One grid, every market

Once you have P(x, y) for every scoreline, every market is a sum:

• Match odds: home = Σ P(x, y) over x > y; draw over x = y; away over x < y.
• Totals: over 2.5 = Σ over x + y ≥ 3.
• Asian handicap −1: home covers over x − y > 1, pushes at x − y = 1.
• Both teams to score: Σ over x ≥ 1 and y ≥ 1.
• Correct score: the cell itself.

Because they all come from one distribution they can never contradict each other. A book built market by market can: an over 2.5 price that implies more goals than the correct-score prices allow. The platform checks this with the Skellam law, the exact distribution of the goal difference, and the largest disagreement it finds is 4 × 10⁻¹¹.

Adding the margin

A fair price is 1 / p. A quoted price is a fair price with a margin: multiply every probability by (1 + m) and invert. The Predict page's margin control does exactly that, and the Every Market tab shows the fair and quoted price side by side.