Locking in a bonus bet: the hedge stake and the conversion rate

To lock in a stake-not-returned bonus bet of S at decimal price d1, place a cash hedge H = S × (d1 − 1) ÷ d2 on the opposite outcome at decimal price d2. The locked-in amount is H × (d2 − 1). With a $50 bonus at 5.00 and a hedge at 1.22, the hedge is $163.93 and the locked amount is $36.07, a conversion of 72%.

The bonus bet calculator returns the hedge, the locked amount and the conversion for your numbers.

Why the hedge is sized this way

The bonus pays S × (d1 − 1) if it wins and nothing otherwise. The hedge pays H × d2 if the other side wins, from a cash stake H. You want your net position the same either way:

• If the bonus bet wins, you gain S × (d1 − 1) and lose the cash stake H.
• If the hedge wins, the bonus pays nothing and you gain H × (d2 − 1).

Setting S × (d1 − 1) − H equal to H × (d2 − 1) gives H = S × (d1 − 1) ÷ d2. The locked amount is H × (d2 − 1), and the conversion rate is that amount divided by S. This is the same method as the one in the hedge stake article, with the bonus stake treated as costing nothing.

A short price converts worse

The pattern matches the unhedged figures in the value article: a longer bonus price converts a larger fraction of the face value. The cost is the cash needed for the hedge, $163.93 against $30.00 in these two cases, and the hedge is a real bet that must be placed and accepted.

The conversion rate formula

Conversion = (d1 − 1) × (d2 − 1) ÷ d2. For a two-way market, the sum of the two prices' implied probabilities sets how high this can go. The less margin in the pair, the nearer to the fair-odds figure. The two pairs above come out at 72% and 50% against fair-odds values of 80% and about 52% respectively (0.5238 for d1 = 2.10). The gap is the margin paid on the hedge.

What can go wrong

• The hedge price moves or is declined. Then one leg is open, and the figures above no longer hold.
• Different rules on each side. If the bonus and the hedge settle differently on a void, an overtime period or a dead heat, the two outcomes are not exact opposites.
• Cash needed. A hedge of $164 must be sitting in an account that accepts bets at that price, and a limit may cap it.
• Terms of the bonus. Minimum prices, market limits and expiry can block the pair you wanted. Read the offer before planning the hedge.

Hedging versus taking the long shot

Locking in turns a 20% chance of $200 into a sure $36.07. The unhedged bet has a higher expected value (about $40 at a fair price) and a much wider spread of outcomes. Which suits you depends on how much risk you can tolerate, and neither is right in the arithmetic. The unhedged route needs a larger number of such bets for the average to appear. The hedge article covers the general idea.

Run your offer. Enter the bonus, its price and the hedge price in the bonus bet calculator to see the hedge stake and the conversion.