Odds Calculator

Convert between different odds formats, calculate probabilities, and analyze betting value with our comprehensive odds analysis tool 📊

Input Format:

Enter Odds Value:

Favorable Outcomes:

Total Outcomes:

Event Description (optional):

Bet Amount ($):

Odds (Decimal):

Your Estimated Probability (%):

Bankroll for Kelly Criterion ($):

Welcome to the ultimate odds calculation and analysis tool! Whether you’re exploring probability theory, analyzing sports betting opportunities, or learning about different odds formats used worldwide, this calculator provides comprehensive insights into odds conversion and value assessment. You’ll master the relationships between probability and odds while understanding how to evaluate the true value of any betting scenario.

🎯 Quick Tip

If you find this tool valuable for probability analysis, you might also want to try our Implied Probability Calculator and Expected Value Calculator for advanced betting strategy and risk assessment applications.

Table of Contents

How to Use the Odds Calculator

Follow our simple tutorial to master odds conversion and probability analysis across different scenarios:

Odds Format Conversion

Convert between the three major odds formats used worldwide:

Choose input format: Select from decimal, fractional, American, or implied probability
Enter your value: Input the odds in your chosen format (e.g., 2.50, 3/2, +150, 40%)
Get all formats: Instantly see the equivalent in all other odds formats
View probability: See the implied probability percentage for the given odds

Probability to Odds Analysis

Calculate odds from probability scenarios and understand the mathematics:

Define favorable outcomes: Enter how many ways your event can occur
Set total outcomes: Input the total number of possible outcomes
Add description: Optionally describe your scenario for context
Calculate results: See probability percentage and equivalent odds in all formats

Betting Value Assessment

Analyze betting opportunities for mathematical value and optimal stake sizing:

Enter bet details: Input your proposed bet amount and the offered odds
Add your assessment: Enter your estimated true probability of the event
Include bankroll: Add your total bankroll for Kelly Criterion calculation
Review analysis: See expected value, edge calculation, and optimal bet sizing

Understanding Different Odds Formats

Decimal Odds (European Format)

Decimal odds represent the total return for every $1 wagered, including your original stake.

Decimal Odds Calculation

Total Return = Stake × Decimal Odds

Profit = (Stake × Decimal Odds) – Stake

Implied Probability = 1 / Decimal Odds × 100%

Take a look at your data: Decimal odds of 2.50 mean you receive $2.50 for every $1 wagered (including your $1 stake back), giving you a $1.50 profit. This implies a 40% probability of the event occurring.

Fractional Odds (UK Format)

Fractional odds show the potential profit relative to your stake.

Fractional Odds Calculation

Profit = Stake × (Numerator / Denominator)

Total Return = Stake + Profit

Implied Probability = Denominator / (Numerator + Denominator) × 100%

Example: 3/2 odds mean you win $3 for every $2 wagered. A $10 bet returns $15 profit plus your $10 stake back, totaling $25.

American Odds (Moneyline)

American odds use positive and negative numbers to represent underdogs and favorites.

American Odds Calculation

Positive (+150): Profit = Stake × (Odds / 100)

Negative (-200): Profit = Stake × (100 / |Odds|)

Positive Probability: 100 / (Odds + 100) × 100%

Negative Probability: |Odds| / (|Odds| + 100) × 100%

American odds tell you how much you need to bet to win $100 (negative) or how much you win for every $100 bet (positive).

Quick Conversion Reference

Decimal	Fractional	American	Implied Probability
2.00	1/1 (Evens)	+100	50.0%
1.50	1/2	-200	66.7%
3.00	2/1	+200	33.3%
1.33	1/3	-300	75.0%
4.00	3/1	+300	25.0%

Value Betting and Mathematical Edge

Expected Value in Betting

Expected value determines the long-term profitability of any betting decision:

Expected Value Formula

EV = (Probability of Win × Profit) – (Probability of Loss × Stake)

EV = (P × (Odds – 1)) – ((1 – P) × 1)

Where P = True probability (as decimal)

Positive expected value indicates a profitable bet over time, while negative EV means you’ll lose money in the long run.

Kelly Criterion for Optimal Bet Sizing

The Kelly Criterion calculates the optimal percentage of your bankroll to wager:

Kelly Criterion Formula

f = (bp – q) / b

f = Fraction of bankroll to bet

b = Odds received on the wager (decimal odds – 1)

p = Probability of winning

q = Probability of losing (1 – p)

Real-World Betting Examples

🏈 Sports Betting Scenario

Offered odds: 2.20 (decimal)

Your assessment: 50% probability

Implied probability: 45.45%

Expected value: +9.1% edge

Kelly bet: 4.1% of bankroll

🎲 Casino Game Analysis

Roulette red/black: 1.95 odds

True probability: 47.37%

Implied probability: 51.28%

Expected value: -7.6% edge

Recommendation: Avoid this bet

🏇 Horse Racing Value

Offered odds: 5.00 (decimal)

Your assessment: 25% probability

Implied probability: 20%

Expected value: +25% edge

Kelly bet: 6.25% of bankroll

⚠️ Important Betting Considerations

Expected value calculations assume your probability assessments are accurate. Overconfidence in your predictions can lead to significant losses. Always bet responsibly and never risk more than you can afford to lose. The Kelly Criterion can suggest large bets with high edges, so many professionals use fractional Kelly (e.g., 25% of suggested amount) for safer bankroll management.

Frequently Asked Questions

How do I convert American odds to decimal odds?

For positive American odds (+150): Decimal = (American odds / 100) + 1 = (150/100) + 1 = 2.50. For negative American odds (-200): Decimal = (100 / |American odds|) + 1 = (100/200) + 1 = 1.50. This gives you the total return including your stake.

What does implied probability mean in betting odds?

Implied probability is the probability percentage that the odds suggest. It’s calculated as 1/decimal odds × 100%. For example, decimal odds of 2.00 imply a 50% probability. Bookmakers build in a margin (vig/juice), so implied probabilities for all outcomes typically sum to more than 100%.

How do I identify value bets using odds?

A value bet occurs when your assessed probability is higher than the implied probability of the odds. Calculate expected value: if it’s positive, you have a value bet. For example, if you believe an event has a 60% chance but odds imply only 45%, you have positive expected value and should consider betting.

What is the Kelly Criterion and should I use it?

The Kelly Criterion calculates the optimal percentage of your bankroll to bet for maximum long-term growth. While mathematically sound, it can suggest large bets that many find uncomfortable. Many professionals use fractional Kelly (betting 25-50% of the suggested amount) for more conservative bankroll management.

Why do odds formats differ between countries?

Different regions developed different systems: decimal odds are popular in Europe and Australia for their simplicity, fractional odds are traditional in the UK and Ireland, while American odds evolved in the US. All formats convey the same information but in different mathematical representations.

How do bookmaker margins affect odds?

Bookmakers build in a profit margin (overround) by offering odds that imply probabilities totaling more than 100%. For example, both sides of a coin flip might be offered at 1.90 instead of 2.00, creating a 5.26% margin. This ensures the bookmaker profits regardless of outcome.

Can I use odds to calculate exact probabilities?

Odds give you implied probabilities, but these include the bookmaker’s margin and may not reflect true probabilities. For mathematical scenarios (dice, cards, etc.), you can calculate exact probabilities. For sports and events, odds provide market consensus but aren’t necessarily accurate probability measures.

What’s the difference between true odds and betting odds?

True odds reflect the actual mathematical probability of an event (e.g., 1/6 for rolling a specific number on a fair dice). Betting odds are set by bookmakers and include their profit margin, market pressures, and may not accurately reflect true probabilities, especially for unpredictable events.

How do I handle negative expected value situations?

Negative expected value means you’ll lose money over time. Avoid these bets unless you’re betting for entertainment value and can afford the loss. Most casino games and lottery tickets have negative expected value by design, which is how these institutions profit.

Should I always bet the Kelly Criterion amount?

Not necessarily. Kelly assumes perfect probability estimation and no other factors. In reality, use fractional Kelly (25-50% of suggested amount), consider your risk tolerance, and remember that large Kelly bets can feel uncomfortable. Conservative betting often provides better long-term sustainability.

🎯 Master Odds Analysis and Value Betting

Understanding odds conversion and expected value calculation is essential for any form of probability analysis, whether in gambling, investing, or decision-making under uncertainty. Use these tools to develop a mathematical approach to risk assessment, identify value opportunities, and make informed decisions based on quantitative analysis rather than intuition alone.