Data Source and Methodology

This calculator uses standard, universally accepted formulas from mathematics and probability theory. The foundational concepts of probability and odds conversion are fundamental principles taught in statistics.

AuthoritativeDataSource: OpenStax. (2018). Introductory Statistics. Rice University.
Reference: Chapter 3: Probability Topics.
Available at: https://openstax.org/books/introductory-statistics/pages/3-1-terminology

All calculations are strictly based on established formulas from probability theory and statistics. This tool provides a direct conversion without accounting for bookmaker margins (vig or juice).

The Formulas Explained

The calculator interlinks several key formulas. When you change one value, all others are recalculated based on these principles.

1. Probability and Basic Odds

Given $F$ (favorable outcomes) and $U$ (unfavorable outcomes):

Probability of Event $P(E) = \frac{F}{F + U}$

Odds For = $F : U$

Odds Against = $U : F$

2. Implied Probability (IP) from Odds

This converts betting odds back into their "implied" probability (excluding the bookmaker's margin).

From Fractional (e.g., $F/N$): $IP = \frac{N}{N + F}$

From Decimal (e.g., $D$): $IP = \frac{1}{D}$

From American Positive (e.g., $+A$): $IP = \frac{100}{100 + A}$

From American Negative (e.g., $-A$): $IP = \frac{|A|}{100 + |A|}$

3. Payout Calculation

Given a Stake ($S$) and Decimal Odds ($D$), the calculations are simplest:

Total Payout = $S \times D$

Net Profit = $\text{Total Payout} - S = S \times (D - 1)$

Glossary of Variables

Term Definition
Favorable Outcomes The number of ways an event you are interested in can happen.
Unfavorable Outcomes The number of ways an event you are interested in can *not* happen.
Stake The amount of money you are wagering or betting.
American Odds Positive (+150) shows profit on a $100 bet. Negative (-110) shows stake needed to profit $100.
Decimal Odds Represents the total payout for every $1 wagered (including the original stake). E.g., 2.50.
Fractional Odds Represents the net profit relative to the stake (e.g., 5/2 means you win $5 for every $2 staked).
Implied Probability The odds converted into a percentage, representing the likelihood of the outcome.
Total Payout Your original stake returned to you, plus your net profit.
Net Profit The total amount won, not including your original stake.

How It Works: A Step-by-Step Example

Let's say you want to bet $50 on an underdog with American odds of +200.

  1. Enter Inputs:
    • In the "Stake" field, you enter 50.
    • In the "American Odds" field, you enter +200 (or just 200).
  2. Instant Conversions: The calculator immediately populates the other fields:
    • Decimal Odds: 3.00 (Calculated as $1 + (200 / 100)$)
    • Fractional Odds: 2/1 (Calculated as $200 / 100$)
    • Implied Probability: 33.33% (Calculated as $100 / (100 + 200)$)
  3. Review Results: The results section updates to show:
    • Net Profit: $100.00 (Your $50 stake wins $100)
    • Total Payout: $150.00 (Your $100 profit + your $50 stake back)

Frequently Asked Questions (FAQ)

What is the difference between "odds" and "probability"?

Probability is the likelihood of an event happening, expressed as a number between 0 and 1 (or 0% to 100%). For example, a 25% probability means an event is expected to happen 1 out of every 4 times.
Odds express the ratio of unfavorable outcomes to favorable outcomes (or vice-versa). A 25% probability ($1 / (1+3)$) is equivalent to "Odds Against" of 3-to-1 (3 unfavorable outcomes for every 1 favorable outcome).

What does "+200" or "-150" mean in American odds?

This is the most common format in the United States.

  • Positive Odds (e.g., +200): This is the underdog. The number indicates how much profit you will make on a $100 bet. A +200 bet means a $100 stake wins $200 (for a total payout of $300).
  • Negative Odds (e.g., -150): This is the favorite. The number indicates how much you must bet to win $100. A -150 bet means you must stake $150 to win $100 (for a total payout of $250).
How do Decimal and Fractional odds work?
  • Decimal Odds (e.g., 2.50): Common in Europe and Australia. This number represents the *total payout* (stake + profit) on a $1 bet. A $10 bet at 2.50 odds returns $25.00 ($15 profit + $10 stake).
  • Fractional Odds (e.g., 5/2): Common in the UK and Ireland. This fraction shows the *net profit* relative to the stake. A 5/2 (read "5-to-2") bet means you win $5 for every $2 you bet. A $10 bet would win $25 (for a total payout of $35).
What is the "vig" or "juice"?

The "vig" (short for vigorish) or "juice" is the bookmaker's built-in margin. If you add up the implied probabilities for all possible outcomes of an event (e.g., Team A wins, Team B wins), the total will be over 100%. That extra percentage is the bookmaker's profit margin. This calculator shows the "true" odds conversions and does not account for the vig.

Why can't I just type "25%" into the Implied Probability field?

The Implied Probability field is a *result* of the odds you enter. To calculate odds *from* a probability, use the "Calculate from Probability" section at the top. For example, a 25% probability means 1 favorable outcome and 3 unfavorable outcomes. Enter "1" and "3" in those fields, and the calculator will show you the true odds (+300, 4.00, 3/1).

Tool developed by Ugo Candido. Mathematical formulas and content verified by the CalcDomain Editorial Board.
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