Betting Risks & Probability Visualizations
These interactive visualizations help you understand the mathematics behind betting odds, probabilities, and expected value. Use them to see why most betting systems fail in the long run.
Decimal odds represent the total return on a 1 unit stake, including the stake.
Conversion Results
Decimal
2.00
American
+100
Fractional
1/1
Probability
50.0%
Understanding the House Edge
Bookmakers build their profit margin into the odds by offering prices that imply a probability greater than 100% when all outcomes are combined. This is known as the "overround" or "vig".
Betting odds are displayed in different formats around the world, but they all represent the same thing: the probability of an outcome and the potential payout.
Decimal Odds (European)
Represent the total return on a 1 unit stake, including the stake. For example, odds of 2.50 mean you'll receive 2.50 units for every 1 unit staked (1.50 profit plus your 1 unit stake back).
Implied probability = 1 / decimal odds
American Odds (US)
Positive numbers (+150) show how much profit you'd win on a 100 unit stake. Negative numbers (-200) show how much you need to stake to win 100 units of profit.
Implied probability (positive) = 100 / (odds + 100)
Implied probability (negative) = |odds| / (|odds| + 100)
Fractional Odds (UK)
Represent the profit relative to the stake. For example, odds of 5/2 mean you'll win 5 units for every 2 units staked (plus your stake back).
Implied probability = denominator / (numerator + denominator)