Hedge & Cash-Out Calculator

The figures come from backHedge and layHedge in math.ts, and math.test.ts pins them against arithmetic done outside the implementation: the 57.14 and the 20/7 lock on the worked example above, equalization of the two branches across five price pairs and three lay prices, the closed form for what commission costs when you lay at the price you backed, and the cash-out indifference point at 20 + 20/7.

The half-hedge figures quoted above are pinned there too: backing the other side at 50% the branches are 220/7 and -60/7 while the lock the Return / stake cell divides is unchanged at 20/7, and the lay-mode test asserts the same invariance separately, that the slider halves the stake and the liability and moves both branches but leaves the lock where it is.

That invariance is what makes the cell a figure about a hedge you have not placed. Two of the identities quoted here are already asserted there. One is that the lock is positive exactly when the two implied probabilities add to less than 1, tested at five pairs either side of the line.

The other is that laying at L is the same bet as backing the other side at L / (L - 1), which is why both modes reach the same lock by different routes and why the exchange liability equals the stake the back-side hedge would need.

The break-even prices, the 3.70% return on total outlay, and the result that a hedge at a fair price returns the position's existing expected value were derived from those same formulas and checked numerically at several inputs on 2026-09-09; they are consequences of the model rather than separate claims about the world.

A passing test means the code computes this model correctly, not that the prices on your screen are prices you will be filled at.

The cash-out margin comes from priceCashOut in math.ts, which calls no-vig-calculator's analyseMarket rather than reimplementing de-vigging, and math.test.ts pins the offer probability, fair probability and margin against a hand-derived example, plus the case where either price cannot describe a real bet or no offer has been entered.

The break-even price and the reader's distance from it come from hedgeThreshold in math.ts.

In back mode it is read off the same implied-probability identity as the lock itself; in lay mode it is the price that lays at zero lock (equal to the back price) shifted by what commission costs in price terms, a one-line basis of its own rather than the same identity. math.test.ts pins it against the four worked figures this page used to hand-type in its FAQ (1.333 and 1.667 backing the other side, 3.94 and 3.85 laying at 2% and 5% commission) and asserts, across a spread of prices in both modes, that its sign always agrees with backHedge's and layHedge's own equalProfit rather than being a second opinion that could disagree with the panel.