%
For positive odds (e.g., +200): Implied Probability = 100 ÷ (200 + 100) = 33.3%
| American Odds | Implied Probability |
| -200 | 66.7% |
| -150 | 60.0% |
| -110 | 52.4% |
| +100 | 50.0% |
| +150 | 40.0% |
| +200 | 33.3% |
| +300 | 25.0% |
Once you have the implied probability, compare it to your own honest estimate. If you think a team has a 60% chance of winning but the odds only imply a 52% chance, you have found a positive EV spot.
Your Estimated Probability Is Everything
Calculating EV is straightforward. The hard part is estimating the true probability of an outcome accurately. This is called finding an edge, which separates sharp bettors from casual ones.
Sharp bettors use things like advanced stats and models, line movement tracking, injury and lineup information the market hasn’t fully priced in, and historical trends in specific situations.
A study published in the Journal of Prediction Markets found that bettors who tracked their own estimated probabilities and compared them to market odds showed a significant improvement in long-term returns compared to those who bet based on instinct alone.
The Difference Between a Good Bet and a Winning Bet
A good bet has a positive expected value, regardless of whether it wins. A bad bet has a negative expected value, regardless of whether it wins.
A great bet is when you bet on a team that you believe has a 70% chance of winning, and you get odds that imply only a 55% chance. If the team loses, it was still a great bet. You made the right decision with the information available.
But picking a 10-game parlay that happens to hit doesn’t mean you made smart bets. The expected value of most parlays is deeply negative. Sportsbooks love parlays because they multiply their edge across every single leg.
| Bet Type | Approximate House Edge |
| Single game spread bet | ~4.5% |
| 2-team parlay | ~10% |
| 4-team parlay | ~25% |
| 10-team parlay | ~60%+ |
Bankroll Management and EV Go Hand in Hand
You can still go broke if you bet too much on any single game, even if you are consistently finding positive EV bets. This is why serious bettors pair EV thinking with a disciplined staking strategy. The most well-known approach is the Kelly Criterion, which tells you what percentage of your bankroll to risk based on your edge.
Kelly % = (Edge ÷ Odds)
Where edge = your estimated win probability minus the implied win probability.
For example, if you think a team has a 60% chance of winning and the odds imply 52.4% (standard -110 odds):
- Edge = 60% – 52.4% = 7.6% or 0.076
- Odds = 10/11 (the decimal payout at -110)
- Kelly % = 0.076 ÷ 0.909 ≈ 8.4% of your bankroll
Most experienced bettors use a “fractional Kelly” approach, which means betting half or a quarter of the Kelly recommendation to reduce variance and protect their bankroll during cold stretches.
Common Mistakes That Destroy EV Thinking
Even bettors who understand expected value can fall into traps that can sabotage their results. Here are the most common ones:
- Chasing losses. The temptation to make bigger bets to “get it back” is strong when you are down. But this has nothing to do with EV. The value of a bet doesn’t change based on your current balance.
- Ignoring line shopping. Getting -110 instead of -115 on the same bet might seem small, but it’s a meaningful difference in expected returns over a season. Always check multiple books.
- Overestimating your edge. Confidence is good, but overconfidence is expensive. Be honest with yourself when estimating probabilities.
- Betting for entertainment. There is nothing wrong with placing a fun bet, but know what you are doing. Recreational bettors pay for entertainment with negative EV. Professional bettors only bet when the math says to.
A Quick EV Checklist Before Every Bet
Before you place your next wager, run through these questions:
| Question | What to Look For |
| What are the odds? | Convert to implied probability |
| What do I think the true probability is? | Be honest and specific |
| Is my probability higher than the implied one? | If yes, potential positive EV |
| How confident am I in my estimate? | Higher confidence = larger stake |
| Have I shopped for the best line? | Always compare at least 2-3 books |
| Does this fit my bankroll plan? | Never bet more than Kelly suggests |
If you can answer all six questions before every bet, you are already thinking at a higher level than the vast majority of bettors out there.
The Long Game Is the Only Game
Expected value is not a get-rich-quick system. It is a framework for making smarter decisions over time. Any single bet can go either way. But positive EV decisions will outperform negative EV ones across hundreds and thousands of bets.
The bettors who win consistently are more disciplined. They think in probabilities and care more about the quality of the decision than the result of any one game. Also, they let the math do the heavy lifting so emotions don’t get a vote.