Margin and expected value
How to measure the margin built into a set of odds and how to work out the long-run average result of a bet, with every step of the arithmetic shown.
Two questions decide what a bet costs: how much margin sits inside the prices, and what the average result of a stake is over a long series. The pages below answer both with formulas you can check by hand, and neither answer is ever in the player's favour.
- What are fair odds, and why bookmakers never offer them
Fair odds are 1 divided by the true probability, with no margin. See the formula, a worked example in KES and why offered prices always sit below them.
- Bookmaker payout percentage: what it is and how to work it out
The payout percentage is the share of stakes a market's prices return on average: 100 divided by total implied probability. Steps and two worked cases.
- Expected loss per KES 1,000 staked at a given bookmaker margin
Average loss on KES 1,000 staked is 1,000 x margin / (1 + margin). See the table from 2% to 15% margin, the steps and why single results differ.
- Variance in betting: why losing streaks are normal
Losing streaks follow from arithmetic, not bad luck. Compute the chance of n losses in a row, how often streaks occur and what they mean for a budget.
- How to work out the expected value of a bet
Expected value is the long-run average result of a bet: stake x (probability x odds - 1). See the formula, a worked case in KES and why it is negative.
- How to calculate the bookmaker's margin on a market
Add the implied probabilities of every outcome and subtract 100%: that is the bookmaker's margin. Worked two-way and three-way cases in plain steps.