Advanced Hedging Math for Tournaments
A hedge changes the distribution of payoffs. It does not automatically increase expected return, and a partial hedge need not produce equal profit. Start with a ledger that includes every possible remaining outcome and every stake.
The examples here are hypothetical external contracts. OwnTheLines does not offer tournament futures or a cash-out feature; these calculations do not imply either capability.
Define Mutually Exclusive and Exhaustive Outcomes
Suppose a $100 future on Team A was accepted at fractional 20/1, American +2000, or decimal 21.00. Its gross return if A wins is $2,100, including the original stake. Now assume A has reached the final against B, and B is offered at +200, decimal 3.00.
For this example, exactly one of A or B becomes champion. Both contracts settle on that same championship, pay in full, and have no fees, limits, voids, or differing cancellation rules. Those assumptions make the two outcomes exhaustive. An opposing semifinal opponent does not cover every way the original future can lose.
Equal-Payoff Equation
Let S be the original stake, d the original decimal return, H the opposing stake, and e the opposing decimal return.
- A wins: net = S(d−1) − H.
- B wins: net = H(e−1) − S.
Equating the two gives Sd = He, so H = Sd/e. Use the offered odds, including their pricing margin; substituting normalized “fair” odds would calculate a payout you cannot receive.
Complete Final-Match Ledger
Here H = $100 × 21/3 = $700. Total stakes are $800.
| Champion | Original ticket return | Hedge return | All stakes | Combined net |
|---|---|---|---|---|
| A | $2,100 | $0 | $800 | +$1,300 |
| B | $0 | $2,100 | $800 | +$1,300 |
Equal net payoffs are possible under these specific assumed prices and settlement conditions. They need not be positive at other prices. For example, if the opposing decimal return were 1.05, H would be $2,000 and both outcomes would net $0 before costs.
The previous $1,900 hedge was not an equal-profit solution. At the same original $100/+2000 and opposing +200 prices, it would net +$100 if A won and +$3,700 if B won, assuming these were the only two championship outcomes.
Partial Hedge and Semifinal Risk
With a partial hedge H = $300 in the final, A winning nets $2,000 − $300 = +$1,700; B winning nets $600 − $100 = +$500. Both are positive in this example, but unequal. At H = $25, the nets are +$1,975 and −$50. A partial hedge therefore does not generally guarantee profit.
Now change the setting: A is only in a semifinal against B, and the $700 opposing selection is B to win that semifinal, not B to become champion. At the same hypothetical +200 price:
| Remaining path | Original future return | Semifinal hedge return | Total stakes | Net |
|---|---|---|---|---|
| A wins semifinal and title | $2,100 | $0 | $800 | +$1,300 |
| B wins semifinal, either finalist later wins title | $0 | $2,100 | $800 | +$1,300 |
| A wins semifinal, then loses final | $0 | $0 | $800 | −$800 |
The uncovered third path defeats the claimed guarantee. A future on B to win the title would require yet another ledger covering the other finalists. A shorter price after a tournament win neither proves overreaction nor makes an opposing contract a complete hedge.
Hedging Questions
Review Implied Probability for price conversion and Bankroll Management for simulation exposure rules.
Q: What is the equal-payoff hedge formula?
A: For exactly two mutually exclusive and exhaustive outcomes with compatible full settlement, use H = S × d / e, where d and e are offered decimal returns including stake. Equal payoffs are not necessarily positive.
Q: Does a partial hedge guarantee equal profit?
A: No. List both net payoffs. In the hypothetical final, a $300 hedge gives +$1,700 or +$500, while a $25 hedge leaves a possible $50 loss.
Q: Should I remove the vig before calculating a hedge stake?
A: No. Payoff arithmetic uses the offered prices. Include fees and settlement differences explicitly; normalized probability estimates do not change what a winning ticket pays.
Q: Can one semifinal opponent fully hedge a title future?
A: Not generally. The original team could win the semifinal and lose the final, leaving both the title future and an opposing semifinal ticket as losses.