Arbitrage, Hedging and Middles
Three strategies involve backing more than one outcome, and they are routinely confused. Arbitrage locks in a profit before anything happens. Hedging gives up upside to buy certainty afterwards. A middle is a bet on a window where both of your positions win.
11 min read
The short answer
- Arbitrage exists when the implied probabilities across books sum to less than 100%.
- A +110 / +105 pair sums to 96.4%, which returns 3.73% of the total stake with no risk.
- Hedging is not arbitrage: it converts an existing position into a guaranteed but smaller outcome.
- Dutching splits a stake across several outcomes in one market so any of them returns the same.
- A middle wins both bets when the result lands between two lines — rare, and not free money.
- Cash-out is a hedge the sportsbook prices for you, and it is priced in their favour.
Arbitrage: when the market disagrees with itself
Every market has a built-in margin, which is why the two sides at one sportsbook always sum to more than 100%. But two different sportsbooks are not coordinating, and occasionally their prices disagree enough that the best available number on each side sums to less than 100%.
When that happens you can back both sides and profit regardless of the result.
Book A: +110 on Team A → 47.62%
Book B: +105 on Team B → 48.78%
───────
96.40%
profit = (1 / 0.9640) − 1 = 3.73% of total stakeAny total below 100% is an arbitrage. The profit is the shortfall, expressed as a return on the total staked.
Staking $1,000 across it: $493.98 on Team A and $506.02 on Team B. Either result returns $1,037.35, for $37.35 of profit. Not a good bet — no bet at all, in the sense that matters. The arbitrage calculator finds and splits these.
Dutching: spreading a stake across one market
Dutching backs several outcomes in the same market, sized so that whichever one wins returns the same amount. It is the natural move when you can rule out most of a field but not narrow it to one.
stake on outcome i = total × (1 / decimal_i) / Σ(1 / decimal_j)
The same allocation the arbitrage calculator uses, applied within a single market rather than across two books.
Unlike arbitrage, dutching is not automatically profitable. If the outcomes you back sum to more than 100% of implied probability — which is normal inside one market — you are paying margin on all of them. It converts a set of opinions into one position at a known return; it does not create an edge. The dutching calculator does the split and reports the return.
Hedging: buying certainty with expected value
Hedging happens after a bet is placed. Your position has moved in your favour, and you back the other side to guarantee an outcome — reducing the best case in exchange for eliminating the worst.
A $100 futures ticket at +400 is now worth hedging because the other side is available at −150. Backing it with $300 equalises the two outcomes: whichever lands, you finish in the same place.
Here is the part worth being honest about. Hedging almost always costs expected value. You are paying margin a second time, on the other side, to remove variance. That can be entirely correct — a guaranteed sum you actually need beats a larger average you might not see — but it is a preference, not an edge, and it should be chosen knowing that.
The hedge calculator sizes the equalising stake, and the futures hedge calculator handles the long-dated case where the position has been open for months.
Cash-out is a hedge you did not price
Cash-out is the same operation, offered by the sportsbook as a button. The convenience is real and so is the cost: the price is calculated by the operator, and it includes a margin on top of the margin already in the original bet.
Which means the offer is essentially always below what hedging the position yourself at market prices would return. The cash-out calculator shows the gap — take the offer if the difference is small and you want it settled, but do it knowing what the button charges.
Middles: the window where both bets win
A middle bets both sides at different lines, so there is a band of results where both tickets cash.
| Your bets | Result | Outcome |
|---|---|---|
| +3.5 and −2.5 | Wins by 3 | Both bets win |
| +3.5 and −2.5 | Wins by 1 | Underdog side wins, favourite loses |
| +3.5 and −2.5 | Wins by 6 | Favourite side wins, underdog loses |
The appeal is obvious and the arithmetic is less so. Most of the time you lose the vig on one side; occasionally you win both. Whether that is profitable depends entirely on how often the result lands in the window, which depends on the sport and on where the window sits.
The middle calculator identifies the window and reports how often it would need to hit to break even. It deliberately does not tell you a middle is free money, because it is not — it is a bet on a specific margin, priced like any other.
Which is which
| Strategy | When | What it does |
|---|---|---|
| Arbitrage | Before, across books | Guaranteed profit from a pricing disagreement |
| Dutching | Before, one market | Equal return across several backed outcomes |
| Hedging | After, position moved | Trades upside for a guaranteed outcome |
| Cash-out | After, at the book’s price | A hedge the operator prices, in their favour |
| Middle | Before, two lines | A bet on the result landing in a window |
Only the first is free money, and only briefly. The rest are positions with their own expected value — which is worth calculating before taking them, not after.
Common questions
- What is arbitrage betting?
- Backing every outcome across different sportsbooks at prices that sum to less than 100% implied probability, which guarantees a profit. A +110 / +105 pair sums to 96.4% and returns 3.73% of the total staked regardless of the result.
- Is arbitrage betting legal?
- It is not illegal, but sportsbooks are private businesses and their terms generally allow them to limit or close accounts that do it. The practical constraint on arbitrage is not the law — it is that operators notice.
- What is the difference between hedging and arbitrage?
- Arbitrage is set up in advance across books and guarantees a profit. Hedging happens after a position has already moved, and converts it into a guaranteed but smaller outcome — usually at a cost in expected value, because you pay margin a second time.
- Should I take the cash-out offer?
- Only knowing what it costs. Cash-out is a hedge the sportsbook prices, and it includes their margin on top of the margin already in your original bet — so it is almost always worse than hedging yourself at market prices.
- Is a middle free money?
- No. Most of the time one side wins and one loses, costing you the vig on both; occasionally the result lands in the window and both cash. Whether that is profitable depends on how often that specific margin occurs.