strategy · 5 min read · April 26, 2026

How to Calculate Arbitrage Stakes

In short: Sizing an arbitrage bet is straightforward math: divide each side’s implied probability by the combined total, then multiply by your total stake. The result is equal payouts on both outcomes, regardless of which one wins. The math is simple. The execution details (rounding, commissions, three-way markets) are where the nuance lives.

This is a math article. If you haven’t read Arbitrage Betting Explained yet, start there for the conceptual overview. Here we focus on the calculations.

The Core Formula

For a two-outcome arbitrage where you want a fixed total stake split across both legs:

stake on outcome A = total stake × (implied_prob_A ÷ combined_implied_prob)
stake on outcome B = total stake × (implied_prob_B ÷ combined_implied_prob)

This is called equal-payout sizing. The stakes are calibrated so that whichever outcome wins, your return is approximately the same.

The combined implied probability is just the sum of the two implied probabilities. For an arb to exist, this number must be less than 100%.

A Worked Example

Take a real arbitrage opportunity. On April 18, 2026: Atlanta Hawks @ New York Knicks.

bet365: Knicks at -141
FanDuel: Hawks at +180

Step 1: Convert to implied probability

For -141: 141 ÷ (141 + 100) = 58.5% For +180: 100 ÷ (180 + 100) = 35.7%

Combined: 58.5% + 35.7% = 94.2%

Combined < 100% means an arbitrage exists. The 5.8% gap is the edge.

Step 2: Calculate stakes for a $100 total wager

Stake on Knicks: $100 × (58.5% ÷ 94.2%) = $100 × 0.621 = $62.09

Stake on Hawks: $100 × (35.7% ÷ 94.2%) = $100 × 0.379 = $37.91

Step 3: Verify the math

If the Knicks win (at -141):

Knicks bet returns: $62.09 + ($62.09 × 100/141) = $62.09 + $44.04 = $106.13
Hawks bet loses: -$37.91
Net total returned: $106.13 (Knicks return) − $37.91 (Hawks lost) + $37.91 (Hawks bet was already in your $100) = $106.13
Profit on $100 outlay: $6.13

If the Hawks win (at +180):

Hawks bet returns: $37.91 + ($37.91 × 180/100) = $37.91 + $68.24 = $106.15
Knicks bet loses: -$62.09
Net total returned: $106.15
Profit on $100 outlay: $6.15

The slight difference between $6.13 and $6.15 is just rounding. In practice, you can adjust to the cent if your books support it.

Three-Way Markets (Soccer and Some Other Sports)

Most sports have two outcomes. Some — most prominently soccer (with home win, away win, or draw) — have three. The math extends naturally:

stake on outcome A = total × (implied_A ÷ combined_implied)
stake on outcome B = total × (implied_B ÷ combined_implied)
stake on outcome C = total × (implied_C ÷ combined_implied)

The combined implied probability is the sum of all three. The arb exists when this sum is below 100%.

Three-way example:

A soccer match with the following prices across three books:

Book A: Home Win at +220 (implied 31.3%)
Book B: Draw at +260 (implied 27.8%)
Book C: Away Win at +175 (implied 36.4%)

Combined: 31.3% + 27.8% + 36.4% = 95.5%

For a $100 total stake:

Home Win: $100 × (31.3% ÷ 95.5%) = $32.77
Draw: $100 × (27.8% ÷ 95.5%) = $29.11
Away Win: $100 × (36.4% ÷ 95.5%) = $38.12

Total: $100. Whichever outcome occurs, profit is approximately 4.7% (the gap between 95.5% and 100%).

Three-way arbs are rarer than two-way because three independent books need to simultaneously misprice. But they appear regularly enough to be worth scanning for.

Handling Exchange Commissions

Betting exchanges charge commission on winning bets, typically 2-5%. This changes the math.

When one leg is at an exchange, the effective odds on that leg are lower than the displayed odds. To calculate properly, adjust the implied probability up to account for the commission:

effective_implied_prob = displayed_implied_prob ÷ (1 - commission)

For example, if Novig is offering +180 (35.7% implied) with a 2% commission:

effective implied = 35.7% ÷ 0.98 = 36.4%

Use 36.4% (not 35.7%) in your arb calculation.

A 3% gross arb where one leg is at an exchange with 2% commission becomes only a ~1% net arb after the adjustment. Many “obvious” exchange-based arbs disappear once commission is properly factored in. Always do this step.

Handling PredictIt’s 10% Profit Fee

PredictIt charges 10% on profit (not on stake), which is unusual and worth special attention.

For a PredictIt YES contract trading at 35¢:

If it resolves YES, you receive $1.00. Profit: $0.65. PredictIt takes 10% = $0.065.
Net you receive: $1.00 − $0.065 = $0.935.

To express this as effective implied probability: instead of $1 per contract, treat the payout as $0.935. The effective implied probability of a 35¢ contract becomes:

0.35 ÷ 0.935 = 37.4% (instead of 35.0%)

This adjustment matters a lot. A 5% gross arb between PredictIt and another platform can easily evaporate to 2% or even negative once the fee is properly factored in.

Always do the fee adjustment before declaring an arbitrage opportunity exists.

Practical Stake Adjustments

Rounding

Most books accept bets to the dollar or, increasingly, the penny. When rounding stakes, always round in the direction that preserves the arb.

Example: math says $62.09 on one side and $37.91 on the other. Round $62.09 up to $63 and $37.91 down to $37. The arb is still intact, just slightly different per-side profit. Round $62.09 down to $62 and $37.91 down to $37, and you’ve under-staked your total — still safe but with reduced profit.

The general rule: small deviations from optimal stakes are fine; they reduce upside slightly but don’t break the arb.

Stake limits

Books cap maximum bet sizes per market and per user. If an arb requires $400 on one side and the book caps your bet at $200, your options are:

Scale the entire arb down to fit the constraint. If the cap is $200 and the math says $400, halve the total stake to $50 instead of $100. Both legs scale proportionally; the arb is preserved.
Accept suboptimal sizing. Bet $200 on the constrained side and $100 (instead of $63) on the unconstrained side. The arb may shrink or even invert depending on the math.
Skip it. If the arb shrinks too much after accounting for the constraint, the time to execute may not be worth the reduced profit.

The first option is almost always correct. Scale down rather than getting clever.

Available bankroll

Your stake is limited by funds in each book. If you have $300 at book A and $50 at book B, you can’t place an arb that requires $200 on each side. Either redistribute funds or scale down.

This is why bankroll distribution across books matters. Many edge finders maintain a “stocking inventory” model — keeping enough money at each active book to act on opportunities without delay.

Frequently Asked Questions

Why not bet equal amounts on both sides?

Equal stakes only work when both sides have identical odds. With any odds difference, equal stakes mean unequal payouts — one outcome profits more than the other. Equal-payout sizing (the formula above) ensures consistent profit regardless of result.

Can I size an arb to maximize profit on one side?

Yes — instead of equal payouts, you can deliberately under-stake one side and over-stake the other. This is called “skewing” the arb. It’s still mathematically guaranteed profit, but the profit is asymmetric. Some bettors do this when they have a directional opinion, but it’s rarely worth the added complexity.

What if the math says I should bet $0.0001 on one side?

This usually indicates a very large odds disparity — probably stale data or an error. Re-check the prices before placing anything. If the odds are real but lopsided enough that one side requires a tiny stake, scale up the total until both stakes are reasonable, or skip it if the per-bet amount becomes excessive.

How precise do I need to be?

For typical 2-5% arbs, you have meaningful room to be slightly off. A 1-2% deviation in stake sizes typically just shifts profit between the two outcomes by a few cents per $100. For very thin arbs (0.5-1% edge), precision matters more — sloppy sizing can flip a profitable arb into a losing one.

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