Understanding Probability in Betting: Odds vs. Reality
See what betting odds really mean. Convert American, fractional, and decimal odds to implied probability percentages.
Quick Answer: What Is Implied Probability?
Implied probability is what the odds say about the likelihood of an outcome—expressed as a percentage.
Key reality: Implied probability always adds up to MORE than 100% due to sportsbook fee (vig). This is how sportsbooks make money.
Converting American Odds to Probability
Negative Odds (Favorites)
Formula:
Probability = Negative Odds ÷ (Negative Odds + 100)Example -110 odds:
110 ÷ (110 + 100) = 110 ÷ 210 = 52.38%| Odds | Calculation | Implied Probability |
|---|---|---|
| -110 | 110 ÷ 210 | 52.38% |
| -150 | 150 ÷ 250 | 60.00% |
| -200 | 200 ÷ 300 | 66.67% |
Positive Odds (Underdogs)
Formula:
Probability = 100 ÷ (Positive Odds + 100)Example +150 odds:
100 ÷ (150 + 100) = 100 ÷ 250 = 40.00%| Odds | Calculation | Implied Probability |
|---|---|---|
| +150 | 100 ÷ 250 | 40.00% |
| +200 | 100 ÷ 300 | 33.33% |
| +300 | 100 ÷ 400 | 25.00% |
Converting Fractional Odds to Probability
Formula:
Probability = Denominator ÷ (Numerator + Denominator)Example 2/1 odds:
1 ÷ (2 + 1) = 1 ÷ 3 = 33.33%| Odds | Calculation | Implied Probability |
|---|---|---|
| 2/1 | 1 ÷ 3 | 33.33% |
| 5/1 | 1 ÷ 6 | 16.67% |
| 10/1 | 1 ÷ 11 | 9.09% |
Quick mental math: For fractional odds, just add numerator + denominator, then divide denominator by that total.
Converting Decimal Odds to Probability
Formula:
Probability = 1 ÷ Decimal OddsExample 2.00 odds:
1 ÷ 2.00 = 50.00%| Odds | Calculation | Implied Probability |
|---|---|---|
| 1.50 | 1 ÷ 1.50 | 66.67% |
| 2.00 | 1 ÷ 2.00 | 50.00% |
| 3.00 | 1 ÷ 3.00 | 33.33% |
The Vig Exposed: How Sportsbooks Profit
Here’s what happens when both sides of a game have -110 odds:
Both Sides at -110
| Side | Odds | Implied Probability |
|---|---|---|
| Team A | -110 | 52.38% |
| Team B | -110 | 52.38% |
| Total | 104.76% |
The math doesn’t lie: 104.76% > 100%. That extra 4.76% is the sportsbook’s fee (vig), taken from every bet.
Real-World Example
NFL Game:
- Chiefs at -110
- Texans at -110
- True probability: 50/50 (coin flip)
- Implied probability: 52.38% each
What this means:
- Every $100 bet, you’re paying ~$4.76 in vig
- To break even, you need to win 52.38% of bets
- But true probability is only 50%
- Built-in disadvantage
Probability vs. Odds: Quick Reference
| True Probability | Fair Odds | Typical Sportsbook Odds | Implied Probability |
|---|---|---|---|
| 10% (1 in 10) | +900/-900 | +850/-850 | 10.5% |
| 25% (1 in 4) | +300/-300 | +275/-350 | 26.7% |
| 33% (1 in 3) | +200/-200 | +180/-220 | 35.7% |
| 50% (1 in 2) | +100/-100 | -110/-110 | 52.4% |
| 75% (3 in 4) | -300/+300 | -350/+275 | 77.8% |
| 90% (9 in 10) | -900/+900 | -1100/+850 | 91.7% |
Pattern: Sportsbooks always give worse odds than fair probability dictates. This is their business model.
Value Betting: Finding +EV Opportunities
Value betting is when you believe true probability is higher than implied probability.
Example: Finding Value
Scenario:
- Sportsbook odds: +200 (implied 33.33%)
- Your research says true probability is 40%
Is this value?
Expected Value = (True Probability × Payout) - Stake
EV = (0.40 × $300) - $100
EV = $120 - $100 = +$20+EV: You have positive expected value. This bet wins money in the long run (if your 40% estimate is correct).
Value Betting Checklist
| Question | If Yes → Value Bet? |
|---|---|
| Is implied probability < your estimate? | ✅ Yes |
| Are you confident in your research? | ✅ Yes |
| Is the bet within your bankroll limits? | ✅ Yes |
| Is the sportsbook reliable/paying? | ✅ Yes |
Reality check: Most casual bettors don’t beat the vig. Value betting requires significant research, discipline, and accepting variance.
Law of Large Numbers: Why One Bet Means Nothing
Flip a Coin 10 Times vs. 1000 Times
| Flips | Expected Heads | Variance Range (95% confidence) |
|---|---|---|
| 10 | 5 | 2-8 heads |
| 100 | 50 | 40-60 heads |
| 1000 | 500 | 470-530 heads |
For betting: One bet tells you nothing. 100 bets tell you if you’re winning or losing.
The sample size trap: “I won 3 bets in a row, I’m good at this” — No, you’re just lucky. Meaningful results emerge after 100+ bets.
Expected Value: The Math Behind Every Bet
Formula:
EV = (Probability of Win × Profit) - (Probability of Loss × Stake)Example: +150 Bet (40% true probability)
EV = (0.40 × $150) - (0.60 × $100)
EV = $60 - $60 = $0Meaning: This is a fair bet (no edge for you or sportsbook)
Example: +150 Bet but you think it’s 50%
EV = (0.50 × $150) - (0.50 × $100)
EV = $75 - $50 = +$25+EV: If your probability estimate is correct, this bet makes money long-term.
Example: -110 Bet but true probability is 55%
EV = (0.55 × $100) - (0.45 × $110)
EV = $55 - $49.50 = +$5.50+EV: This is how professional sports bettors beat the vig—by having better probability estimates than the sportsbook.
Common Probability Mistakes
| Mistake | Why It’s Wrong | Correct Thinking |
|---|---|---|
| ”I’m due for a win” | Gambler’s fallacy | Past doesn’t affect future |
| ”Odds -110 means 50/50” | Forgot vig | Actually 52.4% implied |
| ”I can predict coin flips” | Random events | Can’t predict, only estimate |
| ”Big win means I’m good” | Variance vs. skill | Needs 100+ bets to know |
Probability Tools & Calculators
Quick Conversion Cheat Sheet
Bookmark this: Copy these formulas or use an odds converter.
American to Probability (Negative):
- Odds ÷ (-Odds + 100)
American to Probability (Positive):
100 ÷ (Odds + 100)
Fractional to Probability:
Denominator ÷ (Numerator + Denominator)
Decimal to Probability:
1 ÷ Decimal OddsOnline Tools
Search for:
- “Odds to probability calculator”
- “Betting EV calculator”
- “Implied probability converter”
Summary
Probability in betting is hidden in the odds. American, fractional, and decimal odds all express implied probability—but always include the sportsbook’s fee (vig).
Key takeaways:
- Implied probability always exceeds 100% due to vig
- Convert odds to percentages to understand true chances
- Value betting requires your probability > implied probability
- One bet means nothing—law of large numbers applies
- EV math tells you if a bet is +EV or -EV
Final reality: Most casual bettors have -EV on every bet (they’re paying the vig). Professional bettors find +EV situations through research, but this is hard, inconsistent work—not a reliable income.
Understanding probability helps you make informed bets. It doesn’t make you a winner, but it prevents you from betting blindly. Every bet should have a reason, not just a feeling.
