Prediction Market Arbitrage Calculator: Stakes and Net Returns

A prediction market arbitrage calculator splits capital between complementary outcomes so their settlement payouts match. To calculate net returns across Polymarket and a bookmaker, convert both prices into payout per dollar committed, include fees, and verify that every possible settlement leaves the combined position covered.

OddsFantasy’s arbitrage calculator helps split stakes across outcomes. This guide explains the arithmetic behind those allocations and the checks required before execution. For the broader concept, start with the arbitrage betting guide. Every numerical example below is illustrative, not a live opportunity.

What numbers does a prediction market arbitrage calculation need?

Start with the actual purchase price of the prediction-market shares, the bookmaker’s offered odds, your total budget, and applicable costs. Then establish whether the positions cover opposite outcomes under compatible settlement rules. Similar event names alone do not establish that coverage.

• Prediction-market leg: outcome, executable share price, and quantity available at that price.
• Bookmaker leg: complementary selection, decimal odds, and stake you can actually place.
• Costs: transaction charges, trading fees, or other deductions that apply to your particular trade.
• Settlement: event scope, overtime treatment, cancellation rules, and outcome definitions.
• Execution: quantities filled and odds accepted, rather than requested quantities and displayed quotes.

According to the Polymarket Help Center, a share representing the correct final outcome pays $1.00 USDC at resolution. Buying q shares at price p therefore costs q × p before fees and pays q USDC if that outcome resolves correctly. For the examples here, all amounts are expressed in equivalent dollar units, without conversion costs.

How do you compare share prices with bookmaker odds?

A share bought at $0.45 has a winning gross payout multiple of 1 ÷ 0.45, approximately 2.2222. Decimal bookmaker odds already express that multiple: a $100 winning stake at 2.00 returns $200, including the original stake. Comparing gross payouts avoids confusing bookmaker winnings with total returns.

For American money-line odds, convert positive odds +A using d = 1 + A ÷ 100; convert negative odds −A, where A is the positive magnitude, using d = 1 + 100 ÷ A. The Delaware Lottery’s payout explanation describes +140 as $140 won per $100 wagered and −150 as $150 wagered to win $100. These become decimal odds of 2.40 and approximately 1.6667.

For a prediction-market share on one outcome and bookmaker odds d on its exact complement, the pre-fee test is p + 1 ÷ d < 1. This means buying one unit of payout on each side costs less than that payout. Polymarket describes prices as current market probabilities; that does not make them independently verified probabilities or guarantee executable size.

How do you calculate matched stakes?

Let q be the number of prediction-market shares and s the bookmaker stake. Equal gross payouts require q = s × d, so s = q ÷ d. Before fees, a total budget B buys q = B ÷ (p + 1 ÷ d) shares, with q × p allocated to shares and q ÷ d allocated to the bookmaker.

The matched settlement payout is q, not the sum of both legs’ potential payouts: only one complementary outcome wins. Pre-fee profit is q − B, and return on committed capital is (q − B) ÷ B. This calculation assumes exhaustive coverage, compatible settlement, and complete execution at the specified prices.

How does the calculation work across several outcomes?

For exhaustive, mutually exclusive outcomes with decimal payout multiples d₁ through dₙ, define S = Σ(1 ÷ dᵢ). Before fees, matched payout R = B ÷ S and each stake is R ÷ dᵢ. A prediction-market share price pᵢ contributes pᵢ to S because its payout multiple is 1 ÷ pᵢ. The pre-fee arbitrage condition is S < 1.

What does a complete share-and-bookmaker example look like?

Suppose a prediction-market share on Team A winning costs $0.45 and a bookmaker offers 2.00 on Team A not winning. Assume their definitions match exactly. For this illustration only, buying shares carries a hypothetical $0.01 entry fee per share, with no other charges or payout deductions.

With $960 available, each dollar of matched settlement payout requires $0.45 for shares, $0.50 for the opposing bookmaker stake, and $0.01 in fees. The total is $0.96, so the matched payout is $960 ÷ $0.96 = $1,000.

• Buy 1,000 shares at $0.45: share purchase cost is $450.
• Pay the hypothetical entry fee: 1,000 × $0.01 = $10.
• Stake $500 at bookmaker odds of 2.00: winning gross return is $1,000.
• Total committed capital is $450 + $10 + $500 = $960.
• Either covered outcome returns $1,000, producing $40 net profit and approximately 4.17% on committed capital.

If Team A wins, the shares pay $1,000 and the bookmaker stake loses. If Team A does not win, the shares pay nothing and the bookmaker returns $1,000. Both branches produce $1,000 − $960 = $40. These results depend on the example’s assumptions; they are not a promise of an executable return.

How should fees and rounding change the stake split?

For a share-entry fee f per share and fixed total costs F, the matched quantity is q = (B − F) ÷ (p + f + 1 ÷ d). The bookmaker stake remains q ÷ d if neither winning payout has further deductions. This formula applies only to that fee structure; percentage fees or outcome-dependent charges require their own calculation.

If a charge reduces the winning payout, match net payouts rather than gross payouts. Calculate each settlement branch separately: net profit equals that branch’s receipts minus all capital committed and any costs not already included. Do not subtract an entry fee again if it is already inside the budget.

Rounding can leave a small imbalance. Round quantities and stakes to permitted increments, then recalculate both outcomes from those actual amounts. Delaware Lottery states that its retail payout calculations are rounded to the nearest nickel; this is a specific source rule, not a universal bookmaker standard. Use the applicable venue’s rules and accepted ticket return.

Why can settlement differences invalidate the calculation?

The two legs must remain complementary under the settlement rules, not merely under your expected sporting result. A regulation-only selection and a selection including overtime may leave an uncovered branch. Likewise, a bookmaker refund and a prediction-market resolution need not produce the matched payout used in your calculation.

The paper Unravelling the Probabilistic Forest: Arbitrage in Prediction Markets describes Polymarket condition sets as exhaustive and mutually exclusive, and distinguishes arbitrage within a market from arbitrage across markets. That internal structure does not establish equivalence with a separate bookmaker contract.

1. Compare event identity, selection wording, time period, and overtime coverage.
2. Read how each venue handles postponement, cancellation, abandonment, and void outcomes.
3. List every distinct settlement branch, including refunds or exceptional resolutions.
4. Calculate combined receipts and net profit in each branch; use the lowest result as the conservative estimate.

What happens if one leg does not fill?

An unfilled leg turns a matched calculation into directional exposure. In the worked example, suppose the $500 bookmaker stake is accepted but none of the shares are bought. The position is now simply a wager on Team A not winning; the planned $40 balanced result does not exist.

Limit orders control price, not completion. Public’s prediction-market order guide explains that buy limits execute at the limit or lower, sell limits at the limit or higher, and neither guarantees a fill. These are general order mechanics, not evidence that a specific proposed Polymarket trade will execute.

A partial fill also changes coverage. If only 600 shares fill while the full $500 bookmaker stake is accepted, the prediction-market winning payout is $600 but the bookmaker winning payout remains $1,000. Recalculate using actual fills before deciding whether to complete the position, reduce exposure, or unwind. The missing shares may no longer be available at the original price.

How should you use OddsFantasy’s finder and calculator?

OddsFantasy’s arbitrage finder lists opportunities across bookmakers and Polymarket. Use it to identify candidates, then use the arbitrage calculator to split stakes across outcomes. Treat an allocation as a plan to verify, not proof that both legs will execute or settle identically.

1. Check that the candidate selections cover the same settlement branches.
2. Calculate the split using current prices and the capital you intend to commit.
3. Deduct applicable costs and recalculate after permitted stake rounding.
4. Check executable share quantity and the bookmaker’s accepted stake and odds.
5. Record actual execution, then compare net profit across all settlement branches.

If one position already exists, the hedge calculator can help calculate an opposing allocation. Hedging an existing exposure is a different starting point from opening two matched legs together. Whether placing manually or planning automation, keep the same distinction: a positive calculated margin is conditional on coverage, costs, and completed execution.