Arbitrage Calculator

Display currencyFormatting only. This does not change the calculation.

Odds formatLeave on automatic unless a bare number is ambiguous.

StakeFor arbitrage this is the total to spread across all outcomes.

Odds for each leg or outcomeComma-separated. Parlay legs, arbitrage outcomes or the whole market for a no-vig calculation.

Kelly fractionMultiply full Kelly by this. Half Kelly (0.5) keeps most of the growth with far less variance.

Guaranteed return on stake

3.73494 %

Betting Odds Calculator

Sum of implied probabilities

96.399535 %

Bookmaker overround

-3.600465 %

Arbitrage available

yes

Return per unit staked

1.037349

Guaranteed profit

37.349398

Worked out from Kelly, J.L. Jr (1956), "A New Interpretation of Information Rate", Bell System Technical Journal 35(4), 917-926 and 3 other sources.

This is an arithmetic tool, not betting advice. Bookmaker prices already carry a margin, so the long-run expected value of a bet at posted odds is negative unless you genuinely have an edge. Gamble only what you can afford to lose.

How this is worked out

3 steps

Sum of implied probabilities = 1/2.1 + 1/2.05 = 0.96399535
That is below 1, so an arbitrage exists: every unit staked returns 1.0373494.
Stakes in proportion to 1/d: 493.98, 506.02.

Stake on each outcometable

outcome	decimal	stake	returnIfItWins
1	2.1	493.98	1,037.35
2	2.05	506.02	1,037.35

Results are general information, not financial, tax, legal, medical or engineering advice.