Converting a positive price to a probability

For a positive American price it is 100 divided by the price plus 100. +150 becomes 100 ÷ 250, which is 40 per cent. +300 becomes 100 ÷ 400, or 25 per cent.

A positive price says what 100 wins, so the formula asks what share of the total payout the stake is. The mirror of the negative case, and deliberately so — the two formulas describe the same quantity from opposite sides of even money.

A long price is not evidence of value. +900 implies 10 per cent, and most things priced at 10 per cent happen about 10 per cent of the time. The question is never whether the price is big; it is whether 10 per cent is too low.

Here is the catch. Plus money feels like opportunity because the number is large. It is the format doing the persuading, not the market, and the same bet in decimal odds provokes noticeably less enthusiasm.

What to do with it. Whenever a long price tempts you, state out loud the percentage it implies and ask whether you would take that side at that percentage in a hundred repetitions.

The bet calculator prints the implied probability beside the price, so this arithmetic is there to check rather than to repeat.

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