Three-Way Hedge Calculator

The Three-Way Hedge Calculator (1X2) locks a football-style three-outcome market by laying off the two remaining results against an already-struck ticket. Defaults: Original Stake $100 at decimal 2.40, Outcome 2 odds 3.40, Outcome 3 odds 3.60. Typical mapping is home / draw / away, but the labels are just three mutually exclusive, exhaustive results. Enter the original stake and its odds first, then the two live prices you can still buy.

Payout on the original is 100 × 2.40 = $240.00. The stake on outcome 2 that reproduces that payout is 240 / 3.40 = $70.59. The stake on outcome 3 is 240 / 3.60 = $66.67. Locked profit is payout minus all three stakes: 240 − 100 − 70.59 − 66.67 = $2.75. Whichever of the three results lands, the winning ticket returns $240 and the two losers are sunk, so the net is the same $2.75. That is the entire point of a 1X2 Dutch against a held position.

Read the three result rows in order: Locked Profit ($2.75), Stake Outcome 2 ($70.59), Stake Outcome 3 ($66.67). If either live price is worse (lower decimal) the required stake rises and the lock shrinks. Drop outcome 2 from 3.40 to 3.10 and s2 becomes 240 / 3.10 ≈ $77.42; profit falls to 240 − 100 − 77.42 − 66.67 = −$4.09. The calculator will still print a negative lock. A negative lock is not a bug; it is the market telling you the remaining two prices no longer cover the original liability.

You need three books or one book plus an exchange that still prices the two leftover results. In-play 1X2 markets on a 1–0 football match often leave the draw and the trailing side at usable decimals; a red card or a second goal can void the arithmetic within a minute. Re-type the live 3.40 and 3.60 when they move. The model assumes every stake is matched in full and that there is no push: football 1X2 has no push, which is why the tool exists separately from two-way hedging.

A second check: keep $100 at 2.40 and improve leftovers to 3.80 and 4.00. Then s2 ≈ $63.16, s3 = $60.00, lock = $16.84. Better leftover prices reduce covering stakes and lift the lock. The calculator does not search books; you paste what you can actually bet. Educational arithmetic, not a prompt to lock a live football position.

Three-way hedging exists because European football settled on 1X2 as the default match market: home win, draw, away win. A two-way hedge cannot cover a draw. If you backed the home side at 2.40 and the match is 0–0 on 70 minutes, the live away price and the live draw price are the two remaining holes in the ticket. Filling both holes at stakes that reproduce the original payout converts a 1X2 position into a constant. Asian handicap and moneyline hedges cannot do that job.

The technique is older than online in-play. Layers on British rails laid off a heavy home-win book by buying draw and away with a rival; the same three-stake identity appears in a Dutch book argument. What changed after about 2005 is that retail bettors could see live 1X2 decimals and attempt the same lay-off themselves. Books responded with cash-out, which is an internalized three-way (or n-way) hedge plus margin. This calculator shows the raw three-stake version so you can see what a fair lock would require before you accept a cash-out offer.

On the default numbers the lock is only $2.75 on $237.26 of total outlay ($100 + $70.59 + $66.67). That is a 1.16% return on the combined stakes, not a windfall. It exists because 1/2.40 + 1/3.40 + 1/3.60 = 0.4167 + 0.2941 + 0.2778 = 0.9886 < 1. The leftover overround is slightly negative from the bettor’s side — a small Dutch. If the three prices had summed above 1 in inverse, the lock would have been negative and “hedging” would be paying the market to flatten variance.

Scope limits: the three outcomes must partition the sample space. Extra-time qualifying markets, both-teams-to-score, or correct score are not 1X2 even when they have three listed prices. A void on one selection (player sent off before kick-off, postponed match) collapses the identity. Commission on an exchange lay of one leftover result belongs in a mixed back/lay worksheet, not here; this engine assumes three backs at the typed decimals.

Related tools: a two-way partial hedge if you are willing to leave the draw unhedged; dutching if you do not already hold a ticket and simply want equal profit across two or three runners; cash-out versus hedge if the book is offering a number you can compare with the $2.75 lock. None of those pages will tell you whether flattening a live 1–0 is a good idea. They will tell you the dollar amounts. Use them as ledgers.

A three-outcome lock against a held ticket is a Dutch against two leftover prices. Compute the original payout as stake times original decimal odds. Size the two covering stakes so that each leftover, if it wins, also returns that same payout: leftover stake equals payout divided by leftover odds. Locked profit is payout minus all three stakes, which rearranges as payout times (one minus the sum of the three inverse odds). The sign of the lock is therefore the sign of the Dutch-book residual one minus that inverse sum. Defaults are 100 dollars at 2.40, leftover odds 3.40 and 3.60.

Payout is 240 dollars. Covering stake on the second outcome is 240 over 3.40, which is 70.588 continuing, displayed as 70.59 dollars. Covering stake on the third is 240 over 3.60, exactly 66.666 continuing, displayed as 66.67 dollars. Locked profit is 240 minus 100 minus 70.588 minus 66.667, about 2.745, displayed as 2.75 dollars. Inverse sum: 1/2.40 plus 1/3.40 plus 1/3.60 equals 0.416667 plus 0.294118 plus 0.277778, about 0.98856. Then 240 times (1 minus 0.98856) recovers the same 2.75 dollars. Whichever of the three results lands, the winning ticket returns 240 and the two losers are sunk.

British layers already bought the two leftover results when a home-win book grew too heavy; the three-stake identity is older than in-play screens. Football 1X2 is the retail partition that makes the identity useful, because a two-way hedge cannot cover a draw. Extra-time markets and both-teams-to-score are not that partition even when three prices are listed. If any leftover decimal falls, the required covering stake rises as one over odds. A tenth of a point shortening of 3.40 to 3.30 raises the second stake by about 2.14 dollars and cuts the lock by the same 2.14.

Break-even leftovers given original odds 2.40 satisfy the two remaining inverses summing to 0.58333. If those leftovers were equal, each would be about 3.4286. Defaults 3.40 and 3.60 still Dutch because 3.60 compensates. Swap 3.40 for 3.20 and the inverse sum exceeds the hurdle: second stake 75.00 dollars, third 66.67, lock minus 1.67 dollars. Improve leftovers to 3.80 and 4.00 and the stakes fall to about 63.16 and 60.00 with a lock of 16.84. A negative lock is not a defect; it is the market saying the remaining pair no longer covers the original liability.

Assumptions: mutually exclusive exhaustive outcomes, three backs at the typed decimals, full matching, no voids, no each-way terms, settlement win-pays-decimal and loss-pays-zero. Commission on an exchange lay of one leftover belongs in a mixed worksheet. Omit the draw and you are back in two-way covering; this formula would then overstate the lock. Educational three-stake arithmetic, not a prompt to flatten a live 1–0.