Hedge to lock arbitrage
Both legs pay positive at the current prices. Hedge unconditionally. The Arbitrage badge on the result panel signals the case.
▌ Calculator · hedge bet · updated 2026-04-26
Hedge a bet,
lock in
the profit.
A hedge places a second bet against your original to cap downside or lock in guaranteed profit. The math reduces to one ratio — the equal-profit hedge stake equals the original's gross payout divided by the hedge odds. When the prices line up, both outcomes pay positive and you collect either way.
US sportsbooks bid an average of $15.06 per click for hedge-calculator searches, the highest CPC of any betting calculator term, because the people running this math are the high-LTV bettors operators chase. Calculator below covers balanced, max-profit, and custom-stake variants — derivation sits below. If you want to find the fair line before calculating your hedge, use our no-vig calculator to remove the bookmaker's edge.
Calculator
Live · client-side · zero tracking▌ Inputs
Original was a free bet
Hedge mode
Same net profit either side. The standard equal-profit hedge.
▌ Result
ArbitrageHedge stake
$150.00
If original wins
+$50.00
If hedge wins
+$50.00
Guaranteed
+$50.00
ROI
+20.00%
Total cash staked · $250.00
▌ Methodology · hedge math
How the math works
Decimal odds give the multiplier on a winning stake. A bet of $S
at decimal odds A pays gross
$S × A on a win — that figure already includes the
stake back, so net profit is $S × (A − 1). Free
bets are different: the stake is not returned, so a winning free bet pays only the
(A − 1) profit portion in cash.
For an original stake S at decimal odds
A and a hedge stake H
at decimal odds B, the two outcomes break down
like this:
- Original wins — receive
grossA = S × A(orS × (A − 1)on a free bet), payH. Net =grossA − cashCostS − H. - Hedge wins — receive
H × B, pay the cash cost of both bets. Net =H × (B − 1) − cashCostS.
Setting both nets equal gives the balanced (equal-profit) hedge stake:
H = grossA / B. Substituting back, the matched
profit on each side equals
grossA × (1 − 1/B) − cashCostS. When that quantity
is positive, the position is arbitrage — both legs net positive at any allocation between
zero and the maximum.
The max-profit mode does the opposite. It picks the smallest hedge stake
that still breaks even on the hedge side:
H = cashCostS / (B − 1). If the original wins, you
collect almost the full upside. If the hedge wins, you walk away even. This mode is
undefined for free bets — cash cost is zero, so the break-even hedge stake is zero, which
means no hedge at all.
The custom mode lets you pick H
directly. The calculator applies the same outcome formulas and shows what each side
returns. Useful for partial hedges where the goal is variance reduction without giving up
all of the original's expected value.
▌ Worked example
A concrete walk-through
Pre-fill values: $100 stake at +200 American (decimal 3.0) on the original, hedge available at +100 American (decimal 2.0). Not a free bet.
Gross payout if the original wins: 100 × 3.0 = $300.
Subtracting the original $100 cash cost, original-side profit before any hedge is $200.
Hedge stake H = 300 / 2.0 = $150. Total cash
staked is $250.
- Original wins → receive $300, paid $250 → net +$50
- Hedge wins → receive $300, paid $250 → net +$50
Guaranteed profit $50 · ROI 20% · arbitrage on both sides.
Hedge stake H = 100 / (2.0 − 1) = $100. Total
cash staked $200.
- Original wins → receive $300, paid $200 → net +$100
- Hedge wins → receive $200, paid $200 → net $0 (break even)
Less downside protection — original loss leaves you flat instead of +$50 — but original-side profit doubles.
Toggle the free-bet flag and the original $100 stops counting against cash cost. GrossA
drops to 100 × (3.0 − 1) = $200. The balanced
hedge becomes 200 / 2.0 = $100, locking in $100
either way at zero risk to bankroll. That is why a balanced free-bet hedge is one of the
most reliable +EV moves a recreational bettor can run.
▌ Decision rules
When to hedge — and when not
Hedge when the bet is large
A bet that is meaningful relative to bankroll deserves variance reduction. Late-game live lines that swing in your favor are the textbook case.
Don't hedge a +EV bet you can afford
Hedging burns expected value to buy variance reduction. If bankroll absorbs the loss and the original bet was sound, riding it out earns more long-run.
Always run a balanced free-bet hedge
Free bets carry no cash downside. A balanced hedge converts a portion of the bookmaker's gift to guaranteed cash. Anything less leaves money on the table.
Related calculators
Frequently asked
08 / questionsQ01 What is hedging in sports betting?
Hedging means placing a second bet on an outcome opposing your original wager to reduce risk or lock in profit. The classic case is a futures bet — say $100 on a team to win the championship at +500. When they reach the final, the opponent's price might be +200. Hedging against the opponent at that point guarantees a payout regardless of who wins. The math reduces to one ratio that the calculator above computes.
Q02 How is the equal-profit hedge stake calculated?
For a bet of $S at decimal odds A against a hedge at decimal odds B, the balanced hedge stake is grossA / B, where grossA equals S × A on a normal bet or S × (A − 1) on a free bet. Setting both outcome profits equal yields the same formula — that's why it's called equal-profit. The calculator shows the resulting hedge stake plus the matched profit on each side.
Q03 When does a hedge guarantee profit?
Whenever the original gross payout times (1 − 1/B) exceeds the cash cost of the original. Practically, the hedge odds B must be high enough that the math works. If B is too short — typical when the market has shifted heavily against your original — a balanced hedge locks in a loss instead. The Arbitrage badge in the result panel only appears when both legs net positive at the chosen hedge stake.
Q04 What if my original bet was a free bet?
A free bet's stake is not returned with winnings, so the gross payout drops to S × (A − 1) instead of S × A. The calculator's free-bet toggle handles this — turn it on and the math switches automatically. Because no cash is at risk on the original, every dollar collected on either outcome is profit. The balanced hedge of a free bet is among the most reliable positive-EV moves a recreational bettor makes.
Q05 Can a hedge lose money?
A balanced hedge at hedge odds B that are too short locks in a guaranteed loss — the math still produces a stake, but the matched profit is negative. The result panel flags this case. A custom hedge can also underperform if the stake is too aggressive relative to the original edge. The calculator displays profit on each leg so the trade-off is visible before any money moves.
Q06 Should I hedge or let the original ride?
Hedging trades expected value for variance reduction. Three rules of thumb cover most cases: hedge unconditionally when both legs would be positive (arbitrage); hedge when bet size is large relative to bankroll; let the original ride when the original edge is sound and the bankroll can absorb the loss. None of this is wagering advice — only the math behind the trade-off.
Q07 Do I pay tax on hedge winnings?
US bettors face 24% federal withholding on certain gambling winnings above the thresholds in IRS Publication 525, plus state-specific tax. The calculator above shows pre-tax numbers. UK punters don't pay tax on gambling winnings. Full per-state withholding details are on the methodology page.
Q08 How is hedging different from arbitrage?
Arbitrage is pre-emptive — both bets are placed simultaneously across different sportsbooks because the summed prices leave a guaranteed margin. Hedging starts after the original bet has been placed, usually because the line moved or the situation changed. The math overlaps in the equal-profit case — a balanced hedge that nets positive on both sides is mathematically arbitrage — but the timing and intent differ.
/ — methodology
Want the rest of the math?
The methodology page covers Kelly criterion (Kelly 1956), vigorish derivation, implied probability vs implied odds, UK bookmaker bonus rules, and per-state US tax math — every formula cited to a primary source.