01. From odds to probability
The reciprocal of decimal odds gives the break-even win probability. At 2.50, that is 1 ÷ 2.50 = 40%. If a binary bet truly wins more than 40% of the time at that price, its mathematical expectation is positive before costs.
Bookmakers can price both sides of an event below fair odds. Two outcomes at 1.90 each imply 52.63% + 52.63% = 105.26%. The excess over 100% is called the overround. It is not a direct measurement of a bookmaker’s actual profit.
Explore odds conversion →02. Expected value is an average
Consider a 100-unit bet at 2.10 with a genuine 52% win probability. A win profits 110; a loss costs 100. The probability-weighted profit is 0.52 × 110 − 0.48 × 100 = 9.20. The next bet still finishes at +110 or −100, not +9.20.
Change that estimated probability to 45% and expected profit becomes −5.50. A calculator cannot tell you which estimate is right. Track and evaluate your probability estimates rather than treating confidence as evidence.
Try the EV calculator →03. Variance and losing runs
Even a fair coin can land on tails repeatedly. For independent bets with a 50% win chance, the probability of five specified consecutive losses is 0.5⁵ = 3.125%. The probability of experiencing a run somewhere in a longer series is different and generally larger.
Increasing your stake scales both expected profit and possible loss. It does not improve the probability of winning. Never chase losses; set time and money limits before gambling and stop if it affects your wellbeing.
04. When multiplying probabilities breaks down
Two independent events each with a 50% probability have a 25% joint probability. But “home team wins” and “home team scores” in the same football match are dependent: one changes the likelihood of the other. Multiplying their standalone probabilities is not a valid joint model.
Our accumulator calculator multiplies prices. Its probability figure is price-implied and explicitly assumes independence; it does not estimate correlation or a true chance of success.
Build an accumulator →05. Quarter lines, without the mystery
A −0.25 handicap is half a stake on 0 and half on −0.5. In a draw, the first half pushes and the second loses. A +0.25 line in a draw does the reverse: half pushes and half wins. See each portion separately in the settlement tool.
Explore handicap settlement →