Overround and margin formulas

Add every outcome's implied probability in a market and the total is the booksum, β, always over 100 per cent. From it: overround = β − 1 (the excess over a fair book, in points); margin = (β − 1)/β, equivalently 1 − 1/β (the share of turnover the house keeps). A market summing to 104.50 per cent carries an overround of 4.50 points and a margin of 4.30 per cent; a pound spread across it returns 1/1.045 = 95.7p on average. Stack markets into a multiple and booksums multiply, not add: two legs at 104.50 per cent combine to 1.0450 × 1.0450 = 109.20 per cent, a margin of 8.43 per cent from a single extra leg. That multiplication is the whole of the next table.