Hedging Sports Bets: The Math Behind Locking In a Result

What hedging a bet means

A hedge is a second bet on the opposite outcome of a bet you already hold. If the first bet wins, the hedge loses. If the hedge wins, the first bet loses. Sized correctly, the two together leave you with the same result either way, or with a smaller swing between the two outcomes than the original ticket alone.

Hedging does not create value. It trades some expected value for a narrower range of outcomes. The math below shows exactly how much.

The hedge stake formula

Start with two numbers:

• P: the potential total return of your original bet if it wins, stake included.
• D: the decimal odds of the hedge side. For a negative American price, drop the minus and call it A; D = (A + 100) / A. For a positive price A, D = (A + 100) / 100. The American odds implied probability table lists the matching break-even rates.

The hedge stake that makes both outcomes equal is:

H = P / D

That stake returns exactly P if the hedge wins, the same amount the original ticket returns if it wins. Your locked result is then:

Result = P − original stake − H

Worked example: a futures ticket in the final

You bet $50 on Team A to win a title at +1000. The decimal for +1000 is 1,100 / 100 = 11, so P = $50 × 11 = $550. Team A reaches the final against Team B, and Team B is posted at -150.

• Decimal for -150: (150 + 100) / 150 = 5 / 3, about 1.67.
• Hedge stake: H = 550 / (5 / 3) = 550 × 3 / 5 = $330.

The hedge wins $330 × 2 / 3 = $220 when Team B wins. Either way you finish $170 ahead on $380 staked in total. Without the hedge, the same ticket ends at +$500 or −$50.

The same math on a parlay's last leg

A parlay works the same way: P is what the whole parlay returns if the final leg wins. Say a $10 parlay returns $120 if its last leg comes in, and the other side of that leg is -110, a decimal of 21 / 11.

H = 120 / (21 / 11) = 1,320 / 21, about $62.86. Either way you finish about $47.14 ahead; with the stake rounded to the cent, the two outcomes differ by at most a cent. How parlay odds are calculated shows how that $120 return is built from the leg prices.

Full hedge vs partial hedge

You do not have to hedge all the way. Any stake between zero and H sits between "let it ride" and "same result either way." Two common reference points from the futures example:

The stake-recovery hedge is the original stake divided by the hedge side's profit per dollar: $50 / (5 / 3 − 1) = $50 / (2 / 3) = $75. Each extra dollar of hedge moves the two outcomes closer together.

What the vig on the hedge costs

The hedge is a new bet at the book's price, so it carries the vig. Suppose the final is posted Team A +130, Team B -150. The implied probabilities are 10 / 23 = 43.48% and 3 / 5 = 60.00%, which add to 103.48%. Removing that overround proportionally, as in implied probability and the vig, leaves no-vig chances of 50 / 119 = 42.02% for Team A and 69 / 119 = 57.98% for Team B.

Take those no-vig chances as the true ones. The expected value of the $330 hedge is:

EV = (69 / 119 × $220) − (50 / 119 × $330) = −1,320 / 119, about −$11.09

The unhedged ticket is worth about +$181.09 on average at those chances, counting the $50 already staked. The full hedge fixes the result at +$170.00, so the hedge costs about $11.09 in expected value. The half hedge costs about $5.55. The bigger the hedge, the more vig you pay.

At a fair -150 price with no vig, the same full hedge would lock in about $181.09, matching the unhedged average. The gap between $181.09 and $170.00 is the vig on the hedge side.

Shop the hedge price

Because the hedge is often a large bet at a short price, a small price improvement goes a long way. If another book offers Team B at -140, the decimal is 12 / 7 and the full hedge becomes 550 / (12 / 7) = 1,925 / 6, about $320.83. The locked result rises to about $179.17, an extra $9.17 for the same protection, and the hedge's expected cost at the no-vig chances drops to about $1.93.

Line shopping covers how to compare prices across books you are allowed to use, and the free bankroll and line-shopping worksheet gives you a place to record them.

When a hedge fits your plan

The numbers make the trade clear: a hedge gives up a known slice of expected value in exchange for a smaller swing. Whether that trade is worth it depends on how big the swing is next to your bankroll.

• If the possible win is large relative to your bankroll, narrowing the range can keep your staking plan on track. Bankroll management and unit sizing covers that plan.
• If the swing is small next to your bankroll, letting the ticket ride keeps the full expected value.
• Price the hedge first. Use H = P / D at the best price you can find, then compare the locked result with the unhedged outcomes.
• Log both bets as separate rows so your record stays accurate. How to track your sports bets shows the columns.

Short records swing a lot either way; understanding variance explains why a hedge narrows that swing for one bet but does not change the average.

Hedge with the numbers in front of you

Write down P, find the best hedge price, compute H = P / D, and compare three lines: no hedge, partial hedge and full hedge. Keep the American odds implied probability table open for conversions and the worksheet for prices and stakes.

For how price, bankroll and record keeping fit together into one system, see the book.

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