Arbitrage Calculator

This tool quantifies the pricing gap between bet365 (a traditional bookmaker) and Polymarket (a prediction market). When bet365 implies a higher probability for an outcome than Polymarket is pricing, there may be a convergence trading opportunity.

Enter the Polymarket share price, the bet365 decimal odds, and your bankroll. The calculator instantly shows the gap percentage, a Kelly Criterion position size, expected return if the gap closes, and your maximum downside risk.

The bet365 implied probability is derived from decimal odds: implied % = (1 / odds) x 100. For example, odds of 1.43 imply a 69.9% probability. The Polymarket price in cents directly represents the market's implied probability: a 60c share means the crowd prices the outcome at 60%.

The gap is simply the difference: 69.9% - 60.0% = 9.9%. A positive gap means bet365 considers the outcome more likely than the prediction market does.

Note that bet365 odds include an overround margin (typically 2-5%), which slightly inflates implied probabilities. The raw gap therefore includes some margin, but gaps above 5% are historically significant.

The Kelly Criterion determines the optimal fraction of your bankroll to risk on a given opportunity. The formula is: f* = (p x b - q) / b, where p is the estimated true probability (from bet365), b is the net return per dollar risked, and q = 1 - p.

Full Kelly maximises long-term bankroll growth but comes with significant short-term variance. Half Kelly (0.5x) is the industry standard for conservative traders: it captures roughly 75% of the growth rate while cutting drawdown risk in half. Quarter Kelly (0.25x) is even more conservative.

The expected return assumes the Polymarket price converges toward the bet365 implied probability, stopping when the gap narrows to within 2 percentage points. This is based on historical data showing that when bet365 and Polymarket disagree, the gap tends to close before the event starts.

You do not need to hold the position until the event resolves. If the Polymarket price rises to your target, you can sell your shares at a profit. This is convergence trading, not a bet on the match outcome.

This is not riskless arbitrage. The maximum loss on a Polymarket YES share is 100% of your position: if the outcome resolves NO, your shares are worth zero. Even with convergence trading, you may need to sell at a loss if the gap widens instead of closing.

The Kelly Criterion limits your exposure to a fraction of your bankroll, so a single losing trade should never be catastrophic. Always trade with capital you can afford to lose.