Arbitrage Calculator: How to Find Guaranteed Profits
Master the mathematics of arbitrage betting with our complete calculator guide. Learn the formulas, calculate your stakes perfectly, and maximize your guaranteed returns.
An arbitrage calculator is your most important tool for finding and executing profitable arbitrage bets. Without proper calculations, you risk betting the wrong amounts and potentially losing money on what should be a guaranteed profit.
In this guide, we'll break down every formula you need, show you step-by-step calculations, and explain how to use calculators effectively for both traditional sports betting and prediction markets like Polymarket.
The Fundamental Arbitrage Formula
Before using any calculator, you need to understand the underlying mathematics. The arbitrage percentage formula tells you whether an opportunity exists:
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Arbitrage % = (1/Odds_A + 1/Odds_B) × 100
If the result is less than 100%: Arbitrage opportunity exists
If the result is 100% or more: No arbitrage opportunity
Converting Between Odds Formats
Different platforms use different odds formats. Here's how to convert between them:
| Format | Example | To Decimal | Implied Probability |
|---|---|---|---|
| Decimal | 2.50 | Already decimal | 1/2.50 = 40% |
| American (+) | +150 | (150/100) + 1 = 2.50 | 100/(150+100) = 40% |
| American (-) | -200 | (100/200) + 1 = 1.50 | 200/(200+100) = 66.67% |
| Polymarket Price | $0.40 | 1/0.40 = 2.50 | 0.40 × 100 = 40% |
Polymarket Conversion Tip
On Polymarket, the price IS the implied probability. A YES share at $0.65 means 65% implied probability. To convert to decimal odds: 1/0.65 = 1.538
Calculating Stake Amounts
Once you've found an arbitrage opportunity, you need to calculate exactly how much to bet on each outcome. The formula ensures equal returns regardless of which outcome wins:
Stake Calculation Formula
Individual Stake = (Total Stake × Implied Probability) / Total Implied Probability
Or more simply:
Stake_A = Total × (1/Odds_A) / Arbitrage%
Stake_B = Total × (1/Odds_B) / Arbitrage%
Complete Calculation Example
Let's work through a real example step by step:
NFL Game: Chiefs vs Bills
DraftKings
Chiefs @ -110
Decimal: 1.909
Implied: 52.38%
Polymarket
Bills @ $0.45
Decimal: 2.222
Implied: 45%
Calculate Arbitrage Percentage
52.38% + 45% = 97.38%
Below 100% = Arbitrage exists!
Calculate Profit Percentage
100% - 97.38% = 2.62%
Guaranteed 2.62% return
Calculate Stakes (for $1,000 total)
Chiefs: $1,000 × (52.38%/97.38%) = $537.93
Bills: $1,000 × (45%/97.38%) = $462.07
Verify Returns
If Chiefs win: $537.93 × 1.909 = $1,026.91
If Bills win: $462.07 × 2.222 = $1,026.72
Profit: ~$26.80 either way (2.68%)
Three-Way Arbitrage Calculations
For three-outcome events (like soccer matches with win/draw/lose), the formula extends naturally:
Three-Way Formula
Arbitrage % = (1/Odds_Home + 1/Odds_Draw + 1/Odds_Away) × 100
Calculate each stake the same way:
Stake_Home = Total × (1/Odds_Home) / Arbitrage%
Stake_Draw = Total × (1/Odds_Draw) / Arbitrage%
Stake_Away = Total × (1/Odds_Away) / Arbitrage%
Accounting for Fees and Commissions
Real-world arbitrage must account for trading fees. Here's how fees affect your calculations:
| Platform | Fee Structure | How It Affects Arb |
|---|---|---|
| Polymarket | 2% on winnings | Reduces payout by 2% |
| DraftKings/FanDuel | Built into odds (vig) | Already reflected in odds |
| Betfair Exchange | 2-5% commission | Reduces net winnings |
| PredictEngine | 0.2% trading fee | Small impact on profits |
Fee-Adjusted Formula
To account for Polymarket's 2% fee on winnings:
Adjusted Odds = Original Odds × 0.98
Example: 2.50 odds becomes 2.50 × 0.98 = 2.45
Minimum Profit Thresholds
Not every arbitrage opportunity is worth taking. Consider these thresholds:
| Profit Margin | Recommendation | On $1,000 |
|---|---|---|
| < 1% | Skip - fees eat profit | < $10 |
| 1-2% | Marginal - high volume only | $10-$20 |
| 2-3% | Good opportunity | $20-$30 |
| 3-5% | Excellent - act fast | $30-$50 |
| > 5% | Rare - verify accuracy | > $50 |
Common Calculator Mistakes to Avoid
1. Mixing Odds Formats
Always convert all odds to the same format (decimal recommended) before calculating.
2. Forgetting Fees
A 2% arbitrage opportunity becomes a loss after 2.5% in combined fees. Always factor in platform costs.
3. Rounding Errors
Use at least 4 decimal places in calculations. Small rounding errors compound with large stakes.
4. Ignoring Bet Limits
If a platform limits your bet to $500 but calculations require $800, the arbitrage won't work properly.
Pro Tip
Use automated calculators for speed, but understand the math so you can verify results and spot errors. PredictEngine calculates arbitrage automatically and shows you the exact stakes needed.
Frequently Asked Questions
What's the minimum stake for arbitrage to be worthwhile?
With 2% returns, you need at least $500-1,000 to make meaningful profits. At $1,000 with 2% return, you make $20 per trade. Smaller stakes may not be worth the time and effort.
How do I handle different currencies?
Convert all stakes and odds to a single currency before calculating. Be aware of exchange fees if converting funds between platforms.
Can I use Excel for arbitrage calculations?
Yes, but it's slow for real-time opportunities. Dedicated tools like PredictEngine scan hundreds of markets per second and calculate optimal stakes automatically.
What if the odds change while I'm placing bets?
This is the biggest risk. Recalculate before each bet. Automated tools execute faster and can adjust in real-time.
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