Most of the time, betting is about taking on risk in exchange for a price. But every so often the market hands you the opposite: a chance to reduce risk, or even erase it entirely. There are three tools for these moments — hedging, middling, and arbitrage — and each one runs on exact stake math. Get the arithmetic right and you can lock a guaranteed profit or convert a nervy open position into a calm one. Get it wrong and you leave a gap that quietly turns a “sure thing” into a loss. This course is about doing the math correctly.
Hedging: locking in what you’ve already got
Hedging means placing a bet on the opposite side of a position you already hold, in order to lock in profit or cut your risk. The classic cases: a futures ticket that’s now one game from cashing, or a live line that has moved sharply in your favor. You don’t have to ride your original bet all the way to the end — you can bet against yourself at the new price and bank a result no matter what happens.
To lock an equal outcome on both sides, the formula is simple:
The hedge stake
hedge stake = (original potential total return) ÷ (opposite side's decimal odds)“Total return” is your full payout if the original bet wins — stake plus profit, not profit alone.
The logic: you want the opposite bet to pay back the same gross amount your original ticket would, so that whichever side lands, the same money comes home.
Worked example
You took a futures at +600 for $100, so the ticket returns $700 total if it wins. Your team made the final, and the other outcome is now priced at decimal 1.40. You decide to lock it up:
Hedge stake = $700 ÷ 1.40 = $500 on the opposite side.
- Your team wins: collect $700, lose the $500 hedge, minus your original $100 stake → +$100.
- The other side wins: the hedge pays 500 × 1.40 = $700, you lose the original $100 stake → +$100.
Either way you walk away $100 ahead. You gave up the upside of the full $600 profit, but you removed all the risk of getting nothing.
Middling: a window where both bets win
Middling is sneakier. You bet one side at one number, then the line moves and you bet the other side at a different number — creating a gap in the middle where both of your bets can win at the same time. Outside that gap, one wins and one loses, and all you’re out is the vig. So a middle is a low-cost shot at a double payday.
Worked example
Early in the week you bet Over 44.5. Money pours in on the over and the total climbs, so a few days later you bet Under 48.5.
- If the game lands on a total of 45, 46, 47, or 48 points, the over and the under both win — that’s the middle.
- If the total is 44 or lower, only the under wins; if it’s 49 or higher, only the over wins. You lose one bet, win the other, and pay just the vig.
You typically size both legs the same way (often equal stakes), so the worst case is a small, known cost while the best case is a full double win. The wider the gap between the two numbers, the bigger the middle — and usually the rarer the move that creates it.
Middles show up most around key numbers in football and basketball, where a few points of line movement can open a real window. They’re infrequent, but cheap to take when they appear.
Arbitrage: backing every outcome for a guaranteed profit
Arbitrage — an “arb” — happens when two books price the same game so inconsistently that you can back every outcome and still come out ahead no matter what. It exists whenever the combined implied probability across all outcomes drops below 100%. In decimal terms, you check the sum of the inverse odds.
The arbitrage math
arb exists if Σ(1 ÷ odds_i) < 1 stake on outcome i = Total × (1 ÷ odds_i) ÷ Σ(1 ÷ odds) guaranteed return = Total ÷ Σ(1 ÷ odds)If that sum is exactly 1, the prices are perfectly fair (no edge); above 1 is the normal world where the vig works against you. Only when it dips below 1 is there free money on the table — and you split your total stake between the outcomes in proportion to each one’s inverse odds.
Worked example
Book 1 has Team A at +110 (decimal 2.10). Book 2 has Team B at +105 (decimal 2.05). Check for an arb:
Σ = (1 ÷ 2.10) + (1 ÷ 2.05) = 0.4762 + 0.4878 = 0.9640. That’s below 1, so it’s an arb worth about 3.7% (1 ÷ 0.9640 − 1).
On a $1,000 total bankroll for this play:
- Stake on A = 1000 × 0.4762 ÷ 0.9640 ≈ $494 → 494 × 2.10 ≈ $1,037 back.
- Stake on B = 1000 × 0.4878 ÷ 0.9640 ≈ $506 → 506 × 2.05 ≈ $1,037 back.
Guaranteed return ≈ 1000 ÷ 0.9640 ≈ $1,037, so you lock about $37 of profit whichever team wins — on $1,000 at risk.
The realities (why this is harder than it looks)
The math above is the easy part. In practice, these edges are slim and the obstacles are real:
- Books limit and ban arbers. Sportsbooks watch for accounts that only ever bet sharp prices, and they’ll cap your stakes or close you down. Consistent arbitrage has a short shelf life on a given account.
- Lines move before the second leg. You place the first bet, go to grab the other side, and the price has already shifted — leaving you half-hedged and exposed instead of locked.
- The profits are small. A 3.7% arb on $1,000 is $37. To make real money you need lots of capital spread across many books, and the good arbs vanish fast.
- Fees and holds eat thin edges. Withdrawal fees, payment friction, and money tied up at a dozen books all chip away at margins that were never large to begin with.
Of the three, hedging is the most practical for most bettors — locking a futures ticket or a promo into guaranteed profit is something you’ll actually get to do. Pure arbitrage as a strategy is a grind that books actively fight.
Common mistakes
- Arithmetic errors that leave a gap. Round the stakes the wrong way or fumble the formula and your “locked” profit quietly becomes a loss on one side.
- Getting one leg, then the line moves. If you secure the first bet and the second price slips away, you’re no longer hedged — you’re just exposed at a worse number.
- Ignoring limits and account risk. A guaranteed $37 isn’t worth much if it gets your account flagged or capped before a bet that mattered.
- Hedging a futures too early. Lock in too soon and you hand back EV you should have kept. Hedge to protect a result that’s genuinely at stake, not out of nerves.
Key takeaways
- Hedge stake = original total return ÷ the opposite side’s decimal odds — it equalizes your result whichever way the game goes.
- A middle is betting both sides at different numbers so a band of outcomes wins both bets; outside the band you’re out only the vig.
- An arb exists only when Σ(1 ÷ decimal odds) < 1; split stakes by each outcome’s inverse odds and your return is Total ÷ that sum.
- Edges are thin and books fight back — hedging a futures or promo is the most usable of the three for most people.