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Sports betting odds come in three formats: American (+200 / -150), decimal (3.00 / 1.67), and fractional (2/1 / 2/3). They all encode the same risk, payout, and underlying probability. Understanding how to convert between them is not optional—it is the fundamental math of pricing risk. This article provides the conversion formulas, the parlay payout mechanics, and the implied probability calculations required for systematic trading. We will cover the theory, provide a reference table, and introduce the AGON tools designed to automate this math. The goal is to stop guessing and start sizing positions with precision. This is the primer for building your own models or evaluating the output of others.
Three odds formats encode the same probability. Decimal odds × stake = total payout, including the original stake. American odds show profit relative to a $100 stake: +X means you risk $100 to win $X on an underdog; -X means you must risk $X to win $100 on a favorite. Fractional odds X/Y mean you win $X for every $Y staked. A parlay payout is calculated by multiplying each leg's decimal odds together, then multiplying by the stake. Implied probability is 1 / decimal odds. AGON markets use decimal odds natively for their mathematical simplicity.
Every price on a sports market is just a number representing probability plus a bookmaker's margin (vig). The format of that number differs by region and platform.
Decimal odds represent the total amount returned on a winning bet for every one unit staked. This format is the most direct because it includes your original stake in the calculation.
Total Payout = Stake × Decimal OddsAmerican odds are based on a $100 stake and use positive (+) and negative (-) signs to indicate underdogs and favorites.
+200 price means a $100 stake wins $200 in profit.-150 price means you must stake $150 to win $100.Fractional odds, common in the UK, represent the profit relative to the stake. A fraction X/Y (read "X to Y") means you will win X units of profit for every Y units you stake.
AGON uses decimal odds natively across all markets. The format is universal, unambiguous, and simplifies the math for multi-leg trades like parlays. There is no need to handle separate cases for favorites and underdogs. The payout is a direct multiplication, which is ideal for algorithmic trading and on-chain contracts.
To compare prices across different sportsbooks or platforms, you need to convert odds to a common format. Decimal is the most useful for these calculations.
The formula depends on whether the American odds are positive or negative.
Decimal = (X / 100) + 1
(200 / 100) + 1 = 3.00Decimal = (100 / X) + 1
(100 / 150) + 1 = 0.667 + 1 = 1.667The conversion back to American odds depends on whether the decimal value is greater or less than 2.00.
American = (Decimal - 1) × 100
(3.00 - 1) × 100 = +200American = -100 / (Decimal - 1)
-100 / (1.50 - 1) = -100 / 0.50 = -200This is a straightforward conversion.
Decimal = (X / Y) + 1
(2 / 1) + 1 = 3.00(1 / 2) + 1 = 0.5 + 1 = 1.50Odds directly imply a probability. The implied probability is the break-even point for a bet, including the bookmaker's margin.
Implied Probability = 1 / Decimal Odds
1 / 2.00 = 0.50 or 50%1 / 3.00 = 0.333 or 33.3%1 / 1.50 = 0.667 or 66.7%This table shows common odds values across all three formats and their corresponding implied probability.
| American | Decimal | Fractional | Implied Probability |
|---|---|---|---|
| +500 | 6.00 | 5/1 | 16.67% |
| +200 | 3.00 | 2/1 | 33.33% |
| +100 | 2.00 | 1/1 (Evens) | 50.00% |
| -110 | 1.909 | 10/11 | 52.38% |
| -150 | 1.667 | 2/3 | 60.00% |
| -200 | 1.50 | 1/2 | 66.67% |
| -500 | 1.20 | 1/5 | 83.33% |
A parlay is a single bet that combines two or more individual wagers (legs) into one. For the parlay to win, every single leg must win. The appeal is a high payout for a small stake, but the risk is also significantly higher.
The payout is not the sum of the odds, but the product. This multiplicative effect is why parlay payouts grow exponentially with each added leg.
Total Payout = Stake × (Leg 1 Decimal × Leg 2 Decimal × ... × Leg N Decimal)1.91 × 2.10 = 4.0114.011 × $10 = $40.11 (Profit: $30.11)As you add legs, the total decimal odds multiply quickly.
1.91 × 2.10 × 1.80 × 2.50 × 1.95 ≈ 35.1835.18 × $10 ≈ $351.80 (Profit: $341.80)Parlays are a profit center for sportsbooks. Each leg of your parlay has a house edge (vig) priced into it. When you combine them, this edge compounds. If each leg has a ~5% house edge, a 5-leg parlay has an effective house edge of ~22%. The combined implied probability of the parlay winning ((1/1.91) * ... * (1/1.95) ≈ 2.84%) is lower than the true probability, and this gap widens with each leg.
Honest Disclosure: Parlays are entertainment products, not a positive expected value (+EV) strategy. The probability of winning is significantly lower than the payout suggests once compounded vig is factored in.
To execute these calculations instantly, AGON provides a suite of native tools.
The AGON /tools/parlay-calculator allows you to input any number of legs in any odds format (American, decimal, or fractional). It outputs the total decimal odds, total payout for a given stake, the combined implied probability, and an estimate of the house vig you are paying.
The AGON /tools/odds-converter is a simple, bi-directional tool. Input odds in one format, and it instantly displays the equivalent in the other two formats, plus the implied probability. It is designed for quick reference when comparing lines. For a third-party example, see the Action Network odds converter.
Many bettors coming from traditional platforms like FanDuel or DraftKings think in American odds. These tools provide a seamless on-ramp, allowing users to translate familiar odds into the AGON native decimal format. This improves the user experience and makes it easier to browse all AGON markets and identify value without manual math. It is a bridge from the old system to a more efficient, on-chain one.
Manual calculations are prone to error. Here are the most common failures.
The math of betting is not complex, but it is unforgiving. Manual errors in conversion or parlay calculation lead to bad trades and mis-sized positions. Use the tools to automate the process and focus on finding value in the market. Check your numbers, understand the vig, and trade with a clear view of the risk.
Apply on AGON sports markets. You can find AI agents that calculate parlays algorithmically and verify their logic against these first principles.
Next: Learn how to manage your risk with the Kelly criterion for bankroll sizing.
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The conversion from American to decimal odds depends on the sign. For positive American odds (+X), the formula is Decimal = (X / 100) + 1. For example, +300 American odds become (300 / 100) + 1 = 4.00. For negative American odds (-X), the formula is Decimal = (100 / X) + 1. For example, -200 American odds become (100 / 200) + 1 = 1.50. This conversion is essential for calculating parlay payouts and comparing odds across platforms that use different formats.
To calculate a parlay payout, first convert the odds for every leg into the decimal format. Then, multiply all the decimal odds together to get the total parlay odds. Finally, multiply this total by your stake to find the total return. For instance, a $10 stake on a 3-leg parlay with decimal odds of 1.90, 2.50, and 1.80 would be calculated as 10 × (1.90 × 2.50 × 1.80) = 10 × 8.55 = $85.50. This total includes your original $10 stake.
Implied probability is the likelihood of an outcome occurring as suggested by the betting odds, including the bookmaker's margin. It is a direct conversion from the odds and represents the break-even point for a bet. The simplest way to calculate it is from decimal odds using the formula: Implied Probability = 1 / Decimal Odds. For example, decimal odds of 2.00 imply a 50% probability (1 / 2.00), while odds of 4.00 imply a 25% probability (1 / 4.00).
They are three ways to express the same price. Decimal odds (e.g., 2.50) show the total payout for a 1-unit stake. American odds show profit relative to $100; positive numbers (e.g., +150) show profit on a $100 bet, while negative numbers (e.g., -200) show the amount needed to bet to win $100. Fractional odds (e.g., 3/2) show profit (numerator) relative to the stake (denominator). AGON uses decimal odds for their simplicity, especially in parlay calculations.
AGON uses decimal odds exclusively across all of its sports and crypto markets. This format is the global standard for professional trading and prediction markets due to its mathematical simplicity. It eliminates the ambiguity of positive and negative numbers found in American odds and makes calculating payouts, especially for complex parlays, a straightforward multiplication. For users accustomed to American or fractional odds, AGON provides an on-site odds converter tool for easy translation.
A parlay's payout increases exponentially because the odds of each leg are multiplied, not added. Each leg you add acts as a multiplier on the total odds. For example, adding a fifth leg with 2.00 decimal odds to an existing 4-leg parlay will double the potential payout. This compounding effect creates the potential for massive returns from a small stake, but it also drastically reduces the probability of winning, as every single leg must be correct for the bet to cash.