3 Way Hedge Calculator
“3-way hedge” means three different things depending on who is talking, and most calculator pages only cover one of them. Sports bettors mean dutching: splitting one stake across all three outcomes of a 1X2 market (home win, draw, away win) so every result pays the same. Currency traders mean a triangular loop: USD to EUR to GBP and back to USD, hunting a mispricing between the three rates. Crypto traders run the same loop across three coins. This calculator handles all three, with a tab for each.
One feature matters more than the rest. In betting mode, the calculator adds up the implied probability of your three odds before it splits anything. If the total is 100% or more, no split can make money, and the tool tells you that plainly instead of printing stakes that lock in a loss. Every rival dutching calculator we reviewed will happily split a guaranteed loss for you. This one refuses, and explains why.
| Outcome | Stake | Return if it wins | Profit |
|---|---|---|---|
| Outcome 1 | 0 | 0 | 0 |
| Outcome 2 | 0 | 0 | 0 |
| Outcome 3 | 0 | 0 | 0 |
Quick Answer
Key takeaways
- Dutching works only when the combined implied probability is under 100%. That gap is the entire profit; there is no other source.
- At 103.35% implied (odds 2.10 / 3.40 / 3.80), the equal split still loses $3.24 on $100. This calculator shows you that verdict instead of the stakes.
- Hedging an existing bet is the same math run from a target return: divide the return you need by each remaining odd.
- In the forex and crypto loops, fees are charged on every leg. A mispricing smaller than three legs of fees is not an opportunity.
- Quick Answer
- How the betting mode works: dutching and the arbitrage gate
- Worked example: the $100 split that locks $1.69
- When the calculator says no: the guaranteed-loss split
- Hedging a bet you already placed
- The forex and crypto loops, leg by leg
- What competing calculators miss
- Frequently asked questions
- Add This Calculator to Your Website
- References
How the betting mode works: dutching and the arbitrage gate
Dutching splits one stake across every outcome in proportion to each outcome's implied probability, so the return is identical whichever result lands. The stake on each outcome is the total stake multiplied by (1 ÷ that odd), divided by the sum of all three (1 ÷ odd) terms. The catch is in that sum: below 1.00 (100%), the split returns more than the stake; at or above 1.00, it mathematically cannot.
That is why the arbitrage gate comes first in this tool. Bookmakers price 1X2 markets so the implied total sits above 100%: the excess is their margin, the overround. An arbitrage appears only when the best prices across different bookmakers (or a bookmaker's mistake) push the combined total under 100%. The Wikipedia treatment of the Dutch book shows the same arithmetic from the bookmaker's side: odds whose implied probabilities sum past 1 guarantee the book a profit if stakes arrive in proportion.
Worked example: the $100 split that locks $1.69
The betting tab starts pre-filled with this example, so one click reproduces every number. A match is priced at 2.50 (+150) for the home win, 3.00 (+200) for the draw, and 4.00 (+300) for the away win, using the best price on each outcome across your books:
| Outcome | Odds | Implied probability | Stake | Return if it wins |
|---|---|---|---|---|
| Home win | 2.50 | 40.00% | $40.68 | $101.69 |
| Draw | 3.00 | 33.33% | $33.90 | $101.69 |
| Away win | 4.00 | 25.00% | $25.42 | $101.69 |
| Total | 98.33% | $100.00 | Profit: $1.69 | |
Two honest footnotes. First, $1.69 on $100 is a 1.69% return for real work: finding the prices, placing three bets before any of them moves, and keeping the accounts funded. Second, all three stakes have to land at the quoted odds. If one bookmaker cuts a price after the other two legs are placed, you no longer hold a hedge; you hold a bet. Re-run the numbers with the new odd before placing the remaining legs.
When the calculator says no: the guaranteed-loss split
Try odds of 2.10, 3.40, and 3.80 with a $100 stake, a realistic set of prices from a single bookmaker. The implied total is 103.35%, and the betting tab shows exactly that, with a plain verdict: no arbitrage, and no stake table. Here is what it is protecting you from. The equal-return split for those odds does exist as arithmetic:
| Outcome | Odds | The split a rival tool prints | Return if it wins |
|---|---|---|---|
| Outcome 1 | 2.10 | $46.08 | $96.76 |
| Outcome 2 | 3.40 | $28.46 | $96.76 |
| Outcome 3 | 3.80 | $25.46 | $96.76 |
| Guaranteed result on $100 | −$3.24 | ||
Every outcome "wins" and you still lose $3.24, because a perfectly hedged position in an overround market locks the bookmaker's margin against you. Rival dutching calculators print this split without a warning. This one computes the implied total first and, at 100% or above, refuses to dress a guaranteed loss up as a strategy. Find a longer price on one outcome (the draw is usually where books disagree) and try again.
Hedging a bet you already placed
A common variation starts from a bet that already exists. Say you backed outcome 1 early at 4.00 with $100, and prices have moved in your favor. That bet returns $400 if it lands. To lock a profit whatever happens, buy the other two outcomes so they also return $400: hedge stake = target return ÷ odds.
| Position | Odds | Stake | Return if it wins |
|---|---|---|---|
| Existing bet: outcome 1 | 4.00 | $100.00 | $400.00 |
| Hedge: outcome 2 | 3.40 | $117.65 | $400.00 |
| Hedge: outcome 3 | 3.80 | $105.26 | $400.00 |
| Total staked | $322.91 | Locked profit: $77.09 | |
You can check this in the betting tab: enter a total stake of $322.91 with odds 4.00, 3.40, and 3.80, and the split comes out at exactly $100.00, $117.65, and $105.26 with a $77.09 profit (implied total 80.73%, because your early 4.00 beat the current market). For the two-outcome version, the dedicated hedge calculator sizes a single hedge bet against an existing position.
The forex and crypto loops, leg by leg
The two triangular modes run the same shape of trade in currency and crypto markets: convert the full amount through two intermediate assets and back to the start, charging the fee on every leg. The loop profits only if the three rates are mispriced against each other by more than the fees.
Convert, minus the fee. Each leg deducts its percentage fee first, then converts what remains at your rate. Fees are converted back into the starting currency, so the total fee figure in the results is honest.
Compare the end with the start. The verdict is final amount minus starting amount. Positive means the rates were mispriced in your favor by more than the fees; negative means the loop leaks.
Check the fair cross rate. In the crypto loop, the fair BTC to ETH rate is BTC price ÷ ETH price. At $60,000 and $3,000 that is exactly 20. A quote of 20.5 is a 2.5% mispricing, which makes the worked example below pay.
Forex worked example (the pre-filled values in the Forex loop tab): $1,000 at USD to EUR 0.90, EUR to GBP 0.85, GBP to USD 1.35, with a 0.2% fee per leg. You get 898.20 EUR after the first leg, then 761.94 GBP, then back to $1,026.57. Total fees come to $5.99, and the net profit is $26.57. Binance Academy's triangular arbitrage walkthrough uses the same three-conversion structure, with the same warning that live gaps close in seconds.
Crypto worked example (the pre-filled values in the Crypto loop tab): 1,000 USDT, BTC at 60,000, ETH at 3,000, and a BTC to ETH rate of 20.5 against the fair cross rate of 20, with a 0.1% fee per trade. The loop runs 1,000 USDT to 0.01665000 BTC, to 0.340984 ETH, and back to $1,021.93 USDT: fees of $3.02 and a net profit of $21.93. At a rate of exactly 20, the same loop returns about $997 and loses money to fees, which is the usual outcome. For a single-pair pricing check instead of a loop, the bitcoin premium calculator compares BTC prices across markets, and the arbitrage profit calculator prices a two-market arbitrage without the third leg.
What competing calculators miss
We reviewed the betting-tools ecosystem ranking for this phrase. The tools are competent at the split itself; the gaps are honesty, price, and scope:
Bonusbank paywalls the 3-way mode. The niche leader's free dutching tool handles two outcomes; full three-way dutching sits behind a membership, with Australia-only bookmaker coverage. The betting tab here is the complete three-way tool, free, arbitrage check included.
BetToolkit splits anything, silently. Its dutching calculator is mathematically sound and explains exchange commission well, but it takes decimal odds only and has no arbitrage verdict: feed it a 103.35% market and it prints the loss-locking stakes as your plan. This page shows American odds alongside decimal and refuses the guaranteed loss outright.
SportsGambler admits the gap itself. Its hedge calculator models hedging an existing bet with bias options, a genuinely different job, but it is a two-outcome tool that sends three-way users elsewhere. Fresh splits and existing-bet hedges are both done here.
Nobody else covers the other two meanings. The forex and crypto senses of "3-way hedge" have no dedicated calculator competitors at all: trading content describes triangular arbitrage, but no ranking tool computes the loop with per-leg fees and a profit verdict. Both modes here do.
Frequently asked questions
It is covering all three outcomes of a 1X2 market (home win, draw, away win) with stakes sized in proportion to each outcome's implied probability, so every result returns the same amount. Also called dutching. It locks a profit only when the combined implied probability of the three best prices is under 100%.
Add 1 divided by each decimal odd. Under 1.00 (100%), the arbitrage is real: odds of 2.50, 3.00, and 4.00 total 98.33%. At or over 100%, like 2.10, 3.40, and 3.80 at 103.35%, every split loses money and the calculator says so instead of printing stakes.
Because at an implied total of 100% or more, the equal-return split returns less than your stake on every outcome: it is a guaranteed loss with extra steps. On odds of 2.10, 3.40, and 3.80 the split would be $46.08, $28.46, and $25.46 returning $96.76 on $100, a locked $3.24 loss. The tool shows the implied percentage and tells you to find a longer price instead.
No. Hedging is reducing risk on a position, sometimes at a cost: hedging a bet you placed early can lock a smaller profit or cut a loss. Arbitrage is the special case where covering every outcome locks a guaranteed profit regardless of the result, which only happens when the implied total is under 100%.
A loop through three currency pairs, for example USD to EUR to GBP and back to USD. If the three rates are mutually inconsistent, you finish with more of the starting currency than you began with. Real fees usually erase small mispricings, which is why the Forex loop mode charges a fee on every leg before giving its verdict.
Yes, the math is asset-agnostic: enter any coin's USDT price in the BTC and ETH price fields and the cross rate between the two coins in the rate field. The labels use BTC and ETH because that is the most liquid loop, but any three-asset loop with a stablecoin start follows the same conversions and fees.
US sportsbooks quote American odds (+150, -125) while odds-comparison sites and most of the world use decimals. The read-only American fields update as you type so you can match the calculator to whichever book you are placing each leg with. Decimal odds of 2.00 or more convert to positive American odds; between 1.00 and 2.00 they convert to negative.
They can limit stakes, void palpable-error bets, and restrict or close accounts that only bet arbitrage and matched positions; it is in most terms and conditions. A hedge also fails if one leg is rejected or its price moves first. Place legs promptly, and only ever use money you can afford to lose.
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References
- Britannica Money, "What Is Arbitrage?" - the definition of arbitrage and its main types, including triangular arbitrage in foreign exchange. Britannica Money: What Is Arbitrage?. Accessed October 2026.
- Wikipedia, "Dutch book" - the bookmaker example showing implied probabilities summing above 1, and how a gambler can profit when they sum below 1. Wikipedia: Dutch book. Accessed October 2026.
- Binance Academy, "What Is Triangular Arbitrage and How to Use It?" - how the three-asset loop works in crypto markets, with execution and fee risks. Binance Academy: Triangular Arbitrage. Accessed October 2026.
- Binance Academy, "What Is Arbitrage Trading?" - arbitrage types including the triangular loop, plus execution and liquidity risks. Binance Academy: Arbitrage Trading. Accessed October 2026.
- National Council on Problem Gambling, "NCPG Adopts 1-800-MY-RESET as New National Problem Gambling Helpline Number" - the free, confidential, 24/7 US helpline. NCPG: 1-800-MY-RESET Helpline Announcement. Accessed October 2026.
- Responsible Gambling Council, "Getting Help for Residents Outside of Canada" - international help options, including Gambling Therapy and national helplines. Responsible Gambling Council: Help for US Residents. Accessed October 2026.