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Step one: convert everything to implied probability
Pick implied probability as your common ground. For decimal odds, divide 1 by the price: 2.50 gives 0.40, or 40 percent. For fractional odds, divide the denominator by the sum of both numbers: 3/2 gives 2 divided by 5, also 40 percent. For positive American odds, divide 100 by the odds plus 100: +150 gives 40 percent. For negative American odds, divide the odds, ignoring the sign, by that figure plus 100: -150 gives 60 percent. Once every price is a percentage, formats stop mattering and comparison becomes simple arithmetic you can check by hand.
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Step two: move between formats using decimal
Use decimal as the hub for direct conversions. Fractional to decimal: divide the fraction and add 1, so 3/2 becomes 2.50. American positive to decimal: divide by 100 and add 1, so +150 becomes 2.50. American negative to decimal: divide 100 by the odds without the sign and add 1, so -150 becomes 1.67. Going the other way, decimal at or above 2.00 becomes American by subtracting 1 and multiplying by 100, and below 2.00 by dividing -100 by the figure minus 1. Rounding is where small differences appear, so keep at least three decimals until the final display.
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Step three: check the result and note the margin
Worked example: a bookmaker lists a two-way market at 1.91 on both sides. Each converts to about 52.4 percent, and the pair totals 104.7 percent. The extra 4.7 points are the bookmaker margin, so fair probabilities are each near 50 percent after dividing by the total. Always sanity-check a conversion by turning it back into the original format. Record the source, time and rounding rule beside the figures, because prices move and displays differ. A comparison table that shows converted probability, margin and timestamp together gives readers numbers they can verify rather than trust blindly.