How much should I hedge?

How it works

Both odds become decimal odds as exact fractions: American +A gives d = 1 + A ÷ 100, American −A gives d = 1 + 100 ÷ A (A ≥ 100), fractional a/b gives d = 1 + a ÷ b.

Let S₁ be the original stake at decimal odds d₁, and H the hedge stake at decimal odds d₂ on the opposite outcome.

• Profit if the original bet wins = S₁ × (d₁ − 1) − H
• Profit if the hedge wins = H × (d₂ − 1) − S₁

The hedge stake depends on the goal:

• Same result either way: set the two profits equal. S₁(d₁ − 1) − H = H(d₂ − 1) − S₁ gives S₁ × d₁ = H × d₂, so H = S₁ × d₁ ÷ d₂.
• Break even: set the profit if the hedge wins to 0, so H = S₁ ÷ (d₂ − 1).
• My own stake: H as you type it (0 or more).

It also shows the total staked, S₁ + H, and the original bet’s profit with no hedge, S₁ × (d₁ − 1).

The calculator works in exact fractions on the amounts and odds as typed (a stake of 186,270,907.06 is exactly 18,627,090,706/100) and rounds each result to the nearest number only at the end. So an equal hedge gives exactly the same profit on both sides, and a break-even hedge gives exactly 0, never a tiny negative such as −$0.00.

What you can type: spaces are ignored and − reads as -. Each format has its own shape, so odds typed in another format are never read as this one: the page says which format they are in and gives the same price in the chosen format. American odds have a + or − sign and a size of at least 100 (+150, -110, +1,000; commas are thousands commas). Decimal odds are a plain number above 1 with no sign (2.5); a single comma with no point is a decimal comma (2,5 is 2.5) unless exactly 3 digits follow it (1,000 is 1000), and any other comma is a thousands comma. Fractional odds are a/b, a:b, a-b or a to b with a and b above 0, or evens, even or evs (any letter case, to too); a bare number is not fractional odds. A number with no sign typed as American odds (100 or more), a whole number typed as fractional odds, or a number below 100 typed as a probability gets a message saying what to add (+150, 4/1, 40%). Decimal odds above 1,000,001 (American +100,000,000) give no answer.

Assumptions

• Exactly one of the two bets wins: no draw, push or void.
• No taxes, fees or commission.

Worked examples by hand

100 at +400, hedge at −150, same result. d₁ = 1 + 400 ÷ 100 = 5, d₂ = 1 + 100 ÷ 150 = 5/3. H = 100 × 5 ÷ 5/3 = 300. If the original wins: 100 × 4 − 300 = 100. If the hedge wins: 300 × 2/3 − 100 = 100. Total staked 400; with no hedge the bet would win 400.

The same bet, break even. H = 100 ÷ (2/3) = 150. If the original wins: 400 − 150 = 250. If the hedge wins: 150 × 2/3 − 100 = 0.

50 at decimal 3, a hedge of 40 at decimal 2. If the original wins: 50 × 2 − 40 = 60. If the hedge wins: 40 × 1 − 50 = −10. Total staked 90.

A note on betting

These results are mathematics, not advice. Every bet can lose, and a hedge bet carries the bookmaker’s margin too. If gambling is causing problems for you or someone you know, the US National Problem Gambling Helpline is 1-800-MY-RESET (call or text).