Convert any odds format to the other three plus implied probability. Decimal is EU/RU/AU standard, fractional is UK, American is US — knowing all three lets you compare offers across regions and feed any EV / Kelly calculator without mental gymnastics.
Every odds quote is a price for a probability. Three regions wrote three notations — the math is identical.
EU / RU / AU standard. The number is your total payout per 1 unit staked — stake included. 2.00 means double your money. Implied probability = 1 / odds.
implied = 1 / kUK tradition. The fraction is profit-only over stake. 5/2 means you win 5 per 2 staked (plus get your 2 back). Equivalent decimal = numerator / denominator + 1.
implied = den / (num + den)US standard. Positive: profit on 100 staked (+150 → win 150 on 100). Negative: how much you must stake to win 100 (−200 → bet 200 to win 100). +100/−100 = even money = decimal 2.00.
+: implied = 100/(odds+100) −: implied = |odds|/(|odds|+100)Sharp books quote in decimal, US books in moneyline, UK books in fractional. To pick the best price for the same outcome you have to put them on one scale. Decimal is the lingua franca because the math composes cleanly.
EV = p × (k − 1) − (1 − p). Kelly = (b × p − q) / b. Both formulas need k in decimal. If your book shows +210, convert here first, then plug the decimal into the EV calc — otherwise the sign and the −/+ logic break the formula.
Σ tracks Pinnacle / Betfair / Matchbook in decimal — every paper bet is logged with the taken price and the closing line.