Arbitrage Calculator

What does the Arbitrage Calculator do for 2-way, 3-way, and 4-way bets?

An arbitrage calculator splits your total stake across mutually exclusive outcomes so the gross return is equal (or near-equal) regardless of the result. For decimal odds with no commission, arbitrage exists if the sum of inverse odds across the selected outcomes is less than 1. The calculator converts your total stake into outcome stakes using proportional formulas, handles rounding to the nearest penny, and shows expected return, guaranteed profit, and ROI.

How to calculate 2-way arbitrage stakes step by step

Use 2-way mode when there are exactly two mutually exclusive outcomes that fully cover the market (e.g., tennis Player A vs Player B, or football Draw No Bet lines across two books). The goal is to equalise gross returns.

• Check the arbitrage condition: 1/O1 + 1/O2 < 1 (decimal odds O1 and O2).
• Compute the inverse-odds sum S_inv = (1/O1) + (1/O2).
• Compute equal return R = TotalStake / S_inv.
• Compute stakes: Stake1 = R / O1, Stake2 = R / O2.
• Round stakes to currency precision (e.g., £0.01) and adjust one line by a penny if needed so Stake1 + Stake2 = TotalStake.
• Profit = R − TotalStake. ROI = Profit / TotalStake.

Example (2-way)	Value
Total stake	£100.00
Odds O1 / O2	2.10 / 2.05
Arb check (1/O1 + 1/O2)	0.963995 (arb exists, < 1)
Equal-return R (theoretical)	£103.735
Stake1 / Stake2 (rounded)	£49.40 / £50.60
Return if Outcome1 wins	£49.40 × 2.10 = £103.74
Return if Outcome2 wins	£50.60 × 2.05 = £103.73
Guaranteed profit (min return − stake)	£3.73
ROI	3.73%

• Tip: If using exchanges, adjust for commission before calculating (e.g., effective back odds = odds × (1 − commission)).
• Tip: Always verify market rules (voids/palpable errors can nullify an arb).

3-way arbitrage: how do you split stakes across outcomes?

Use 3-way mode for markets with three mutually exclusive outcomes (e.g., football 1X2: Home–Draw–Away). The same principle applies: allocate by inverse odds to equalise gross returns.

• Check the arbitrage condition: 1/O1 + 1/O2 + 1/O3 < 1.
• Let S_inv = (1/O1) + (1/O2) + (1/O3).
• Equal return R = TotalStake / S_inv.
• Stakes: Stake1 = R / O1, Stake2 = R / O2, Stake3 = R / O3.
• Round to the nearest penny; adjust one stake so the sum equals TotalStake.
• Profit = R − TotalStake; ROI = Profit / TotalStake.

Example (3-way)	Value
Total stake	£100.00
Odds O1 / O2 / O3	2.60 / 3.60 / 3.10
Arb check (1/O1 + 1/O2 + 1/O3)	0.984974 (arb exists, < 1)
Equal-return R (theoretical)	£101.525
Stakes (rounded)	£39.06 / £28.21 / £32.73
Return if Outcome1 wins	£39.06 × 2.60 = £101.56
Return if Outcome2 wins	£28.21 × 3.60 = £101.56
Return if Outcome3 wins	£32.73 × 3.10 = £101.46
Guaranteed profit (min return − stake)	£1.46
ROI	1.46%

• Rounding can cause a few pence of spread between outcome returns; the arb remains valid as long as the minimum return exceeds the total stake.
• If a bookmaker applies different settlement rules (e.g., special draw rules), align outcomes so they are truly mutually exclusive and collectively exhaustive.

4-way and extra outcomes: when should you use them?

4-way mode applies when the market has four mutually exclusive outcomes that fully cover all possibilities (common examples: method of victory in boxing/MMA: KO/TKO, Submission, Decision, Draw; tennis match correct score in best-of-three sets: 2–0, 2–1, 1–2, 0–2). The same equal-return logic extends to any number of outcomes n.

• Arb condition (no commission): (1/O1 + 1/O2 + 1/O3 + 1/O4) < 1.
• Equal return: R = TotalStake / Σ(1/Oi); Stakes: Stake i = R / Oi for i = 1..4.

When to use:

• Method-of-victory markets (four outcomes including Draw/Technical Decision).
• Correct-score in short formats with exactly four outcomes (e.g., best-of-three tennis match scorelines).
• Three-runner “with tie” markets that list a separate “any tie” outcome as a fourth option.

Practical cautions:

• Settlement rules: ensure all selections settle on every result (no partial voids or “other” buckets that add hidden outcomes).
• Dead-heat or split-decision rules can change the effective payout; model these before staking.
• Rounding: with more outcomes, cumulative rounding drift increases—apply a final penny adjustment to one outcome.

Illustrative 4-way check (no commission): with odds 2.90, 4.60, 4.80, 6.50, the inverse-odds sum is 0.924398 (arb exists). For a £100 total stake, the theoretical equal return is £108.178, implying an £8.18 profit (8.18% ROI) before rounding. You would size each stake as Stake i = R / Oi and round to the nearest penny, ensuring the stakes sum to £100.

How to use the formula: margin, implied probability, and stake sizing?

Arbitrage exists when the sum of implied probabilities from independently sourced prices is less than 100%. In decimal odds, this means the sum of reciprocals is below 1 after adjusting for any fees or commission. Stake sizing then allocates your total stake proportionally to equalise the gross return across outcomes. For n outcomes with effective decimal odds Oi, the break-even check is Σ(1/Oi) < 1 and the equal-return stake for outcome i is Stake i = (TotalStake / Σ(1/Oj)) / Oi.

What is the arbitrage formula and break-even threshold?

The arbitrage condition compares the total implied probability against 100%. Using decimal odds, implied probability for outcome i is Pi = 1/Oi. For a market fully covered by n outcomes (mutually exclusive, collectively exhaustive):

• Arbitrage condition (no commission): Σ(1/Oi) < 1.
• Equal-return constant: R = TotalStake / Σ(1/Oi).
• Stake sizing (each outcome): Stake i = R / Oi.
• Guaranteed profit: Profit = R − TotalStake. ROI = (1 / Σ(1/Oi)) − 1.

With platform fees or commission, first convert each quoted price to an effective decimal Oi,eff that reflects net payout after all charges, then apply the same formulas to Oi,eff. The break-even threshold remains Σ(1/Oi,eff) < 1; the margin (or overround) of a set of quotes is Overround = Σ(1/Oi) − 1. Arbitrage margin is ArbEdge = 1 − Σ(1/Oi,eff).

How do I convert fractional, decimal, and American odds in the UK?

UK-facing sites often show fractional odds, while exchanges and tools default to decimal. These are exact conversions: decimal = fractional + 1; American odds convert piecewise based on sign. Implied probability is 1/decimal (expressed as a percentage).

• Fractional (A/B) → Decimal: 1 + A/B.
• Decimal (D) → Fractional: D − 1, simplified to a fraction.

American (US) → Decimal:

• If US ≥ 0: 1 + (US / 100).
• If US < 0: 1 + (100 / |US|).

Decimal (D) → American:

• If D ≥ 2.0: US = (D − 1) × 100.
• If 1.01 ≤ D < 2.0: US = −100 / (D − 1).

• Implied probability: P = 1 / D.

Fractional	Decimal	American	Implied probability (%)
1/2	1.50	-200	66.6667
4/5	1.80	-125	55.5556
1/1 (EVS)	2.00	+100	50.0000
5/4	2.25	+125	44.4444
6/4	2.50	+150	40.0000
9/2	5.50	+450	18.1818

Note: For fractional to percentage, you can also use P = B / (A + B). The table values are exact to four decimal places in percentage terms.

How do you account for commission and exchange lay odds?

Exchanges typically charge commission c on net winnings (e.g., 2%–5%), applied only on the side that wins the market. Adjust odds before running the arbitrage check and stake sizing:

• Back bets on an exchange (commission c): effective decimal Oeff(back) = 1 + (O − 1) × (1 − c). Example: O = 3.00 at 5% → Oeff = 1 + 2 × 0.95 = 2.90.
• Bookmaker back bets (UK) usually have no commission; Oeff = O, but still confirm any promo terms or deductions.

Lay bets (exchange) are best modelled by case outcomes. To equalise a bookmaker back with an exchange lay on the same selection:

• Let Sb be the bookmaker back stake at odds Ob (no commission).
• Let you lay the same selection at lay odds Ol with commission c.
• Lay liability: Liability = (Ol − 1) × L (where L is lay stake).

Net profits:

• If the selection wins: Pwin = Sb × (Ob − 1) − (Ol − 1) × L.
• If the selection loses: Plose = L × (1 − c) − Sb.

• Equal-profit lay stake: L = (Sb × Ob) / (Ol − c).

Two-way arb check using a lay as the contra side: convert the lay price on A into an effective “back” price on Not-A, then apply Σ(1/Oeff) < 1:

• Equivalent back odds for Not-A from a lay at Ol with commission c: Onot,eff = 1 + (1 − c) / (Ol − 1).
• Then check: 1/Ob + 1/Onot,eff < 1. If true, an arb exists after commission.

Worked example (bookmaker back + exchange lay): Back Team A £100 at Ob = 2.40 (no commission). Lay Team A at Ol = 2.52 with c = 5%. Equal-profit lay stake L = (100 × 2.40) / (2.52 − 0.05) = 240 / 2.47 ≈ £97.17. Liability = (2.52 − 1) × 97.17 ≈ £147.69. Net if A wins: £100 × 1.40 − £147.69 ≈ −£7.69. Net if A loses: £97.17 × 0.95 − £100 ≈ −£7.69. No arb here (a controlled hedge loss); improving either Ob upward or Ol downward can flip this to a sure profit after fees.

Where can you run it: web tool, Android APK, and crypto markets?

You can run an arbitrage calculator in a web browser on desktop or mobile, install it as an Android APK for offline use, or adapt it to price crypto and exchange fees. The core math is identical across platforms: convert all prices to effective odds or effective buy/sell rates, apply the arbitrage check, and size stakes (or position sizes) to equalise returns after fees and rounding.

Is there an Arbitrage Calculator APK for Android?

Yes—arbitrage calculators can be packaged as Android APKs, but many users prefer installing the web tool as a Progressive Web App (PWA) for security and automatic updates. Both options run the same stake-sizing formulas locally on your device.

Installation options:

• PWA: In Chrome on Android, use “Install app” to add the web tool to your home screen. It runs fullscreen, caches assets, and supports offline calculations.
• APK: If you use a direct APK, enable “Install unknown apps” on your device. Only install from a trusted publisher and verify the SHA-256 signature against the developer’s release notes.

Recommended capabilities for mobile:

• 2-way, 3-way, and 4-way stake splits with rounding to £0.01.
• Odds formats: decimal, fractional, American; quick converters.
• Exchange commission inputs (per outcome) and stake caps.
• Preset profiles (e.g., “Exchange 1 at 2%”, “Bookmaker A no commission”).
• Sanity checks: avoid partial coverage, warn on void/NR conditions.

Security and privacy:

• No special permissions are required for calculators; offline math runs locally.
• Avoid APKs requesting SMS, contacts, or background network access unrelated to updates.

Crypto arbitrage: how to plug in exchange prices and fees

For crypto spot arbitrage between Exchange A and Exchange B, convert quotes to effective per-unit buy and sell rates including taker/maker fees and any transfer (withdrawal/on-chain) cost amortised over the quantity you move. An arbitrage exists if the net sell proceeds per unit exceed the net buy cost per unit plus transfer cost per unit.

• Effective buy (per unit): Pbuy,eff = Pbuy × (1 + fee_buy).
• Effective sell (per unit): Psell,eff = Psell × (1 − fee_sell).
• Transfer cost per unit (moving quantity Q of asset with a fixed withdrawal fee Fasset): Ctransfer,unit = (Fasset / Q) × Pref, where Pref is a reference price (use Psell or mid) in your quote currency.
• Arbitrage condition: Psell,eff − Pbuy,eff − Ctransfer,unit > 0.
• Profit for quantity Q: Profit = Q × (Psell,eff − Pbuy,eff) − Fasset × Pref.

Parameter	Value	Notes
Buy price on A (Pbuy)	£40,000.00 per BTC	Spot taker fill
Sell price on B (Psell)	£40,300.00 per BTC	Spot taker fill
Taker fee (both sides)	0.10% (0.001)	Applied on notional
Withdrawal fee from A (Fasset)	0.0003 BTC	Fixed in asset units
Quantity moved (Q)	0.50 BTC	Per transfer
Effective buy (Pbuy,eff)	£40,040.00	£40,000 × (1 + 0.001)
Effective sell (Psell,eff)	£40,259.70	£40,300 × (1 − 0.001)
Transfer per unit (Ctransfer,unit)	£24.18	(0.0003 / 0.50) × £40,300
Net edge per BTC	£195.52	£40,259.70 − £40,040.00 − £24.18
Total profit (Q = 0.50 BTC)	£97.76	0.50 × £195.52

Practical considerations: include maker/taker differences, potential conversion spread if you use stablecoins (GBP to USDT/USDC), on-chain confirmation times (affects live viability), and, for derivatives, funding rates and basis risk. Set a minimum edge threshold above zero to cover slippage and spread changes while orders are in flight.

• Spot-to-spot is constrained by transfer time; cross-exchange hedging with perpetuals removes transfer but adds funding and liquidation risk.
• Use pre-funded balances and faster networks (where supported) to reduce confirmation delays; always check the current withdrawal fee table before calculating.

Live vs offline data: how do latency and slippage affect results?

Arbitrage windows are often measured in seconds. Latency (quote age, network round-trip, order routing) and slippage (fills worse than top-of-book) can erase a theoretical edge. Treat delay and depth as explicit costs and require a buffer above the pure fee-adjusted threshold.

Latency sources:

• Data freshness: screen-scrape or delayed APIs can add 1–5+ seconds of staleness.
• Network and matching: routing and queueing can move your fill back in the book.

Slippage modelling:

• Estimate expected slippage s per unit (e.g., ticks or basis points) from recent depth.
• Revised condition: Edge > Fees + Transfer + s.
• Prefer limit orders for control; use partial fills logic in the calculator.

Mitigations:

• Pre-fund accounts to avoid transfer delays; choose markets with consistent depth.
• Set a minimum target edge (e.g., ≥ 0.50% above total costs) before execution.
• Cap stake size to top-of-book depth and add a time-to-live on quotes.
• Cache profiles for venue fees and auto-apply a slippage buffer from recent trades.

Evolution in the UK: from spreadsheets to smart arbing workflows

Arbitrage in the UK moved from forum-shared spreadsheets and manual price checks to automated, API-driven workflows that price outcomes consistently, model commission, and enforce staking and settlement rules. Today’s process emphasises latency control, fee-aware odds normalisation, and robust sanity checks to prevent partial coverage, void mismatches, and rounding drift that can erase edge.

What changed since early matched betting and surebet forums?

Early UK arbers typically copied prices from multiple books into spreadsheets, used simple reciprocal sums to detect arbs, and posted leads on forums. This approach was slow, error-prone, and offered little defence against sudden price moves or settlement quirks. Modern stacks use programmatic feeds where available, continuous conversion across odds formats, commission-aware models for exchanges, and guardrails (exposure caps, rounding logic, and rule harmonisation) that keep realised returns close to theoretical.

• Data acquisition shifted from manual entry to a mix of official APIs, exchange feeds, and rate-limited scraping with cache coherence.
• Settlement awareness improved: exchanges charge commission on net winnings; UK books can apply deductions (e.g., horse racing Rule 4) and sport-specific tie rules.
• Stake control matured: penny-accurate rounding with final reconciliation, exposure limits per book/exchange, and balance-aware sizing.
• Operational discipline increased: latency budgets, quote time-to-live, and minimum edge buffers to absorb slippage.

Which dead-end tools failed and why (no commission, slow updates)?

Several tool patterns proved unreliable because they ignored real frictions. Calculators that assumed zero commission overstated edge on exchange legs; refresh cycles measured in tens of seconds allowed prices to drift; and parsers that did not model market rules (push/draw handling, non-runner deductions) produced only partial coverage. These tools increased gubbing risk and could turn a theoretical surebet into a negative EV trade.

• No-commission calculators: exchange wins were overpaid on paper but underpaid in practice when commission applied to winnings.
• Slow or stale scrapers: by the time odds were evaluated, spreads often collapsed; results diverged from “paper” profits.
• No rule mapping: treating 1X2, Draw No Bet, Asian handicaps, and exchange markets as interchangeable led to mismatches.
• Rigid rounding: fixed per-leg rounding without reconciliation caused stakes not to sum to the intended total, leaking edge.
• Ignoring limits/acceptance: tools that didn’t consider per-book maximums or partial acceptance left positions unhedged.

Area	Earlier approach (forums/spreadsheets)	Modern approach (2020–2026)	Operational impact
Data refresh	Manual copy; ad hoc page reloads	Programmatic feeds and scheduled scrapes with caching	Faster, more consistent quotes; fewer stale decisions
Odds normalisation	Decimal-only; mixed formats handled by hand	Auto convert fractional/decimal/American; unify to decimal	Reduces entry errors; consistent implied probabilities
Commission modelling	Ignored on exchange legs	Per-venue commission applied to net winnings	Accurate edge and break-even thresholds
Stake rounding	Round each leg independently	Penny rounding with final reconciliation to total stake	Minimises drift; preserves equal-return target
Rule harmonisation	Assumed markets were equivalent	Maps draw/push/NR and deductions (e.g., Rule 4 in racing)	Prevents partial coverage and settlement surprises
Risk controls	None beyond bankroll notes	Stake caps, balance checks, time-to-live, edge buffers	Fewer unhedged legs; tighter realised vs paper P&L

In practice, these improvements converge on the same goal: equalise returns that actually settle in cash after fees and rules, not just in theory. The more frictions a tool models up front, the smaller the gap between calculated and realised profit.

What does a modern stack include: auto conversions and sanity checks?

A modern UK arbing stack centres on reliable inputs, fee- and rule-aware normalisation, and execution safeguards. The calculator is one component inside a workflow that standardises odds, verifies coverage, sizes stakes to the penny, and enforces practical limits derived from balances, book constraints, and latency targets.

Auto conversions:

• Odds formats: fractional ↔ decimal ↔ American, plus implied probability.
• Commission: per-venue rates applied to net winnings on exchange legs.
• Lay/back transforms: effective “not” prices from lay quotes for two-way checks.

Sanity checks:

• Coverage: outcomes are mutually exclusive and collectively exhaustive.
• Rules: align push/draw handling; account for racing deductions and non-runners.
• Rounding: reconcile to the exact total stake; warn on sub-penny drifts.
• Latency and TTL: reject prices older than a set threshold; apply edge buffers.
• Limits: per-book max stake, per-market exposure, and account balance checks.

Operational features:

• Profiles for venues (commission, min/max stakes, odds precision).
• Audit trail: store quotes, timestamps, and final stakes for reconciliation.
• Device support: web app or PWA for mobile; optional APK for offline math.

The other side of the coin: why won’t a calculator guarantee profit?

An arbitrage calculator equalises theoretical returns under fixed prices and rules. In the UK market, real frictions—palpable error clauses, bet limits or partial acceptance, settlement rules (voids, Rule 4 deductions, dead-heats), exchange commission, and account restrictions—can break those assumptions. Price moves during placement and operational delays introduce slippage, turning a paper edge into a loss. Robust workflow, buffers, and bankroll discipline are required to convert calculations into realised profit.

What can go wrong: palpable errors, limits, voids, gubbing?

Even perfect math can fail if operational or rules-based risks materialise. Plan for the following failure modes and build safeguards into your process.

Palpable error (palp):

• Definition: a clear pricing mistake; many bookmakers reserve the right to void or adjust such bets per their T&Cs.
• Impact: your hedge may stand while the mispriced leg is voided, leaving unbalanced exposure.
• Mitigation: avoid extreme outliers versus market consensus; use time-stamped screenshots and keep stake sizes conservative on anomalous quotes.

Limits and partial acceptance:

• Issue: maximum stake limits, per-account risk flags, or “bet referred” delays; exchanges have depth limits at top-of-book.
• Impact: only part of your intended stake is matched, breaking equal-return sizing.
• Mitigation: query min/max stakes before sizing, cap per-leg stakes, and pre-check exchange depth; allow rebalancing logic.

Voids and settlement mismatches:

• Examples: event cancellations; non-runners (horse racing) triggering Rule 4 deductions; sport-specific push/draw rules; dead-heats reducing payout.
• Impact: one side voids while the other settles, or pays less than assumed, eliminating the edge.
• Mitigation: harmonise market rules (1X2 vs DNB vs Asian lines), model deductions, and avoid legs with ambiguous settlement.

Account restrictions (“gubbing”):

• Issue: sustained arbing or promo extraction can trigger stake restrictions or market exclusions.
• Impact: sudden inability to place hedges at required sizes or prices.
• Mitigation: diversify venues, moderate stake sizes, avoid obvious arbing patterns, and maintain exchange alternatives.

Operational delays:

• Sources: stale screen prices, slow page loads, manual entry errors, MFA prompts at checkout.
• Impact: prices drift while you enter stakes, eroding or reversing EV.
• Mitigation: pre-fill profiles, use PWA/mobile workflows, set quote time-to-live, and require minimum edge buffers.

How do price moves and delays change your expected value?

For two-way arbitrage with decimal odds O1 and O2, the fee-adjusted break-even is (1/O1 + 1/O2) < 1. Any adverse drift increases the reciprocal sum and reduces ROI, potentially turning it negative before you complete all legs. The table shows how small moves on one side change ROI for a £100 theoretical arb starting from O1 = 2.10 and O2 drifting worse during placement.

O1 (fixed)	O2 after delay	Sum 1/O1 + 1/O2	Resulting ROI	Comment
2.10	2.05 (no drift)	0.963995	+3.7369%	Initial edge
2.10	2.00	0.976190	+2.4390%	Still profitable
2.10	1.95	0.989011	+1.1111%	Edge compressed
2.10	1.90	1.002506	-0.2502%	Turns negative

Practical guidance: require a minimum pre-trade buffer (e.g., ≥ 0.50–1.00% above all fees/commission), cap stake sizes to observable top-of-book depth, and enforce a time-to-live on quotes. If a leg changes beyond tolerance, cancel or rebalance before committing further capital.

Bankroll management: what staking caps protect you?

Although a correctly hedged arb carries low market risk, operational and rules risks remain. Bankroll policy should cap exposure per arb, limit concentration by venue and event, and maintain cash buffers to absorb failed hedges or voids.

Per-arb exposure caps:

• Pre-match, stable markets: 2–5% of bankroll per completed arb.
• In-play or thin markets: 0.5–2% due to higher slippage/void risk.

Venue concentration:

• Cap exposure to any single bookmaker or exchange at 20–30% of bankroll to reduce counterparty and restriction risk.

Event correlation:

• Limit total exposure across correlated markets on the same event (e.g., main line and derivatives) to 5–10% of bankroll.

Operational buffers:

• Maintain 10–20% of bankroll as liquid reserve for re-hedging, fees, or unexpected voids.
• Use penny-accurate rounding with final reconciliation to the intended total stake.

Edge thresholds:

• Only execute when fee-adjusted ROI exceeds your latency/slippage buffer (e.g., minimum net ROI ≥ 0.75–1.50%).

Frequently Asked Questions

Is arbitrage betting legal in the UK and are profits taxed?

Arbitrage betting is legal in the UK, but bookmakers can limit or refuse bets under their terms. HMRC does not tax gambling winnings for individuals, whereas non-gambling activities such as crypto arbitrage may be taxable as capital gains or income depending on circumstances. Keep bookmaker arbing and any crypto trading separate, keep records with timestamps and stakes, and seek tax advice if you operate beyond casual betting.

How can I check a 2-way surebet in under five seconds?

Add the reciprocals of the two effective decimal odds; if the sum is below 1, a surebet exists and ROI equals (1/sum) − 1. Example: 2.20 and 2.10 give 1/2.20 + 1/2.10 = 0.9307, so ROI ≈ 7.44% and a £100 stake targets about £7.44 profit before rounding and fees.

What buffer should I require for in-play arbitrage to cover latency and slippage?

Target a net ROI buffer of about 0.5% to 1.5% above all fee-adjusted costs for live markets. As a quick rule, if recent fills show about 0.3% average slippage per leg and you place two legs, require at least 0.6% extra edge plus a small latency allowance (for example 0.2%), so a minimum net ROI threshold near 0.8%.

How do I adjust exchange prices for commission without a calculator?

For a back on an exchange with commission c, use Oeff = 1 + (O − 1) × (1 − c); for a lay at Ol, the effective “Not‑A” back odds are Onot,eff = 1 + (1 − c) / (Ol − 1). Example with c = 2%: an exchange back at 4.00 becomes 3.94; a lay at 2.20 becomes Not‑A odds 1.8167, so a 2-way arb with a bookmaker back at 2.30 has 1/2.30 + 1/1.8167 = 0.9848 and ≈1.55% ROI.

What rounding rule keeps 3‑way and 4‑way stakes consistent to the penny?

Round each leg to the nearest £0.01, then reconcile by adjusting a single leg by £0.01 so the stakes sum exactly to your total. The resulting return spread stays within a few pence; the worst‑case deviation from equal return is approximately max_odds × £0.01, for example with max odds 6.50 the spread is roughly £0.065.

Can I use a stake‑not‑returned free bet in an arbitrage and how do I size it?

Yes; treat the free bet as profit‑only with effective odds Oeff = O − 1 and pair it with a lay sized for equal profit. Example: a £25 SNR free bet at 5.0 vs a lay at 5.2 with 2% commission gives L = FreeStake × (O − 1) / (Ol − c) = 25 × 4 / 5.18 ≈ £19.31, which locks about £18.9 on either outcome, a ≈75.6% return on the free bet’s face value.

Which settlement rules most often break surebets and how do I protect myself?

Rule 4 deductions, dead‑heats, draw/push mismatches, and palpable errors are the common failure modes, so align rules before staking and avoid obvious misprices. As a quant check, a Rule 4 deduction of 25p per pound reduces the winnings component by 25% so decimal 5.00 becomes 1 + (5.00 − 1) × 0.75 = 4.00, which can erase a marginal edge if not modelled.

Does the calculator work with UK odds formats and can I mix them in one calc?

Yes; convert all quotes to decimal before the arb check, since conversion is exact. For example 6/4 equals 2.50 and +150 American, 1/2 equals 1.50 and −200, and implied probability is always 1/decimal.

How do I cap stakes to exchange depth and estimate ROI impact if I slip to the next price level?

Limit each exchange leg to the size available at the top of book and estimate the ROI change from any portion filled at worse odds by recomputing the reciprocal sum with a weighted average. Example: if half a leg slips from 2.50 to 2.48, 1/odds rises from 0.4000 to 0.4032, adding about 0.0016 to the 2‑way sum and trimming ROI by roughly 0.16%.

Can I combine crypto and bookmaker legs in the UK?

UK‑licensed bookmakers generally do not accept direct crypto deposits, so treat crypto arbitrage as a separate exchange‑to‑exchange workflow. In crypto mode, require the sell price after fees to exceed the buy price after fees plus transfer cost per unit, and add a practical buffer of at least 0.20% to 0.50% for slippage during transfers or hedges.

What’s the fastest way to compare two candidate arbs and pick the better one?

Compute S = Σ(1/Oi,eff) for each and select the smaller S because ROI = (1/S) − 1. If Arb A has S = 0.972 (ROI ≈ 2.88%) and Arb B has S = 0.965 (ROI ≈ 3.63%), B is superior before rounding, limits, and slippage checks.

What data does the Android APK or PWA store and which permissions are necessary?

A calculator APK or PWA should store odds format, commission profiles, and last inputs locally on your device and perform all math offline, so no special permissions are required. Avoid builds requesting SMS, contacts, or background network access unrelated to optional updates, and verify the publisher’s signature before installation.