Probability is not the same thing as odds

Probability is a share of all outcomes. Odds are a ratio between the outcomes that happen and the ones that do not. A 25 per cent chance is 3 to 1 against, not 4 to 1.

The ratio counts failures against successes; the probability counts successes against everything. Mixing them produces an error of exactly one unit, which is small enough to survive a sanity check and large enough to matter.

Decimal odds are the format that makes this hardest to get wrong, because the probability is simply one divided by the price. Fractional odds are the format that makes it easiest to get wrong.

What follows from that is less comfortable. Nearly every conversion mistake in betting comes from mixing these two inside a single calculation, and the result is always in the direction that flatters the bet.

What to do with it. Work in decimal, convert once at the end if you need to, and never do arithmetic across two formats.

The bet calculator shows both readings of one price side by side, which is the quickest way to stop conflating them.

Work it out. The odds converter turns any American, decimal, fractional or percentage price into the other three.