What is hedging?

Hedging is the practice of placing a second bet on the opposing side of an existing bet, in order to reduce the potential loss or to lock in a guaranteed profit regardless of the outcome. The hedge bet partially or fully offsets the risk of the original bet.

Hedging does not create value — it redistributes it. A hedge reduces the variance of the outcome at the cost of reducing the maximum potential profit. Whether to hedge is a decision that depends on the player's risk tolerance, bankroll situation, and the expected value of the available odds.

Full hedge: locking in profit

A full hedge guarantees the same profit regardless of the outcome. This is mathematically identical to an arbitrage bet, except that the two sides are placed at different times rather than simultaneously.

Suppose a player placed a ¤100 bet on option A at a decimal odd of 4.00 before the event. During the event, option A's situation has improved substantially, and the odd for option B (the only other option) is now 3.50. The player can hedge by betting on option B.

To calculate the hedge stake that produces equal profit on both outcomes:

s₁: original stake on A = ¤100
d₁: odd of original bet on A = 4.00
d₂: current odd of B = 3.50
s₂: hedge stake on B

If A wins, the player receives s₁ · d₁ = ¤400, but loses s₂. Total: ¤400 − s₂.
If B wins, the player receives s₂ · d₂, but loses s₁ = ¤100. Total: s₂ · 3.50 − ¤100.

Setting these equal:

¤400 − s₂ = s₂ · 3.50 − ¤100
¤500 = s₂ · 4.50
s₂ = ¤500 / 4.50 ≈ ¤111.11

Verification:

If A wins: ¤400 − ¤111.11 = ¤288.89 profit (net of both stakes: ¤400 − ¤100 − ¤111.11 = ¤188.89)
If B wins: ¤111.11 · 3.50 − ¤100 = ¤388.89 − ¤100 = ¤288.89 profit (net: ¤388.89 − ¤100 − ¤111.11 = ¤177.78)

Wait — let us be precise. The total money spent is s₁ + s₂ = ¤100 + ¤111.11 = ¤211.11. The return in either case:

If A wins: s₁ · d₁ = ¤400. Net profit: ¤400 − ¤211.11 = ¤188.89.
If B wins: s₂ · d₂ = ¤388.89. Net profit: ¤388.89 − ¤211.11 = ¤177.78.

The small difference arises because achieving exactly equal profit requires solving:

s₁ · d₁ − s₂ = s₂ · d₂ − s₁
s₁ · d₁ + s₁ = s₂ · d₂ + s₂
s₁ · (d₁ + 1) = s₂ · (d₂ + 1)
s₂ = s₁ · (d₁ + 1) / (d₂ + 1)

s₂ = ¤100 · (4.00 + 1) / (3.50 + 1) = ¤100 · 5 / 4.5 ≈ ¤111.11

If A wins: return = ¤400, total staked = ¤211.11, net = ¤188.89.
If B wins: return = ¤388.89, total staked = ¤211.11, net = ¤177.78.

To equalize net profit exactly:

s₁ · d₁ − (s₁ + s₂) = s₂ · d₂ − (s₁ + s₂)
s₁ · d₁ = s₂ · d₂
s₂ = s₁ · d₁ / d₂

s₂ = ¤100 · 4.00 / 3.50 ≈ ¤114.29

If A wins: ¤400 − ¤214.29 = ¤185.71
If B wins: ¤114.29 · 3.50 − ¤214.29 = ¤400 − ¤214.29 = ¤185.71

The guaranteed net profit is ¤185.71 on a total outlay of ¤214.29, regardless of the outcome. The player has locked in profit.

Partial hedge

A partial hedge reduces the risk without eliminating it entirely. The player bets a smaller amount on the opposing side than what a full hedge would require. This guarantees a smaller minimum profit (or limits the maximum loss) while preserving a larger profit if the original bet wins.

Using the same example, if the player hedges with only ¤50 on option B at 3.50:

If A wins: ¤400 − ¤100 − ¤50 = ¤250 profit.
If B wins: ¤50 · 3.50 − ¤100 − ¤50 = ¤175 − ¤150 = ¤25 profit.

The player has reduced his downside (from a ¤100 loss to a ¤25 profit) while keeping a substantial upside (¤250 vs. ¤185.71 from a full hedge).

When to hedge

The decision to hedge is not purely mathematical — it involves the player's risk tolerance and bankroll context. However, several principles apply:

— Hedging reduces expected value when the hedge bet itself has negative expected value. If the player's original bet has positive expected value and the hedge bet has negative expected value (as is typical when hedging with a bookmaker's odds), the hedge lowers the overall expected profit. The player is paying a cost — the negative expected value of the hedge bet — in exchange for reduced variance.

— Hedging is more justifiable when the potential loss represents a large fraction of the player's bankroll. A bet that was appropriately sized at the time it was placed may become disproportionately large relative to the bankroll if the bankroll has since decreased. In such cases, hedging is a form of retroactive bankroll management.

— Hedging is most attractive when the odds available for the hedge are favorable — close to or above fair odds. If the hedge can be placed at a betting exchange with low commission, the cost of the hedge is minimized.

— Futures bets and parlays are common candidates for hedging, because their potential payouts can become very large relative to the player's bankroll as the bet progresses through its stages.

Hedging on exchanges

Betting exchanges facilitate hedging by allowing the player to lay (bet against) an option he previously backed. If a player backed option A at 4.00 and the odds have since shortened to 2.50, the player can lay option A at 2.50 on the exchange, effectively locking in a profit. This practice is sometimes called trading a position, as the player has bought at a high price (backed at high odds) and sold at a low price (laid at low odds), analogous to buying low and selling high in a financial market.